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U UNIVERSITY OF CINCINNATI

Date:

I, ,

hereby submit this original work as part of the requirements for the degree of:

in

It is entitled:

Student Signature:

This work and its defense approved by:

Committee Chair:

Approval of the electronic document:

I have reviewed the Thesis/Dissertation in its final electronic format and certify that it is an

accurate copy of the document reviewed and approved by the committee.

Committee Chair signature:

02/02/2009

Xin Hu

Master of Science

Electrical Engineering

An Improved 2D Adaptive Smoothing Algorithm inImage Noise Removal and Feature Preservation

William G. Wee

Jing-Huei Lee

Chia-Yung Han

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An Improved 2D Adaptive Smoothing

Algorithm in Image Noise Removal and

Feature Preservation

A thesis submitted to the

Graduate Schoolof the University of Cincinnati

In partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE

in

ELECTRICAL ENGINEERING

in the Department of Electrical and Computer Engineering

of the College of Engineering

2009

By

Xin Hu

B.S. Tsinghua University

P.R.China, 2005

Committee Chair: Dr. William G. Wee

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Abstract

We introduce an improved 2D adaptive smoothing algorithm for noise removal and

feature preservation. Comparing to the original 2D adaptive smoothing algorithm, this new

algorithm is also based on the novel idea of utilizing contextual discontinuity and local

discontinuity jointly to detect and distinguish edges and noise. The new algorithm improves the

main concept -- contextual discontinuity by introducing a novel homogeneity region definition

with a corresponding method for contextual discontinuity measurement. Comparing to the

original algorithm and other smoothing algorithms, the improved algorithm can preserve edges

more effectively while removing noise.

The improved 2D algorithm has been implemented and extensive experiments have been

carried out to compare the algorithm to the original algorithm and other smoothing strategies to

quantitatively demonstrate improvement in performance. Measurements are applied to evaluate

the noise removal and edge preservation performance. Simulation results show that this

improved algorithm has a superior performance over both the original algorithm and other

popular smoothing strategies in noise removal as well as feature preservation.

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Acknowledgement

I would like to express my gratitude to all those who gave me the possibility to

complete this thesis.

I am deeply indebted to my advisor Prof. William G. Wee for his supervision and

encouragement in all the time of my research and completion of this thesis. Also, I

would like to thank Dr. Jing-huei Lee and Dr. Chia-Yung Han for their kindly help and

valuable advices.

My former colleagues from the Department of ECE supported me in my research

work. I want to thank them for all their help, support, interest and valuable suggestions.

Especially I am obliged to Xiang Cai, Hui Peng and Joe Kesler for their professional

advice in my research.

Last but not the least, my special thanks go to my parents and my fianc Wei

Huai whose patient love enabled me to complete this work.

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1

Table of Content

List of Figures ................................................................................................................................. 4

List of Table .................................................................................................................................... 7

Chapter1 Introduction................................................................................................................... 10

1.1Overview of Image Noise and Image Smoothing................................................................ 10

1.2 Review of Image Smoothing Algorithms ............................................................................ 12

1.3 Thesis Organization............................................................................................................. 17

Chapter2 2D Adaptive Smoothing Algorithm and Its Deficiencies............................................. 18

2.1Overview ............................................................................................................................. 18

2.2 The Basic Ideas of Adaptive Smoothing Algorithm ........................................................... 19

2.2.1The Contextual Discontinuity Measurement ................................................................ 20

2.2.2Use Discontinuity Map to Smooth Image .................................................................... 22

2.3 The Resulting Adaptive Smoothing Algorithm................................................................... 24

2.4 Advantages and Deficiencies of this 2D Adaptive Smoothing Algorithm.......................... 28

2.4.1Advantages of this 2D Adaptive Smoothing Algorithm............................................... 28

2.4.2Deficiencies of this 2D Adaptive Smoothing Algorithm.............................................. 29

2.4.2.1 Error in Homogeneity Neighborhood Definition................................................... 29

2.4.2.2 Error in Contextual Discontinuity Design ............................................................. 31

2.5 Conclusion........................................................................................................................... 32

Chapter3 Research Problem, Objective........................................................................................ 34

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3.1 Research Problem ................................................................................................................ 34

3.2 Research Objective .............................................................................................................. 35

Chapter4 Improved 2D Adaptive Smoothing Algorithm ............................................................. 37

4.1 Overview ............................................................................................................................. 37

4.2 Proposed Improvements ...................................................................................................... 38

4.2.1 Generation of a Correct Homogeneity Neighborhood.................................................. 38

4.2.2 Incorporation of Direction Information in H Design.................................................... 41

4.3 Resulting Improved Algorithm............................................................................................ 42

4.4 Advantages and Disadvantages of the Proposed Algorithm................................................ 44

4.5 Implementation of the Improved Smoothing Algorithm..................................................... 45

Chapter5 Experimental Results .................................................................................................... 46

5.1 Overview ............................................................................................................................. 46

5.2Comparison Experiment Results ......................................................................................... 46

5.2.1 Simulated Image Experiment Results........................................................................... 47

5.2.2 Real Image Experiment Results ................................................................................... 52

5.2.3Simulated MRI Image Experiment Results .................................................................. 75

5.3Experimental Parameter Determination .............................................................................. 81

5.3.1 Parameter Sensitivity Investigation .............................................................................. 82

5.3.2 Applicable Parameter Selection Algorithm................................................................ 102

5.4 Conclusion ........................................................................................................................ 107

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Chapter6 Conclusions.................................................................................................................. 109

Bibliography ................................................................................................................................ 110

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Figure 5.11 Simulated Image - Iteration number corresponding to best SNR obtained under

different parameter ........................................................................................................................ 86

Figure 5.12 Simulated Image - SNR performances under different h and Iteration number........ 87

Figure 5.13 Lena Image - SNR performance along with iteration number increase ..................... 88

Figure5.14 Lena Image - Best SNR obtained under different parameter h.................................. 89

Figure5.15 Lena Image - Iteration number corresponding to best SNR obtained under different

parameter h .................................................................................................................................... 89

Figure5.16 Lena Image - SNR performances under different h and Iteration number................. 90

Figure5.17 Camera man Image - SNR performance along with iteration number increase......... 91

Figure5.18 Camera man Image - Best SNR obtained under different parameter h...................... 92

Figure5.19 Camera man Image - Iteration number corresponding to best SNR obtained under

different parameter h ..................................................................................................................... 92

Figure5.20 Camera man Image - SNR performances under different h and Iteration number.... 93

Figure5.21 Image - SNR performance along with iteration number increase .............................. 94

Figure5.22 Scene Image - Best SNR obtained under different parameter h................................. 94

Figure5.23 Scene Image - Iteration number corresponding to best SNR obtained under different

parameter h .................................................................................................................................... 95

Figure5.24 Scene Image - SNR performances under different h and Iteration number............... 96

Figure5.25 Human Face Image - SNR performance along with iteration number increase......... 97

Figure5.26 Human Face Image - Best SNR obtained under different parameter h...................... 98

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Figure5.27 Human Face Image - Iteration number corresponding to best SNR obtained under

different parameter h ..................................................................................................................... 98

Figure5.28 Human Face Image - SNR performances under different h and Iteration number.... 99

Figure5.29 Pepper Image - SNR performance along with iteration number increase ................ 100

Figure5.30 Pepper Image - Best SNR obtained under different parameter h............................. 100

Figure5.31 Pepper Image - Iteration number corresponding to best SNR obtained under different

parameter h .................................................................................................................................. 101

Figure5.32 Pepper Image - SNR performances under different h and Iteration number............ 102

Figure5.33 A 3D performance illustration for Figure 5.2a......................................................... 104

Figure5.34 Best stopping iteration number versus h for all 5 images in Figure 5.2................... 105

Figure5.35 Illustration of obtained SNR/best SNR versus h for all images in Figure 5.2.......... 105

Figure5.36 Best stopping iteration number versus h for all 5 images in Figure 5.2 using Chens

Algorithm .................................................................................................................................... 106

Figure5.37 Illustration of (obtained SNR/best SNR) versus h for all images in Figure 5.2 using

Chen algorithm ............................................................................................................................ 107

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Table 5.12 Smoothing results comparison for Scene image (without small region removal process)

....................................................................................................................................................... 64

Table 5.13 Smoothed results of Scene image for Chens Algorithmand my algorithm (Threshold

value =0.05 & no small region removal process) .......................................................................... 65

Table 5.14 Smoothed results of Scene image for Chens Algorithm and my algorithm (Threshold

value =0.05 & small region removal process) ............................................................................... 66

Table 5.15 Smoothing results comparison for Human Face image (without small region removal

process).......................................................................................................................................... 67

Table 5.16 Smoothed results of Human Face image for Chens Algorithmand my algorithm

(Threshold value =0.05 & no small region removal process) ....................................................... 68


(Threshold value =0.05 & small region removal process) ............................................................ 69

Table 5.18 Smoothing results comparison for Pepper image (without small region removal

process) ........................................................................................................................................ 70

Table 5.19 Smoothed results of Pepper image for Chens Algorithmand my algorithm (Threshold

value =0.05 & no small region removal process) .......................................................................... 71


value =0.05 & small region removal process) ............................................................................... 72

Table 5.21 moothing results for Chens Algorithm and my algorithm (SNR).............................. 74

Table 5.22 Smoothing results comparison for 5 real images (without small region removal

process).......................................................................................................................................... 74

Table 5.23 Smoothing results comparison for 5 real images (with small region removal process)

....................................................................................................................................................... 75

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Table 5.24 Smoothed results of MRI image for Chens Algorithmand my algorithm (SNR)..... 77

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Chapter1

Introduction

1.1Overview of Image Noise and Image SmoothingNo matter how good the imaging devices are, images acquired from the real world are

inevitably corrupted by noise from various sources. The term of image noise, in the image

processing, usually refers to the high spatial frequency random perturbations of pixel brightness

[1]. The most common types of noise are Gaussian noise as well as salt and pepper noise [1].

A digital image is generally encoded as a matrix of grey-level or color values. Taking a

2D gray-level digital image I(x, y) as an example, (x, y) corresponds to a pixel on a 2D grid and

I(x, y) is a real value usually raging from 0-255. In the case of 3D images, (x, y) is extended to

be (x, y, z) representing a point in 3D space.

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Due to the limitation of the device and the influence of the environment, the resulting

image is always contaminated with noise. In a rough approximation one can write I(x, y) = u(x, y)

+ n(x, y), where (x, y) represents a particular pixel in an image, I(x, y) is the observed gray value,

u(x, y) would be the true value at pixel (x, y), and n(x, y) is the noise perturbation.

There are numerous types of noise that exist in images. Various noise models are

designed to simulate n(x, y). The most widely used noise models are Gaussian noise and salt and

pepper noise [1]. In the case of Gaussian noise, the overall noise is generally assumed to be an

additive Gaussian distribution with a zero-mean and a constant variance. The salt and pepper

noise assumes a constant proportion of pixels are corrupted to be extreme white or black. In these

noise models, the normalized values of n(x, y) and n(i, j) at different pixels are assumed to be

independent random variables or white noise.

Generally speaking image smoothing is a method for image enhancement with the

objective of removing image noise. If the image noise can be modeled as I(x, y) = u(x, y) + n(x,

y), where (x, y) represents a particular pixel in an image, I(x, y) is the observed gray value, u(x, y)

would be the true value at pixel (x, y), and n(x, y) is the noise perturbation. The goal of an

image smoothing algorithm is to recover u(x, y) from I(x, y). However in most situations it is

impossible to find n(x, y). Thus it is impossible to completely remove noise and recover the

original image. In most cases an image smoothing algorithm will blur the image to some extent

while removing the image noise.

In image processing, smoothness is a generic assumption that many types of images have

approximately piece-wise constant gray levels [1]. Based on this widely adopted assumption, an

image can be viewed as the combination of many constant areas. Inside each of this area the gray

value is approximately constant. The conjunctions of those constant areas, or say boundary areas,

can be defined as image edges. Pixels in these boundary areas are called edge pixels. These

image edges are very important in charactering image contents.

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To effectively enhance image quality, the image smoothing algorithm must be able to

preserve image edges while removing the image noise. Most of current image smoothing

algorithms do not have a proper image edge feature definition and therefore can not effectively

separate edge pixels from other image pixels. Thus either the smoothing result is blurred or the

image noises are not effectively removed.

1.2 Review of Image Smoothing Algorithms

Generally image smoothing algorithms can be roughly classified into two categories:

linear image smoothing algorithms and nonlinear image smoothing algorithms [1]. Linear image

smoothing algorithms apply the same smoothing operation on all image pixels and normally have

fixed smoothing filter shape and size. They are simple in design and fast in application. However,

the shortcoming is that they may blur important features.

Another type of image smoothing algorithm is nonlinear image smoothing algorithm.

The general goal of various nonlinear smoothing algorithms that have been developed is to

preserve important edge features while noise is removed during the smoothing process. The

intrinsic idea of nonlinear smoothing algorithm having better performance over linear smoothing

algorithm is that nonlinear one may vary their shapes and sizes, or modify their smoothing update

strategies accordingly and perform different filtering at different parts of an image, i.e. to apply a

smoothing operator which adapts itself to the local topography of the image [3]. Extensive

research on how to adaptively modify the smoothing operation according to image content has

been conducted in the last two decades [1, 2, 3, 4, 5].

Since nonlinear image smoothing algorithms have much better performance over linear

smoothing algorithms in image edge feature preservation and noise removal, we will only focus

on nonlinear image smoothing algorithms.

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Smoothing Algorithms

Classification from

iteration point of

view

Classification from

scale point of view

Classification from

contextual information

point of view

Order statistic neighbor filters

[1,4,5] Non-iterative Non-scale-based Non-contextual

K-nearest neighbor operator, the

-trimmed mean and the sigma

filter [6, 7,8]

Non-iterative Non-scale-based Non-contextual

Peak Noise Filter [1] Non-iterative Non-scale-based Non-contextual

Adaptive Template Filter [9] Non-iterative Scale-based Contextual

Adaptive Wiener Filter [1] Non-iterative Non-scale-based Contextual

SUSAN [10] Non-iterative Scale-based Contextual

0,1 Mask adaptive smoothing

filter [11]

Non-iterative Scale-based Contextual

Adaptive smoothing filter

derived from a clustering method

[12, 13]

Iterative Scale-based Contextual

Fuzzy-connectedness based

methods [14, 15,16, 17, 18]


Local & contextual

discontinuities combined method

[19, 20]


Table 1.1 Classification of difference non-linear smoothing algorithms

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The implementation of fuzzy connectedness concepts and objection definition were first

introduced by Udupa and his collaborators [14, 15]. Their work extended the mathematic fuzzy

concepts to image processing. Fuzzy connectedness was used as a measurement of image context

closeness of two adjacent pixels in an image. The fuzzy connectedness between two pixels was

computed based on both their spatial distance and intensity difference. It was computed as the

weighted sum of the intensity and the intensity gradient in the neighborhood of the pixel in order

to capture the intensity features and patterns of intensity variations. Though any neighborhood

size was allowed for the connectedness calculation, it was not practical to perform the calculation

for an unreasonably large size. It may also be inaccurate and not robustness to perform the

calculation for a very small size. By applying previous work of object scale in the framework of

fuzzy connectedness, the size of the neighborhood was allowed to be changed dynamically in

different parts of the image. Saha and Udupa argued that scale-based connectedness was natural

in object definition and also proved that it led to more effective object segmentation [16, 30].

This fuzzy based connectedness concept was then used in many image processing

applications. Fig 1.1 shows the framework of applying fuzzy connectedness concept in image

smoothing and image segmentation.

Udupa and Saha first realized this concept in medical image segmentation [17]. In this

application, as showed in Fig 1.1, the fuzzy connectedness combined two features together, the

object-based feature and homogeneity-based feature. Then a thresholding method that accounted

for fuzzy connectedness was used to perform image segmentation.

Ke Chen follows another way to develop a novel feature preserving scale-based iterative

adaptive smoothing algorithm as shown in Fig 1.1 [19, 20, 21, 22, 23, 24, 25, 26, 27]. He only

applies the homogeneity-based feature in defining one pixels surrounding property, contextual

discontinuity, which is further used to control the smoothing procedure. The proposed concept of

contextual discontinuity was first introduced as a measurement of inhomogeneity value which

was calculated in a larger neighborhood of every pixel. Based on both contextual and local

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analyze these problems and propose improvements to obtain better edge preservation and noise

removal performance.

1.3Thesis Organization

The remainder of this thesis is organized as following: In Chapter 2, Chens image

smoothing algorithm will be introduced in detail including the limitations of the algorithm. The

research problem is presented in Chapter3. A list of research objectives are proposed in Chapter3

as well. In Chapter 4, an improved 2D smoothing algorithm based on a new contextual

discontinuity computation method will be presented. The simulation experiment results and

analysis of the parameter settings and stopping criterion for the improved algorithm are presented

in Chapter 5. Conclusions and future work are presented in Chapter 6.

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Chapter2

2D Adaptive Smoothing Algorithm and

Its Deficiencies

2.1 OverviewIn this Chapter, Chens 2D Adaptive Smoothing Algorithm (Chens Algorithm in the

following) will be presented and analyzed in detail. Then we will discuss the deficiencies in

Chens Algorithmwhich indicate the potential improvements.

There are several reasons that make us start our research from Chens Algorithmwhile

the most important reason is Chens Algorithm is the best till now in this area based on the

literature review in Chapter 1. As we discussed in Chapter 1, adaptive smoothing algorithms can

provide better smoothing result than non-adaptive smoothing algorithms since the former one can

adaptively modify the smoothing operation according to the image content such that how good

one adaptive smoothing algorithm can determine the image content can almost decide the

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The following sections will emphasize on introducing and analyzing two important

concepts/operations in Chens Algorithmwhich are also the core of the algorithm: 1). contextual

discontinuity measurement; 2). Use discontinuity map to smooth the image.

2.2.1 The Contextual Discontinuity MeasurementTo effectively evaluate the smoothness of a larger area, local measurements like gradient

are not enough since measurements based on derivatives are sensitive to all kinds brightness

change and cant separate noise from image content change. So we need some kind Contextual

Discontinuity measurement to detect the differences between brightness changes caused by

noise and image content change. Thus there are at least two requirements for this measurement:

1). New measurement must be defined in a larger area much bigger than local 3 by 3 neighbors;

2). New measurement should not be based on the simple derivatives.

To meet the above requirements, a Homogeneity Neighborhood (HN or short for the

rest of this thesis) is defined first to generate the Contextual Discontinuity measurement in

Chens Algorithm. It is defined that each pixel has a HN within which all pixels have the

similar image propertysimilar brightness. Or in the other way this pixel and its HN belong to

the same object which is very smooth in brightness. The HN is defined as an isotropic ring shape

(square shape in practical applications) while the radius of the ring is the only parameter to be

decided. The size of the HN grows until some defined variance of the intensities inside the HN

meets a chosen threshold. However this isotropic HN can be quite small when the pixel is close

to the 'boundary' (could be the real boundary, also could be the fake boundary generated by noise).

The mathematical definition for HN is as [20]:

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Based on HN, the contextual discontinuity measurement or inhomogeneity, H(x, y), is

defined to represent the brightness roughness of a larger surrounding around (x, y) and used to

determine the smoothing speed at pixel (x, y). In Chens Algorithm to derive H(x, y): first a

mutual size of HN for each pair of (x, y) and one of its 3 by 3 neighbors is selected by choosing

the smaller size of HN such that two pixels among each pair have the same size HNs. Then the

difference between pixels in corresponding positions in the pair of HN are weighted averaged to

reflect the brightness change in this pixel pair direction (from (x, y) to its neighbor). At last the

eight differences are averaged to generate H(x, y). The mathematical definition of calculating

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H(x, y) is as (9), (10), (11), (12) in [36]. Theoretically the influences caused by noise in this

comparison can be ignored due to statistically reason.

Introducing the contextual discontinuity measure H(x, y) (or inhomogeneity) is the most

important contribution of this smoothing algorithm. The H(x, y) is crucial in this adaptive

smoothing algorithm since it is used to decide the smoothing speed at different locations. It is

also the most powerful part of this algorithm to use H(x, y), a region based discontinuity measure

instead of local discontinuity measure like local derivatives comparing to some classic algorithms.

Thus H(x, y) must be carefully selected to reflect how smooth the small region centered by (x, y)

is. The current H(x, y) computation algorithm is a product of applying fuzzy theory which has

very strong mathematical fundamentals into image processing. The basic concept is to find the

differences between neighbor pixels respective homogeneity neighborhood. This concept is

novel and reliable based on much research product of fuzzy theory [14, 15, 16, 17, 18].

2.2.2 Use Discontinuity Map to Smooth ImageSo far we introduce two different discontinuity measurements used in Chens Algorithm:

local discontinuity and contextual discontinuity. Figure 2.1 demonstrates a noisy image as well

as its two different discontinuities map. It is obvious that the local discontinuity measurement is

very sensitive to all kinds of brightness change while the contextual discontinuity measurement is

more robust to noise. Contextual discontinuity map provides a clear clue leading to image

content change which also indicates the most important image feature -- edges.

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Figure 2.1 Comparison of local discontinuity and contextual discontinuity

Noisy image (Upper Left), Local discontinuity measurement map (Upper Right), Contextual

discontinuity measurement map (Lower Center)

In Chens Algorithmboth discontinuities are combined to decide the smoothing speed for

a particular pixel but playing different roles. Contextual discontinuity measurement reflects the

potential image edges existing so it is used to decide how fast to update this pixels brightness

while the local discontinuity reflects the difference of one pixel with its surrounding so it is used

to decide how big that the brightness of this pixel should be considered in updating its neighbors

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brightness. Take an example that large H(x, y) indicates (x, y) may locate in a rough area with

image content change such that brightness of (x, y) should be updated less. While large gradient

in (x, y) only indicates that its brightness is very different with its neighbors due to either image

content change or noise. In either situation brightness of (x, y) should not be seriously considered

in updating other pixels brightnessbecause of its uniqueness. The mathematical definition for

image smooth using both discontinuity measurements are listed as (13), (14), (15) in [20].

2.3 The Resulting Adaptive Smoothing Algorithm

Figure 2.2 shows the steps of Chens Algorithm. As it is shown below, for each noisy

image contextual discontinuity will be only calculated once. The brightness updated speed at (x,

y) in each iteration during this iterative smoothing process is decided by contextual discontinuity

H(x, y) while the local discontinuity is computed every iteration. As we mentioned above the

local discontinuity measurement is used to decide how big the brightness of this pixel should be

considered in updating its neighbors brightness. Keep updating gradient during the iteration in

case that some noise pixels are smoothed out and their brightness can be used to update their

neighbors brightness. Thisiterative smoothing will be stopped once some absolute value of the

brightness change in single iteration is smaller than pre-defined minimal threshold value or after

completing pre-selected number of iterations.

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Figure 2.2 Flow chart of Chens Adaptive Smoothing Algorithm

The detailed steps are stated as following:

Step 1: Initialization Process.

Target noisy image is input and proper parameters are specified. Parameter S is usually

specified as S = 20. Parameter h which is selected from 0-1 and T the iteration number will be

also specified at beginning and their selection will be addressed in detail in Chapter 5.

Step 2: Compute Inhomogeneity map.

This step introduces how to generate an inhomogeneity map or map for the target noisy

image. The idea of inhomogeneity or contextual discontinuity is addressed in Section 2.2.1.

Basically it is a measurement for each pixel describing the image content in a relative larger area

centered by this pixel and this measurement is further applied in deciding the primary smoothing

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speed at this pixel. (x, y) together with (x, y) derived from local discontinuity decide the

overall smoothing speed at pixel (x, y). Due to the high important role of inhomogneity, this step

is the most important step in Chens Algorithmand the most time consuming part.

As stated in Section 2.2.1, a homogeneity neighborhood is generated first for each pixel

in the noisy image. For each pair of adjacent neighborhoods centered by (x, y) and (i, j)

respectively the difference of the neighborhood [Nxy(Rxy;ij), Nij(Rxy;ij)] is defined as:

Rxy;ij is defined as the minimum value between Rxy and Rij. d(xy,vw) is defined as:

Dxy;ij+ and Dxy;ij

defined below are used together to offer a measure for detecting intra and iter-

object directional intensity variation.

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The inhomogeneity value H(x, y) is further derived based on the defined difference

between neighborhoods . H(x, y) is defined as the average of the neighborhood differences

between HN of (x, y) and HNs of (x, y)s 8-neighbors. H(x, y) is defined as:

Bzy(1) represents pixel (x, y)s 8-neighbors and |Bzy(1)| is the number of its neighbors.

As shown in Figure 2.2, H(x, y) is further transformed to be (x, y) through a non -

increase function while local gradient is transformed to be (x, y). and at pixel (x, y) together

decide the smoothing speed at pixel (x, y).

Step 3: Iterative Smooth Process

Noisy image is smoothed through an iterative smooth procedure during which the

smoothing speed at each pixel is decided by (x, y) and (x, y) as following:

The termination of this iterative smoothing procedure is decided by pre-defined parameter T

which means the iterative steps executed.

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2.4 Advantages and Deficiencies of this 2D Adaptive Smoothing Algorithm

2.4.1 Advantages of this 2D Adaptive Smoothing AlgorithmThis section provides a brief summary of the advantages of Chens Algorithm

As introduced in the review section, Chens Algorithmis based on Fuzzy Connectedness

which is proved to be a strong mathematical tool to describe the relationship or the closeness

between image pixels. The Fuzzy Connectedness theory is first introduced into image processing

by Saha and Udupa [15, 16] to describe the possibility that two pixels belong to one single object.

The tool was proved very useful in image segmentation algorithms. Chen further develop the

usage of this tool to describe if the belonging objects changed for two adjacent objects and use

this change to decide if one pixel is close to a boundary which should be preserved or not [20].

Basically these two usages are similar and thus it is reasonable to expect good performance of

Chens Algorithm.

Another advantage in Chens Algorithm is brought by combining the two discontinuity

measurements together to control the iterative smoothing process. Unless the regular adaptive

smoothing algorithms Chens Algorithm uses contextual discontinuity which is very robust to

predict the image feature and indicate the potential edge pixel. At the same time the local

discontinuity is not abandoned but used to control the pixels used is brightness update. The

combination usage of these two measurements assures the convergence of the iterative smoothing

and makes the algorithm insensitive to the termination time [20].

Chens Algorithmalso created a good framework for the adaptive smoothing algorithm.

Essentially Chens Algorithm can be viewed as a high level structure that a new smoothing

algorithm can be created by substituting the contextual discontinuity map as well as local

discontinuity map with any similar roadmap indicating the image features or image edge pixels.

From this respective Chens Algorithmis very important and worth to be carefully reviewed.

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such situations, current H(x, y) computation algorithm will assume 3 by 3 neighborhood as the

default homogeneity neighborhood. This 3 by 3 neighborhood is too small and it could be nnot

even homogeneity at all. Both these two situations actually violate the fundamental requirement

of H(x, y). This disadvantage of the HN used in Chens Algorithm will result in wrong

contextual discontinuity calculation which is stated in the following paragraph and finally

influence the smoothing result.

The H(x, y) in Chens Algorithm will use the small HN which could possibly be non-

homogeneity neighborhood to compute H(x, y) in some locations which directly violates the

theoretical fundamental of H(x, y) and causes inaccuracy H(x, y) value. In the basic theory, a

homogeneity region which can represent the local region property is selected to be compared with

the nearby homogeneity region to detect if this small region locates in a flat area or not. However,

if this homogeneity neighborhood shrinks to be its 3 by 3 neighbors, H(x, y) value cant pass any

information about the region but just local derivatives which is easily influenced by noise. Thus

the smoothing algorithm loses its most important power of using contextual discontinuityrobust

to noise. Similarly, H(x, y) computed based on non-homogeneity neighborhoods can not reflect

the real situation either. First, differences between non-homogeneity neighborhoods may not

correctly reflect the area change. Assume 3 by 3 neighbors of pixel (x, y) in the flat area are

corrupted by noise. H(x, y) will be calculated based on 3 by 3 non-homogeneity neighborhood of

pixel (x, y) and its nearest pixels neighborhood. Since noise the H(x, y) will be wrongly

calculated high. The reason causing this is non-homogeneity neighborhood may include wrong

information into its consideration. Second, the non-homogeneity neighborhoods for pixels near

edges may cross the edges. Those neighborhoods will wrongly decrease H(x, y) in the following

computation. Besides, the most powerful part for this algorithm to smooth noise while preserving

edges is it employs statistical concepts to avoid noise influence in H(x, y) computation. However,

in the current algorithm the neighborhoods for pixels near edges and pixels serious corrupted by

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noise, which are most concerned, can only be very small. Thus H(x, y) can be very sensitive to

noise.

2.4.2.2 Error in Contextual Discontinuity DesignAnother deficiency of Chens Algorithm is no directional information is considered in

H(x, y) calculation. Chens Algorithm assumes the HN differences in all 8 directions are

equivalent the same in H(x, y) calculation. However it is reasonable that the HN differences in

different directions should be considered with the direction information instead of taking simple

average. The following example illustrates this problem.

Figure 2.3A and 2.3B illustrate two different situations of pixel *. The different

brightness values are marked with white and gray. Figure 2.3B simulates a pixel * is located in

an area corrupted by noise while the Figure 2.3A simulated a pixel * located close to the image

boundary. It is expected that H(*) in Figure 2.3A much bigger than Figure 2.3B to represent the

content change in * pixels surrounding. However based on Chens Algorithmthese two Hs are

similar. The primary reason causing this is there is no direction information considered.

Contextual discontinuity calculation doesnt consider the HN change in directions close to each

other which could indicates existing of an image boundary. Thus the deficiency in failure of

considering direction information could lead to bad contextual discontinuity calculation result and

further influence the smoothing performance.

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improved. Chens Algorithm provides a good framework which can be used to adopt in

developing improved smoothing Algorithm.

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Chapter 3

Research Problem, Objective

3.1 Research Problem

From the result of our review and our study on the most recent Chens Algorithmwhich

has the best performance so far, there are still some important problems needed to be addressed in

this area though much of the previous research has been done in this area. Two most important

research problems which will be addressed here in this thesis are stated below.

The first research problem is Chens Adaptive Smoothing Algorithm should be improved

by correcting the errors and deficiencies revealed in Chapter 2 to provide an improved smoothing

algorithm with better performance of noise removal and image feature preservation. By applying

fuzzy connectedness theory and using combination of two discontinuity measurements in image

smoothing task Chens Algorithm provides a very nice smoothing result at the same time

preserves the important image features. However there are still many deficiencies and errors in

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Chens Algorithmwhich prevent it from better performance especially on real images. Most of

these deficiencies/errors are caused by inaccurate assumptions and insufficient information usage.

It is expected that the performance of image smoothing with feature preservation could be further

improved by providing more accurate definitions and designs considering more possible

information.

Another problem preventing the practical use of Chens Algorithm is the selection of

parameter. The parameter used in Chens Algorithmis very sensitive to different image contents,

iteration termination number especially for the real images smoothing task. Without solving the

parameter selection problem Chens Algorithm cant be implemented to automatically solve

image smoothing tasks. Without automation Chens Algorithmwill lose its most strength. Based

on this we list parameter selection as one important research problem for our improved smoothing

algorithm.

3.2 Research Objective

Our major objective is to provide an improved adaptive smoothing algorithm with better

noise removal and image feature preservation together with a practical way of parameter selection

in order to enable the practical use of the improved smoothing algorithm. Based on the research

problems proposed to solve we have the detailed itemized research objectives as following:

1.

Our first research objective is to provide an improved adaptive smoothing algorithm

to provide better noise smoothing result with preservation of image features.

2. Provide a practical parameter selection method which can direct the use of ouralgorithm in real image smoothing tasks and provide acceptable good result.

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3. To demonstrate the improvement of our algorithms and the parameter selectionmethod a set of complete comparison and practical experiment plan should be

designed and executed. The experiment results can also be used as a reference of the

practical implementation.

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Chapter 4

Improved 2D Adaptive Smoothing

Algorithm

4.1 Overview

As we stated in the previous Chapter, the primary objective of this thesis is to improve

Chens Algorithmto provide better noise smoothing result with preservation of image features by

correcting the errors occurring in Chens Algorithm. To achieve this objective, the major

problem to solve is to correct the errors and deficiencies revealed in Chens Algorithm and

provide improved smoothing algorithm.

For the first research problem presented, we believe a good H map depends on a correct

HN and correct HN depends on having a correct shape of homogeneity neighborhood which is

not a square in general. Our research starts from correcting the wrong the wrong assumption

made in defining homogeneity neighborhood in Chens Algorithm, considering more information

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in estimating H map to provide more accurate edge estimation. By providing the improvements

in these two areas we believe an improved adaptive smoothing algorithm can be obtained.

In this Chapter, section 4.2 presents the proposed improvements to Chens Algorithm.

Section 4.3 introduces the resulting improved smoothing algorithm. Section 4.4 analyzes the

advantages and disadvantages of this improved smoothing algorithm. Section 4.5 provides some

implementation details.

4.2 Proposed Improvements

4.2.1 Generation of a Correct Homogeneity Neighborhood

A good H map is critical in deciding performance of Chens Algorithmand it depends on

a correct HN with a correct homogeneity neighborhood. In general the shape of HN would not be

square. The assumption of isotropic HN is made for simplicity but not reflecting the situation of

the real image. Take pixels close to the image boundary as an example. The image content

changes sharply in the direction towards boundary while the image could remain smooth along

other directions. It is hard to assume an isotropic or square shape HN existing for those pixels.

However Chens Algorithm assumes each pixel has such a square shape HN. With this

assumption either size of HN will be limited to be very small (determined by the minimum length

of HN among all direction) or HN could violate the homogeneity requirement in some directions.

From this aspect, Chens Algorithmhas deficiency in its fundamental definition which brings bad

smoothing actions.

A correct neighborhood has the following properties: it takes the shape of homogeneous

neighborhood and is not necessarily a square one, meets a selected smoothness criterion, and

finally, has the largest neighborhood area (larger than 3 by3). The larger is the HN size the better

(more accurate) is the statistics on the intensity calculations.

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HN is the neighborhood containing the pixels which belong to the same image object

with its center pixel. Each HN represents the local image content and are the further combined to

compare the difference to determine the image smoothness in a relative larger area. So it is

critical that the HN must be homogeneity or in the other way only contains pixels with the similar

property. The reason to use HN instead of single pixel in comparison is to avoid noise influence.

From the statistic aspect, when the homogeneity is guaranteed, the larger the size of HN is the

better the estimate of the smoothness is derived. So the basic requirements for good HN are: 1).

Homogeneity; 2). Size should be large enough.

Since the primary problem preventing HN in Chens Algorithm meeting the above

requirements is that the isotropic HN assumption does not exist for many pixels, we try to find an

anisotropic neighborhood for those pixels. In this proposed idea, each pixel is assumed to have a

local homogeneity neighborhood region and there are no limits on the neighborhood region shape.

This anisotropic homogeneity region can be used as the new HN. To locate this anisotropic HN,

complex mathematic tool like deformable contour algorithms can be applied. These tools can

adapt their shape to the image content while the size and speed can be controlled by setting

proper parameters. Later these new anisotropic HNs can be further processed to generate H map.

Here, we propose the following improvement using level set method to define HN which

meets the above HN requirements.

Level Set method is one of the most popular deformable contour algorithms [28, 29, 31,

32]. It is an iterative algorithm and grows by steps until reaching the high contrast image

boundaries. Level Set algorithm can produce different shapes of boundaries while the grow

speed and sensitivity to image contrast are controlled by preset parameters. These features

provide us convenience to find anisotropic HN by using Level Set algorithm.

The level set method is used to search for the HN since the method is an iterative process

derived from a selected smoothing criterion and guarantees a connected region from an initial

starting local region around a pixel. The smoothing criterion is embedded in the deforming speed

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function in deforming the HN. The speed function used in our implementation is the commonly

adopted inverse of a gradient function. The initial contour is placed around the interested pixel

and consists of its 4 neighbors. To reduce the computation time, the maximum number of

iterations is set to be 5, and the maximum size of HN is set to be 150 pixels. A morphological

erosion operation is applied to the resulting close region to produce a smoother HN. H of each

pixel is the average brightness of the pixels in its HN. Obviously with this modification, the

problem of having 3 by 3 HN in Chens Algorithmis overcome.

In this proposed improvement, the homogeneity of HN can be guaranteed by set the step

of the Level Set which controls the tolerance of the non-smoothness. The size of the HN is

controlled by setting the maximum number of iteration. Under the normal situation the Level Set

boundary can grow at least in some directions and this can assure the resulting HN is larger than 3

by 3.

Figure 4.1 is a demonstration of HN formed using this Level Set HN definition. Blue

boundary and red boundary represent the anisotropic HN for blue pixel and red pixel respectively.

Figure 4.1.An illustration of two HN of two pixels close to edge

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4.2.2 Incorporation of Direction Information in H Design

The H map is derived from the HN map to extract the inhomogeneity (context

discontinuity) of a pixel and its 8 neighboring pixels. As stated earlier, it reflects whether a pixel

is adjacent to an edge element or not.

The basic idea behind this is the difference between HN of one pixel and its adjacent

pixel can reflect the image content change along this direction. In Chens Algorithm H(x, y)

which represents the roughness of its neighborhood is derived by taking the average of the HN

differences between its HN and its 8-neighbors HNs. The directional information is not

considered in this average calculation. However the directional information is an important

knowledge needed in the adaptive method to identify the neighboring edge pixels as illustrated in

Figure 4.1. For the pixel close to the boundary, the image content change caused by the existence

of image boundary should happen in several adjacent directions. In the other way similar image

content change in several adjacent directions strongly indicates possible existence of image

boundary while the image content change caused by noise should be random and is less possible

to happen in adjacent directions. In this aspect, the direction information is important and should

be considered in H map deriv.

Here we provide an improvement of H map calculation with incorporation the directional

information.

A large average intensity difference between two adjacent pixels HNs in a particular

direction is an indication of either the presence of a large noise or an adjacent edge segment. To

distinguish these two situations, a threshold value is used to compare with these directional

differences. If three or more adjacent pixels differences exceed this threshold, then the present of

an edge segment is declared and smoothing weights are change accordingly. To accomplish this,

HN(i) is computed as the average intensity difference of the center pixels (*) HN and the HN

of its ith adjacent pixel with i being from 1 to 8.

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The HN(i) indicates the directional intensity difference, and referring back to Figure 4.1

illustration of having an edge as shown, the HN(i) in the diagonal direction will be larger than

all other direction. The weight i will be set larger to emphasize the directional discontinuity.

The detail steps to decide the weight i are: 1). All i (i=1 ~8) is set to be 1/8. 2)

Differences between center pixels HN and its 8-neighbors HN are calculated and only the

directions on which the differences are larger than the threshold are recorded. 3) If the number of

the recorded directions is equal or bigger than three and these directions are adjacent, the weight

i for these directions are doubled. The other weighs are adjusted by taking average of (1-2*

1/8*number of the directions recorded).

There are two major advantages brought by considering direction information in H map

calculation. First it can strengthen the image edge feature. For the pixels close to boundary area,

comparing to the original H map calculation, the weights are adjusted larger on the directions

towards the boundary and results in larger H value. Thus the original brightness of these pixels

can be better preserved such that image edge feature is better preserved. While the image feature

is better preserved larger H value caused by noise is not enlarged since the weighs are not

adjusted assuming noise distribute in several random directions instead of in adjacent directions.

Thus the noise removal performance is kept.

4.3 Resulting Improved Algorithm

All the improvements are concentrated in producing an improved H map so that a better

smoothing result can be obtained with edge features being properly preserved. The rest of the

adaptive iterative smoothing algorithm stays the same as Chens original algorithm. Figure 4.2

.8~1;1;)((*) iiHNH ii

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shows the flow chart of Chens original algorithm. Ourimprovements are focused only in the red

block which is part generating the in-homogeneity (contextual discontinuity) or H map. Basically

we develop a new H map generation algorithm. Then the derived H map will used into Chens

original smoothing framework as shown in Figure 4.2.

The detail steps of the improvements on H map are stated above in section 4.2.

Comparing to the original Chens Algorithm, our improved algorithm is using an improved H

map generation algorithm while keeping the major frame work. There are two reasons why we

believe applying this improvement will help improved the smoothing performance with better

edge preservation. First, the in-homogeneity (contextual discontinuity) or H map is the key

measurement which decides the performance of smoothing and edge preservation to a large

extent and Chens Algorithm has deficiencies in this part. Second the overall smoothing

framework of Chens Algorithmis good especially the combining use of local discontinuity and

contextual discontinuity in deciding the smoothing speed.

Due to the adopting of the overall strategy of Chens Algorithm, our improved algorithm

has the similar issue in deciding parameters for practical use. This problem will be addressed in

Chapter 5.

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Figure 4.2 Flow chart of Chens Algorithm

4.4 Advantages and Disadvantages of the Proposed Algorithm

The major advantage of this improved algorithm is it can provide better H map and

finally help in providing better smoothing performance with edge preservation. In saying better

we mean higher H value for pixels near the image edge which are the pixels we want to preserve

and higher H value assure less smoothing action applied. At the same time the improved H

derive algorithm wont increase the H value for those pixels located in smooth but noised area

thanks to the bigger HN used.

In the other side, the major disadvantage for this improved algorithm is the computation

burden. The primary reason causing the computation burden is the wide adopt of level set

method in locating HN. Though the grow of level set is limited to be 5 for in calculating HN for

each pixel the computation amount is huge considering the number of pixels grow in square of

the image size.

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4.5 Implementation of the Improved Smoothing Algorithm

This improved smoothing algorithm is implemented in Matlab and C++.

In the consideration of computation time the most computation burden part, level set

algorithm, is implemented in C++ while the rest part is implemented in Matlab.

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Chapter 5

Experimental Results

5.1 Overview

In this Chapter rich experiment results using Chens Algorithm, our improved smoothing

algorithm as well as some other popular smoothing algorithms are presented in Section 5.2. Then

we focus on experimental determination of parameter settings of h and T in Section 5.3.

5.2 Comparison Experiment Results

In this section we will first illustrate the advantage of adaptive smoothing algorithms over

some of the more common non-adaptive algorithms on a single simulated image in section 5.2.1.

Then section 5.2.2 presents comparisons of performances of our proposed algorithm and Chens

Algorithm based on SNR, DR(edge feature detection rate) and FAR(edge feature false alarm rate)

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on both a simulated image and a set of 5 real images contaminated with various degrees of

additive noise. Section 5.2.3 presents another set of experiment on simulated human brain MRI

images.

5.2.1 Simulated Image Experiment Results

Simple simulated image is usually adopted in comparison test due to its simplicity and

clear boundaries. A simulated image as shown in Figure 5.1a with four different brightness

intensity values is selected as our first experiment target. The initial comparison test is to give a

simple illustration on the improvements provided by our improved 2D adaptive smoothing

algorithm comparing with Chens 2D adaptive smoothing algorithm.

In this initial experiment our improved adaptive smoothing algorithm and Chens

Algorithm are both applied to noise added simulated image. Both smoothed results are evaluated

using traditional SNR measurement and FAR\DR measurement which describes the image edge

preservation performance. Results are compared using both measurements and the comparisons

show that our improved smoothing algorithm is generally more effective than Chens Algorithm

in increasing SNR and edger preservation of an image.

Figure 5.1a Simulated test image

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Table 5.1 shows the comparison result of our improved smoothing algorithm and Chens

Algorithm in SNR measurement. A different level of Gaussian noise specified in first row is

added to original simulated image in Figure 5.1a as test target for each column. The SNR result

for noisy image, smoothed results by Chens Algorithm and our improved algorithm are

presented in the following rows. SNR used here is defined as:

For both Chens Algorithm and our improved smoothing algorithm the combination of

parameters under which best SNR achieved is listed under the SNR figure.

Noise

Added

Std=10,mean=0 Std=20,mean=0 Std=30,mean=0 Std=40,mean=0 Std=50,mean=0

Noisy

Image SNR

168.9 49.5 24.1 14.6 9.8

Smoothed

Result

SNR(Chen)

434

(h=0.3,S=20)

328

(h=0.09,S=20)

248

(h=0.1,S=20)

193

(h=0.12,S=30)

162

(h=0.14,S=31)

Smoothed

Result

SNR(me)

447

(h=0.1,S=20)

341

(h=0.11,S=20)

256

(h=0.11,S=20)

201

(h=0.13, S=20)

157

(h=0.1,S=20)

Table 5.1 Smoothing results for Chens Algorithmand my algorithm (SNR)

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The comparison shows our improved smoothing algorithm generally has better

performance than Chens Algorithmwhile both algorithms can increase SNR sharply from the

noisy image. Figure 5.1b shows a comparison of smoothed results. One thing needs to be

pointed out is SNR is not a good measurement of image feature preservation but a measurement

in signal processing area. In the other way, the image feature preservation may not be as good as

reflected by SNR. Figure 5.1b shows this point too.

In order to effectively compare the image feature preservation performances, we

developed another measurement.

Figure 5.1b Smoothing results comparison

Lower the original noisy image, upper left smoothed result by Chens Algorithmand

upper right is the smoothed result by our smoothed algorithm.

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Noise

Added

and SNR

Result

Test 1 Test 2 Test 3 Test 4 Test 5

Noise

Added

Std=10,mean=0 Std=20,mean=0 Std=30,mean=0 Std=40,mean=0 Std=50,mean=0

Noisy

Image

DR=99.7%

FAR=9.2

DR=99.7%

FAR=19.5

DR=99.1%

FAR=20.9

DR=98.5%

FAR=21.0

DR=98.4%

FAR=21.7

Smoothed

Result

(Chen)

DR=99.5%

FAR=0.02

DR=99%

FAR=0.1

DR=98.9%

FAR=0.11

DR=98.7%

FAR=0.17

DR=98.4%

FAR=0.23

Smoothed

Result

(me)

DR=99.6%

FAR=0.02

DR=99.2%

FAR=0.07

DR=99%

FAR=0.08

DR=98.9%

FAR=0.1

DR=98.7%

FAR=0.14

Table 5.2 Smoothing results for Chens Algorithmand my algorithm (DR & FAR)

Table 5.2 further proved the superior of our improved algorithm to Chens Algorithmin image

edge preservation.

The performance comparison on 5 cases of different degrees of added noise is shown in

Table 5.3. The results show slight improvements in SNR when comparing our algorithm with

that of Chens with the exception in one case of very high additive noise. Most importantly, these

results indicate that the application of an adaptive smoothing algorithm significantly reduces the

FAR while preserving the DR of the extracted contour in the smoothed image. Our algorithm

shows further improvements of having lower FARs when compares to that of Chens Algorithm.

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This simulated image may not be the best image to compare performances using SNR of

two algorithms although the exact edge pixels are known. A reason is that the total number of

edge pixels is very small in general compared to the total size of the image, and also the image

consists of a number of large but flat brightness regions and thus reducing the significance of the

SNR figure. While not shown in this writing due to space limitation, our experience shows that a

high SNR in many cases of using simulated images does show visibly significant improvement in

image quality.

5.2.2 Real Image Experiment Results

Since the simulated image only contains limited brightness value with clear image edges,

it is quite different with actual real image. To more effectively evaluate one image smoothing

algorithm, it is necessary to examine its performance on real images. To the end, simulated

image test is to provide a quick idea on the performance while improving the smoothing

performance on the real noisy image is the final target.

In this section a set of comparison experiments of our improved adaptive smoothing

algorithm and Chens Algorithmare presented to show the strength of our improved smoothing

algorithm in noise removal and image edge preservation.

The 5 images used in our experiment are selected to reflect a broader class of images so

as to provide a more critical comparison of performance. These images are carefully selected to

reflect different image data collection situations from an object with smooth background image to

a highly texture image, from a single person image to a very dense crowd, and from an in-door

image to an out-door scene. It is expected that the experimental results derived from these

images can provide a preliminary and practical conclusion on the applicability of the two

algorithms.

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The 5 selected images are showed in Figure 5.2. Here is a brief explanation on why each

image is selected here. Figure 5.2.a Lena is a popular image adopted extensively in image

processing area due to this image contains very detailed image feature like hairs and brightness

changing in eyes as well as clear object and image boundary like the background. Figure 5.2.b

and Figure 5.2.c is selected due to the similar reason combinations of detailed foreground and

simple background. Figure 5.2.d is a good represent of image with extensive image details. It is

a very big challenge for image smoothing algorithm since small unclear image features are very

difficult to be separated from noise. Figure 5.2.e is an example of images with sharp brightness

change and shadow.

The actual size for these 5 selected images is 512 by 512.

Figure 5.2 Noise Free Images: a) Lena; b) Cameraman; c) Scene; d) Human face; e) Peppers

In most of the following real image tests two different levels of Gaussian noise are added

to the noise free selected images as the tested noisy images. Additive Gaussian noise of STD of

10 and 20 are considered like most others reported in the literature.

a b c

d e

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Figure 5.3 Left Noisy Lena Image with Gaussian noise added (mean=0, STD=10) Center

smoothed result with Chens Algorithm, Right Smoothed result by our improved algorithm.

In the following Table 5.4 only different levels of Gaussian Noise are added to generate

test noisy images. The SNR results show our improved algorithms superiority.

Image Name Lena(Fig. 5.2.a)

Test Setting Test 1

[0,10]*

Test2

[0,20]

Noisy

Image

SNR 125 32

Smoothed

Image

(Chen)

SNR 220 139

Smoothed

Image

(Our)

SNR 248 149

*: [0, 10]: Gaussian noise with 0 mean and std 10;

Table 5.4 Smoothing results comparison for Lena image (without small region removal

process)

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Noise Added

and SNR Result

Test 1 Test 2

Noise Added Std=10,mean=0 Std=20,mean=0

Noisy Image DR=0.92

FAR=0.91

DR=0.9

FAR=0.72

Chens

Smoothed

Algorithm

DR=0.7

FAR=0.19

DR=0.69

FAR=0.21

Our Smoothed

Algorithm

DR=0.76

FAR=0.1

DR=0.72

FAR=0.12

Table 5.6 Smoothed results of Lena image for Chens Algorithmand our algorithm (Threshold

value =0.1 & no small region removal process)

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Noise Added

and SNR

Result

Test 1 Test 2


Noisy Image DR=0.93

FAR=1.7

DR=0.91

FAR=2.17

Chens

Smoothed

Algorithm

DR=0.68

FAR=0.11

DR=0.58

FAR=0.14

Our Smoothed

Algorithm

DR=0.79

FAR=0.09

DR=0.63

FAR=0.10

Table 5.7 Smoothed results of Lena image for Chens Algorithmand our algorithm (Threshold

value =0.05 & no small region removal process)

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Two level Gaussian noises are added into original noise free Camera man image to

generate noisy test images. Both Chens Algorithmand our improved algorithm are applied. The

SNR results are presented in Table 5.9. Our improved algorithm can produce better SNR result

than Chens Algorithm.

Image Name Cameramen (Fig 5.2.b)

Test Setting Test 1

[0,10]

Test2

[0,20]

Noisy Image SNR 185 48

Smoothed

Image (Chen)

SNR 456 185

Smoothed

Image (Our)

SNR 462 199


Table 5.9 Smoothing results comparison for Camera man image (without small region removal

process)

The smoothed results are reevaluated by DR/FAR measurements in the following Table

5.10 and Table 5.11. For both evaluation results with or without small region removal process

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smoothed result by our improved algorithm has higher DR and lower FAR values than result

produced by Chens Algorithm.

Noise Added

and SNR Result

Test 1 Test 2


Noisy Image DR=0.85

FAR=0.07

DR=0.83

FAR=0.65

Chens

Smoothed

Algorithm

DR=0.69

FAR=0.05

DR=0.58

FAR=0.13

Our Smoothed

Algorithm

DR=0.75

FAR=0.02

DR=0.62

FAR=0.03

Table 5.10 Smoothed results of Camera Man image for Chens Algorithmand my algorithm

(Threshold value =0.07 & no small region removal process)

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Noise Added

and SNR

Result

Test 1 Test 2


Noisy Image DR=0.93

FAR=0.17

DR=0.88

FAR=0.82

Chens

Smoothed

Algorithm

DR=0.8

FAR=0.11

DR=0.64

FAR=0.2

Our Smoothed

Algorithm

DR=0.86

FAR=0.06

DR=0.72

FAR=0.06

Table 5.11 Smoothed results of Camera Man image for Chens Algorithmand our algorithm

(Threshold value =0.07 & small region removal process)

3. Scene Image Experiment ResultTwo level Gaussian noises are added into original noise free Scene image to generate noisy

test images. Both Chens Algorithm and our improved algorithm are applied. The SNR results

are presented in Table 5.9. Our improved algorithm can produce better SNR result than Chens

Algorithm.

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Image Name Scene(Fig. 5.2.c)

Test Setting Test 1

[0,10]

Test2

[0,20]


Chens Smoothed

Algorithm

SNR 121 82

Our Smoothed

Algorithm

SNR 128 87


Table 5.12 Smoothing results comparison for Scene image (without small region removal process)





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Image Name Human Face

(Fig. 5.2.d)

Test Setting Test 1

[0,10]

Test2

[0,20]


Chens

Smoothed

Algorithm

SNR 224 117

Our Smoothed

Algorithm

SNR 243 129


Table 5.15 Smoothing results comparison for Human Face image (without small region

removal process)





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Noise Added

and SNR Result

Test 1 Test 2


Noisy Image DR=0.89

FAR=0.17

DR=0.84

FAR=0.24

Chens

Smoothed

Algorithm

DR=0.68

FAR=0.08

DR=0.63

FAR=0.1

Our Smoothed

Algorithm

DR=73%

FAR=0.03

DR=69%

FAR=0.04


(Threshold value =0.05 & no small region removal process)

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Noise Added

and SNR

Result

Test 1 Test 2


Noisy Image DR=0.93

FAR=0.17

DR=0.88

FAR=0.37

Chens

Smoothed

Algorithm

DR=0.75

FAR=0.1

DR=0.70

FAR=0.2

Our

Smoothed

Algorithm

DR=0.79

FAR=0.04

DR=0.74

FAR=0.09


(Threshold value =0.05 & small region removal process)

5. Pepper Image ResultTwo level Gaussian noises are added into original noise free Pepper image to generate noisy

test images. Both Chens Algorithm and our improved algorithm are applied. The SNR results

are presented in Table 5.18. Our improved algorithm can produce better SNR result than Chens

Algorithm.

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Noise Added

and SNR

Result

Test 1 Test 2


Noisy Image DR=0.96

FAR=0.81

DR=0.93

FAR=0.98

Chens

Smoothed

Algorithm

DR=0.84

FAR=0.1

DR=0.75

FAR=0.21

Our Smoothed

Algorithm

DR=0.88

FAR=0.05

DR=0.77

FAR=0.08


value =0.05 & small region removal process)

The overall SNR performance comparison on the five selected images is shown in Table

5.21. The overall DR/FAR (without small region removal) performance comparison on the five

selected images is shown in Table 5.22 while Table 5.23 shows the DR/FAR comparison result

with small region removal.

The 5 images are selected to reflect a broader class of images so as to provide a more

critical comparison of performance. These images are carefully selected to reflect different image

data collection situations from an object with smooth background image to a highly texture image,

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from a single person image to a very dense crowd, and from an in-door image to an out-door

scene. It is expected that the experimental results derived from these images can provide a

preliminary and practical conclusion on the applicability of the two algorithms. Additive

Gaussian noise of STD of 10 and 20 are considered like most others reported in the literature.

The ground truth edge pixels are extracted using the Sobel operator with a threshold

on the original image. Note that different threshold settings give different total number of edge

pixels. Our experiments have indicated that the comparison results of performances are

consistence using different threshold values. Be noted that Sobel operator preserves high

frequency texture edge features. The results are presented in Table 5.21, 5.22 and 5.23. The

results show slight improvements on SNRs and significant improvements on FARs in all 5 cases

when comparing the two algorithms. While our algorithm provides lower DRs compared to that

of original images, they are consistently higher than using the Chens Algorithm. Also the DRs

are reduced by 10% to 20% due to the smoothing operation with the order of magnitude

improvements in the FARs which maybe significant to any further image segmentation operations.

Note that some high frequency texture pixels are also eliminated in the process in producing

lower DRs, and therefore, the DRs are even lower for more complicated or busy images like

Figures 5.2d and 5.2e. These Low DR numbers should not affect the true edge pixels for most

object segmentation applications since they are non-texture data.

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Image Name Lena(a) Cameramen(b) Scene(c) Human Face(d) Peppers(e)

Test Setting Test 1

[0,10]

Test2

[0,20]

Test 1

[0,10]

Test2

[0,20]

Test 1

[0,10]

Test2

[0,20]

Test 1

[0,10]

Test2

[0,20]

Test 1

[0,10]

Test2

[0,20]

Noisy Image SNR 125 32 185 48 63 17 170 43 272 71

DR 0.94 0.93 0.93 0.88 0.89 0.86 0.93 0.88 0.96 0.93

FAR 1.76 1.9 0.17 0.82 0.25 1.04 0.17 0.37 0.81 0.98

Smoothed

Image

(Chen)

SNR 220 139 456 185 121 82 224 117 443 267

DR 0.73 0.6 0.8 0.64 0.77 0.56 0.75 0.70 0.84 0.75

FAR 0.09 0.11 0.11 0.2 0.09 0.12 0.1 0.2 0.1 0.21

Smoothed

Image

(Own)

SNR 248 149 462 199 128 87 243 129 454 281

DR 0.81 0.67 0.86 0.72 0.79 0.58 0.79 0.74 0.88 0.77

FAR 0.07 0.08 0.06 0.06 0.08 0.1 0.04 0.09 0.05 0.08

Table 5.23 Smoothing results comparison for 5 real images (with small region removal

process)

5.2.3 Simulated MRI Image Experiment Results

We also have the results on an MRI brain image with various degrees of added noise with

significant improvements in SNR.

As shown in Figure 5.4 we have a simulated MRI brain image. It can be considered as noise

free image. Four different levels of noise are added to this simulated image to generate noisy

image. Both Chens Algorithmand our improved algorithm are applied to smooth the noisy

image. The SNR experiment results are shown in Table 5.24. The parameter combination is

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selected based on the best SNR ever obtained. It is shown that our improved algorithm provides

better SNR smoothed result.

Due to the complexity of the MRI brain image, it is hard to use simple edge detection

operator like Sobel filter to generate trustable image edges. So we do not have DR and FAR

figures in this case.

Figure 5.4 Left noisy Image with 5% noise added, right smoothed result by our improved smooth

algorithm

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Noise Added and

SNR Result

Test 1 Test 2 Test 3 Test 4

Noise Added 3% 5% 7% 9%

Noisy Image SNR 178 73 43 24

Smoothed Result

SNR(Chen)

208

(h=0.3, S=20)

91

(h=0.28, S=20)

62

(h=0.29,S=20)

38

(h=0.26,S=20)

Smoothed Result

SNR(me)

222

(h=0.36, S=20)

97

(h=0.04, S=20)

66

(h=0.5, S=20)

43

(h=0.4, S=20)

Table 5.24 Smoothed results of MRI image for Chens Algorithmand my algorithm (SNR)

To further illustrate the strength of our improved smoothing algorithm, another set of

noisy image acquired under real situations are processed by our improved smoothing algorithm.

These images are acquired by actual MRI equipment and considered containing noises. Since we

do not have ground truth for those real images, we cant calculate smoothed results SNR or

DR/FAR. So the smoothed results can be only evaluated by observation.

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Figure 5.5 MRI real brain image smoothing result: left original noisy image, center smoothing

result after 5 iterations, right smoothing result after 15 iterations

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Figure 5.6 MRI real brain image smoothing result: left original noisy image, center smoothing

result after 5 iterations, right smoothing result after 15 iterations

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\

Figure 5.7 MRI real brain image smoothing result: Upper left original noisy image, upper right

smoothing result after 5 iterations, lower left smoothing result after 15 iterations

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proposed. Thus the proposed smoothing algorithm can be effectively applied in a real image

analysis task. A typical example in an image analysis project is one or several noisy images are

available for smoothing purpose while the noise free images are not available. Questions need to

be answered before apply one smoothing algorithm requiring parameter specification are: How

we can choose parameter for this\these unknown noisy image? How we know if particular

parameter selection is good enough remembering we dont have noise free image such we cant

compare smoothing results using pre-defined measurements like SNR or DR/FAR?

This section emphasize on answering the above two questions using experimental

methods. Subsection 5.3.1 will focus on presenting the different parameter selections and

resulting smoothing performances on one simulated image and five selected real images. With

these experimental results Subsection 5.3.2 continues to propose an applicable parameter

selection method for real image noise removal and get further verified by experimental results on

the very same images.

5.3.1 Parameter Sensitivity Investigation

Since our improved algorithm adopts the same iterative smoothing procedure as Chens

Algorithm, important parameters whose selection would bring big influence on smoothing

performance is h and T (the total iteration number) [35]. Due to this reason the following

experiment results as well as most analysis are also valid for Chens Algorithm. These two

parameters will be briefly introduced and followed by a set of experiment results. During the

following experiment other non-important parameters like S will be fixed to particular value

S=20.

As stated in Chapter 2 parameter h is from 0-1 and used to control the transform format

from the inhomogeneity value H to the smoothing speed as shown in the following formula:

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g(.) is a monotonically decreasing function, like:

Giving the same H value, larger h will increase the smoothing speed at particular pixel

(x, y). Thus very small h results in no smoothing action at all while big h close to 1 results image

feature removed.

Parameter T, an integer selected from1 to infinite, is the stop time for the iterative smoothing

procedure. Similar to h, small T results in little smoothing action while big T results in image

feature removal.

The following experiments are designed to investigate parameter sensitivity and stopping rule

of the improved smoothing algorithm. Test target images are the same as section 5.2 including

one simulated image and 5 selected real images. For each tested real image and simulated image,

a set of results are presented and analyzed. Experiments for each image include:

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1) SNR performance vs. iterative smoothing procedure under different parameter h.2) Best SNR obtained under particular parameter choice h.3) Corresponding iterative number under which the best SNR is obtained.4) 3D illustration of the relationship between parameter choice h, iteration number and SNR

performance.

Simulated image in Fig 5.1 is added with Gaussian noise (mean =0, STD = 50) and used

as the test noisy image. Fig. 5.9 shows the SNR performance along the iteration number &

different h values. Fig 5.10 shows the best SNR ever obtained under different h values. From

these two re

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