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SEGMENTATION OF NOISY COLOURIMAGES USING CAUCHY

DISTRIBUTION IN THE COMPLEX

WAVELET DOMAIN

by:

V.KRISHAN BHARADWAJ (095U1A0458)

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INTRODUCTION:

Image segmentation is a fundamental problem in image

processing and image analysis.

To overcome the shortcomings, noise reduction andsegmentation are performed separately.

Image de noising and segmentation can also be

incorporated into a unified framework where a priorknowledge gained from the denoising process is used to

aid the image segmentation.

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FRAME WORK OF THE ALGORITHM:

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COLOUR IMAGE DENOISING WITH

CAUCHY DISTRIBUTION:

To design a statistical estimator that recovers the signal

component of the wavelet coefficients in noisy color

images by using a bivariate Cauchy signal prior to

distribution.

Noise component can be modeled as a zero-meanGaussian random variable.

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CAUCHY DISTRIBUTION:

The univariate Cauchy distribution has the PDF defined

as

The Cauchy model provides a better fit on these heavy

tails than the generalized Gaussian model.

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STATISTICAL PROCESSOR FOR

NOISE REDUCTION:

The 2-D wavelet transform is a powerful tool, providing a

natural arrangement of image wavelet coefficients into

Multi scale and oriented sub bands and allowing the study

of each sub band separately.

The parameters are estimated using maximum likelihood

method from noisy observations.

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MAP ESTIMATION OF CAUCHY SIGNALS

IN ADDITIVE WHITE GAUSSIAN NOISE: We assume the original image is contaminated with

signal-independent additive white Gaussian noise.

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SIGNAL PARAMETERS ESTIMATION IN

NOISY OBSERVATIONS: First, we find the level of noise.

For the purpose of bivariate Cauchy model parameter

estimation from observed data, a method based on

empirical characteristic function has been proposed.

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IMAGE SEGMENTATION ALGORITHM:

The model parameters obtained from the de noising

stage can be used in the segmentation stage.

This section describes a multi scale image segmentation

algorithm as shown in the dotted box of the frame work of

the algorithm.

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INITIAL TEXTURE SEGMENTATION:

An image discontinuity from one band is likely to occur in

at least some of the remaining bands.

Texture segmentation is applied to all image bandsseparately to obtain a texture map per image band.

The parameter corresponding to the noise-free

coefficients is used in this stage to estimate the texturefeatures within the original image.

Therefore the feature value Tc(x, y) in the c color band at

the pixel location (x, y) is defined as

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INITIAL TEXTURE SEGMENTATION

(contd..):

If pixel Q belongs to a textured region in all the three

color bands, Q is assigned to a textured region.

If pixel Q belongs to a textured region in any two among

the three color bands, Q is assigned to a textured region.

Otherwise, pixel Q is classified to a non-textured region.

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INITIAL TEXTURE SEGMENTATION

(contd..):

a Texture map using multiple bands

b Texture map using monochrome band

c Texture map without de noising

d Texture map on the clean image using

Cauchy model

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Multi scale image segmentation:

The textured and non-textured regions are further

segmented.

The dominant colors are first extracted based on peergroup filtering and the generalized Lloyd algorithm.

A pixel is assigned to the neighbor class that has the

minimum D value using the following function.

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Statistical region merging:

The main difference lies in the way the features are

extracted within the regions.

Euclidean distance of the color histograms extracted fromthe neighboring non-textured segments is calculated.

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Experimental results:

Validating the de noising performance.

To test the proposed segmentation algorithm on differentimages containing artificial and natural noise.

The default values of the thresholds were set to 0.4 fornon-textured regions and to 0.6 for textured regions,

respectively.

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SEGMENTATION RESULTS FOR

NATURAL IMAGES:

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APPLICATION TO MULTISPECTRAL

IMAGES: Noise-removal processor based on the bivariate Cauchy

distribution makes it possible to preserve fine image signal

details.

The initial texture segmentation is able to generate a preciseimage texture map via improved texture feature extraction.

Statistical region merging stage enhances the final

segmentation results.

All these three components are combined effectively to build a

robust and efficient image segmentation framework.

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CONCLUSIONS AND FUTURE WORK:

The main contribution of this work is that it provides an

accurate and repliable image segmentation algorithmes

for Noisy coloured image which integrates statistical

methods, de noising techniques and multi resolution

analysis into a single framework.

Extension of the proposed method to the case of

multidimensional data, such as video sequences

contaminated with heavy-tailed noise.

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Thank you