ifsr_Preprocessing

8/3/2019 ifsr_Preprocessing

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Image Registration:

Arthur Goshtasby

Wright State University

Image Registration and Fusion Systems



improve the registration performance. These

– Noise filtering

–

– Region extraction

– ge e ec on

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Noise smoothing

Given image f(x,y) and smoothing filter h(i,j), noise

smoothing is defined by:

The intensity of pixel (x,y) in the output is obtained

from a weighted sum of intensities of pixels at and

around (x,y) in the input. h(i,j) is the weight of pixel(x+i,y+j) in the neighborhood of (x,y), and the sum of

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.



• When the weights defined by the filter are all the same, the

.

• Intensities of all pixels at and around a point in input have the sameeffect on the intensity at the same point in output.

• This operation is not rotationally invariant if the filter kernel is not

circular.

Image containing Filter-radius 2 pixels Filter-radius 4 pixels

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Zero-mean noise Computed using FFT algorithm



• If the wei hts in filter kernel re resent

Gaussian coefficients, a Gaussian filter isobtained.

• Gaussian filtering is effective when image noise is

zero-mean.• Gaussian filtering is rotationally invariant.

• A 2-D Gaussian can be decomposed into 2 1-D

auss ans: x,y = x y; ere ore, er ngcan be carried in 1-D rather than in 2-D

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Computation of mean and

aussian iltering

Although filtering is a convolution operation and can be computed using

the FFT algorithm, since FFT considers an image is a periodic signal, if left

and right image borders, or top and bottom image borders are not the same,

artifacts will appear near the image borders. To avoid this, carry out the

computations directly.

Image containing Computed with FFT Computed directly

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Zero-mean noise Gaussian filter of σ = 2 pixels



into meaningful parts. There are two main.

– Methods that use information within regions

–

between regions

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• Assuming an image that contains objects with intensities thatrepresent a auss an str ut on an a ac groun w tintensities that represent a different Gaussian distribution, theobjects can be separated from the background using the

.

• This method works well when an image contains

homogeneous objects and a homogeneous background and the.

Threshold

value

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Original Smoothed Histogram Thresholded image



Intensity thresholding

Threshold

value

A Landsat image Histogram of the image

Thresholding at the Thresholding at the

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valley between the average intensity of

first two peaks. highest-gradient pixels.



•

– Finding the valley between the modes of the

.

– Finding the intensity that represents the average of

intensities of hi h- radient ixels.

– Finding the intensity at which a change in the

intensit will minimall chan e the se mentation

result.

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Delineated tumor

Data courtesy of Kettering Medical Center

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,



• Ed e detection methods can be cate orized into those

that search for locally maximum image gradientmagnitudes and those that search for zero-crossingso e ap ac an o an mage.

• Methods that search for gradient peaks do not pick

disconnected.

• Methods that search of the zero-crossings of the

Laplacian image find closed boundaries, but parts of the boundaries could be false.

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involves computation of:

or,

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-

An x-ray angiogram LoG zero-crossing edges

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-

A volumetric MR brain image LoG edges

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Data courtesy of Kettering Medical Center



• Zero-crossing edges can be

eterm ne y convo v ng

the negative and positive parts of the LoG with an

operator in

2-D

subtracting the convolved

images and locating the zero-crossin s.

• If instead of subtractingcorresponding values in theconvolved ima es, we divide

part

the values and locate theone-crossings, intensity-ratioedges will be obtained.

part

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(a) Intensity ratio edges. (b) 30% highest-gradient ratio

edges. (c) Intensity difference edges. (d) 30% highest-

gradient difference edges.

Intensity ratios detect more edges in dark areas

while intensity differences detect more edges

A. Goshtasby 17(d)

.



• This method smoothes the ima e with a Gaussian to reduce

noise and then locates locally maximum gradient magnitudesin the gradient direction and uses them as the edges.

An x-ra an io ram Cann ed es with σ = 2.5 ixels

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Edges in color images

• Edge detection in a color image can be considered edge- .

• If u(x,y) and v(x,y) represent color gradients in x and ydirections, edges can be considered points where color .

• If R(x,y), G(x,y), and B(x,y) represent red, green, and bluecolor components at (x,y), respectively, color gradients are:

r, g, and b are unit vectors along red, green, and blue axes,

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respectively, in the color space.



Color edges

• ,

maximizing

and is obtained from

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ge e ec on n co or mages

A color image Edges of the color image

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1. D. Marr and E. Hildreth, Theory of edge detection, Proc. R. Soc. Lond .,

– .

2. J. J. Clark, Authenticating edges produced by zero-crossing algorithms, IEEE Trans. Pattern Analysis and Machine Intelligence, 11(1):43–57 (1989).

3. J. Canny, A computational approach to edge detection, IEEE Trans. Pattern, – .

4. L. Ding and A. Goshtasby, On the Canny edge detector, Pattern Recognition,34:721–725 (2001).

5. M. Bomans, K.-H. Hohne, U. Tiede, and M. Riemer, 3-D segmentation of MR - , ransac ons on e ca mag ng,

9(2):177–183 (1990).

6. A. Goshtasby and H-L Shu, Edge detection by curve fitting, Image and VisionComputing, 13(3): 169–177, 1995.

. . , , mage an s on ompu ng, – ,1994.

8. L. Zagorchev, A. Goshtasby, and M. Satter, R-snakes, Image and VisionComputing, 25: 945–959, 2007.

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