4.Do& Martion- Contourlet transform (Backup side-4)

Contourlet Transform

Photo Source:http://commons.wikimedia.org/wiki/File:Contourlet_Transform_Double_Filter_Bank.jpg

Department of Computer Science And Engineering

Shahjalal University of Science and Technology

Nashid AlamRegistration No: 2012321028

[email protected]

Masters -2 Presentation

(Paper Reading

Backup Slides# 5)

http://commons.wikimedia.org/wiki/File:Contourlet_Transform_Double_Filter_Bank.jpg

Contourlet Transform GOAL

Capture the intrinsic geometrical structure-A key feature in visual information

(Dealing with enhancement.)

Natural images are not simply stacks of 1-D piecewise smooth scan-lines;

Discontinuity points (i.e. edges) are typically located along smooth curves

(i.e. contours) owing to smooth boundaries of physical objects.

Thus, natural images contain intrinsic geometrical structures

Contourlet Transform Main challenge

Exploring geometry in images:- Duo to discrete nature of the data.

--All we human can see is continuous--Image is discrete (Sampling and Quantization)

Approach



Approach starts with :

1.Constructing a discrete-domain :

-Multiresolution and Multidirectional expansion

-using non-separable filter banks

(in much the same way that

wavelets are derived from filter banks)

This construction results :

flexible multiresolution,

and directional

Image expansion

(using contour segments)

Thus it is named the

contourlet transform.

The concept of wavelet: University of Heidelburg

Approach

flexible multiresolution

• Multi resolution means that the same image content is available

in two or more sizes (resolutions).

L:\M2work\M2-implementation\5.CT_realization(to_compare_with_NSCT)

Original Image

(mdb252.jpg)

Contourlet Coefficients

in multiresolution images

(mdb252.jpg)

More details on multiresolutionIs provided in Laplacian pyramid concept

Upcoming Slide

ApproachContourlet Transform


Approach

Decomposes The Image Into Several Directional Subbands And Multiple Scales

The CASCADE STRUCTURE allows:

- The multiscale and directional decomposition to be independent

- Makes possible to:Decompose each scale into

any arbitrary power of two's number of

directions(22=4, 23=8, 24=16, …)


The CT is implemented by:Laplacian pyramid followed by directional filter banks (Fig-01)

Input image

Bandpass

Directional

subbands

Bandpass

Directional

subbands

Figure 01: Structure of the Laplacian pyramidtogether with the directional filter bank

The concept of wavelet:University of Heidelburg

Figure 01


Approach

Details ………….


Laplacian Pyramid

Image Pyramid

Image Pyramid

Content Courtesy:

Prof.Mubarak Shah, PhD

Director of the Center for Research in Computer Vision, UCF

resolution

(different in resolution)

Image Pyramid

Image Pyramid

Gaussian Pyramid

Image Pyramid Gaussian Pyramid


Gaussian Pyramid

g0 = IMAGE

g1 = REDUCE[gL-1]

g0

g1

g2

0

Image PyramidGaussian Pyramid

(Example)

Image Pyramid

Laplacian Pyramid

Image Pyramid Laplacian Pyramid

Contourlet Transform Concept

To perform multiscale decomposition we have applied LP :for generating a down sample version

of the original image at each decomposition level.

See paper page: 3 Sub-topic: Pyramid frames

Each pyramid level creates only one bandpass image :without generating any scrambled frequencies;

Pyramidal decomposition:

In our approach we have only down sampled the low pass channel to get rid of this effect.

which happens in the wavelet filter bank when:

A highpass channel, after down sampling, is folded back into the low frequency band.


Directional Filter

Bank

http://sazizi.ece.iut.ac.ir/content/accelerating-contourlet-transform



Figure :The contourlet filter bank.

Multiscale decomposition into octave bands is computed -by applying Laplacian pyramid

and then a directional filter bank is used to each bandpass channel.


Approach

Enhancement of the Directional Subbands

This DBF is implemented by using a k-level

binary tree decomposition that leads to 2k

subbands with wedge shaped frequency

partition as shown (b).

(a)

(b) Frequency partitioning (l= 3, 2l = 8)

wedge shaped frequency subbands.

Directional filter bank. (a) Frequency partitioning:

where l = 3 and there are 23 = 8 real wedge-shaped frequency bands.

Subbands 0–3 correspond to the mostly horizontal directions, while subbands 4–7 correspond to the mostly vertical directions.

(a)

(b)

Contourlet TransformEnhancement of the Directional Subbands


See paper page: 4Sub-topic: Iterated directional filter banks

C. Directional filter bank

(a) Main image

(b) Smooth Image(LP at highest level)

(c) Contourlet coefficient at level 2

Contourlet Transform Example


(d) Contourlet coefficient

(Horizontal direction)

(e) Contourlet coefficient at

(Vertical direction)


(f) Contourlet coefficient Angular direction (-60,-45, 45, 60)

(a) Main image




Approach

Figure 01: (a)Structure of the Laplacian pyramid together with the directional filter bank(b) frequency partitioning by the contourlet transform(c) Decomposition levels and directions.

Input

image

Bandpass

Directional

subbands

Bandpass

Directional

subbands

Details….

DenoteEach subband by yi,j

Wherei =decomposition level and J=direction

(a) (b)

(c)

Contourlet Transform Approach


The processing of an image consists on:-Applying a function to enhance the regions of interest.

In multiscale analysis:

Calculating function f for each subband :

-To emphasize the features of interest

-In order to get a new set y' of enhanced subbands:

Each of the resulting enhanced subbands can be

expressed using equation 1.

)(', , jiyfjiy ………………..(1)

-After the enhanced subbands are obtained:-

The inverse transform is performed:

to obtain an enhanced image.

Denote

Each subband by yi,jWherei =decomposition level and J=direction

Details….More in main slide #56


Details….

The directional subbands are enhanced using equation 2.

)( , jiyf)2,1(

,1 nnWjiy

)2,1(,2 nnWjiy

If bi,j(n1,n2)=0

If bi,j(n1,n2)=1………..(2)

Denote

Each subband by yi,jWherei =decomposition level and J=direction

W1= weight factors for detecting the surrounding tissueW2= weight factors for detecting microcalcifications

(n1,n2) are the spatial coordinates.

bi;j = a binary image containing the edges of the subband

Weight and threshold selection techniques are presented on upcoming slides



The directional subbands are enhanced using equation 2.

)( , jiyf)2,1(

,1 nnWjiy

)2,1(,2 nnWjiy

If bi,j(n1,n2)=0

If bi,j(n1,n2)=1………..(2)

Binary edge image bi,j is obtained :-by applying an operator (prewitt edge detector)

-to detect edges on each directional subband.

In order to obtain a binary image:A threshold Ti,j for each subband is calculated.


Image in different subbands

4.Do& Martion- Contourlet transform (Backup side-4)

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