Region-based segmentation - CREATIS

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Digital Image Processing Image Analysis: Part 2

IMESI - 2009

Summary I. II. III. IV.

Introduction Digital image fundamentals Discrete 2D processing Image improvement

V. Image analysis

(6 houres)

Département GE - TI - Olivier Bernard

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Image analysis Books Gonzales : Digital Image Processing, Prentice Hall (3th Ed.)


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Summary V. Image Analysis

Part 1

Mathematical Morphology Contour detection and analysis

Part 2

Region-based segmentation

Part 3

Shape analysis Shape recognition Département GE - TI - Olivier Bernard

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Summary V. Image Analysis

Part 1

Mathematical Morphology Contour detection and analysis

Part 2

Region-based segmentation

Part 3

Shape analysis Shape recognition Département GE - TI - Olivier Bernard

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Region-based segmentation Context

Definition Principle

Two kinds of methodology

Histogram based Region transformation based


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Region-based segmentation Context - Definition Segmentation consists on partitioning an image into a set of connected regions

Find homogeneous regions according to a specific criterion (intensity value, texture)


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Region-based segmentation Context - Definition The aim of region detection is to provide the possibility to characterize the detected object by parameter analysis (shape, position, size...)

Example of the need of region-based segmentation: object labeling


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Region-based segmentation Context - Definition Region segmentation is an ill-posed problem the perfect segmentation does not exist The choice of a particular method is linked to the nature of the image (texture, intensity, ...) the shape of the object to extract The time constrain


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Region-based segmentation Context – Two different methods Region-based Segmentation

Region transformation based

Histogram based

- Region growing - Region splitting - Region merging Département GE - TI - Olivier Bernard

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Histogram based


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Region-based segmentation Histogram-based methods - Example The main idea is to individually select each specific histogram mode, and then select the corresponding area by thresholding

B A C

Initial image

Separation of A and B classes from class C (background)


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Region-based segmentation Histogram-based methods - Example Extraction of a specific mode of the histogram Detection of the corresponding area by thresholding Among the different area that contribute to this mode, select the biggest connected region from high level tools (for example: mathematical morphology) Apply this scheme for each histogram mode


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Region-based segmentation Histogram-based methods - Example Extraction of a specific mode of the histogram

Initial image

Image histogram Département GE - TI - Olivier Bernard

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Region-based segmentation Histogram-based methods - Example Detection of the corresponding area from thresholding


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Region-based segmentation Histogram-based methods - Example Selection of the biggest connected region

Proposed scheme - Hysteresis thresholding - Mathematical morphology (erode, fill, close)


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Region-based segmentation Corresponding matlab code % Read image img = imread(‘brain.png'); img = double(img(:,:,1)); % Selection of pixels corresponding to the selected histogram mode e = find(img>118); mask = zeros(size(img)); mask(e) = 255; % Region erosion through math morph se = strel('disk',3); maskErode = imerode(mask,se); % Hysteresis thresholding maskHyst = hysteresis(mask,maskErode); % Fill holes through math morpho maskFill = imfill(maskHyst,'holes'); % Region closing through math morpho se = strel('disk',1); final = imclose(maskFill,se);


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Region-based segmentation Corresponding matlab code % Read image img = imread(‘brain.png'); img = double(img(:,:,1));

Selection of pixels mode

% Selection of pixels corresponding to the selected histogram mode e = find(img>118); mask = zeros(size(img)); mask(e) = 255; % Region erosion through math morph se = strel('disk',3); maskErode = imerode(mask,se); % Hysteresis thresholding maskHyst = hysteresis(mask,maskErode); % Fill holes through math morpho maskFill = imfill(maskHyst,'holes'); % Region closing through math morpho se = strel('disk',1); final = imclose(maskFill,se);


mask 20


Region erosion



maskErode 21


Hysteresis thresholding



maskHyst 22


Fill holes



maskFill 23


Region closing



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Region-based segmentation Histogram-based methods - Example


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Proposed scheme - Hysteresis thresholding - Mathematical morphology (erode, close)


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Proposed scheme - Hysteresis thresholding - Mathematical morphology (erode, close)


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Proposed scheme - Mathematical morphology (erode, fill holes)


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Region-based segmentation Histogram-based methods - Example Final result

Initial image

Segmented image


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Region-based segmentation Histogram-based methods – choice of the threshold value What is the best way to choose a threshold value ? There exist a lot of methods based on probability Example: thresholding from learning


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Region-based segmentation Histogram-based methods – choice of the threshold value Example: thresholding from learning thresh = 94 object back

Goal: Separate the two modes, by choosing the minimum histogram value between two extremities Département GE - TI - Olivier Bernard

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Region-based segmentation Histogram-based methods – Analytic method Model each mode through a priori distributions (for example two Gaussian models p1 et p2) Maximization of the following energy function s

N

0

s

Γ( s ) = ∫ p1 (n)dn + ∫ p2 (n)dn Γ( s ) = 1 − F2 (n = s ) + F1 (n = s ) where

Fi is a cumulative function Département GE - TI - Olivier Bernard

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Region-based segmentation Histogram-based methods – Analytic method Maximization of function Γ( s )

thresh = 91

Approximation of the continuous integral by a discrete version Département GE - TI - Olivier Bernard

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Region-based segmentation Histogram-based methods – Empirical method Find the threshold value which minimize the variance of the corresponding two classes Let h[n] be a histogram function G is the center of gravity of one class

∑ nh[n]

Gi ( s ) =

n∈Ci

∑ h[n]

var is the variance of one class vari ( s ) =

2 ( n − G ) h[n] ∑ i

n∈Ci

n∈Ci


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Region-based segmentation Histogram-based methods – Empirical method Find the threshold value that minimize the variance sum

sopt = arg min(var1 ( s ) + var2 ( s )) s

After simplification, the previous problem is equivalent to maximize the following energy criterion 2 2 J(s) :      ∑ nh[n]   ∑ nh[n]  n∈C1 n∈C2     J ( s) = + ∑ h[n] ∑ h[n] n∈C1

n∈C 2


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Region-based segmentation Histogram-based methods – Empirical method Minimization of function

sopt

thresh = 102

Approximation of the continuous integral by a discrete version Département GE - TI - Olivier Bernard

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Region-based segmentation Histogram-based methods – properties Implementation is quite simple Performance relatively low because of the non use of spatial coherence Method to be used when: images have regions which are easily separable (objects with high contrast) images are defined on multi-channels (multispectral images) which gives more information on the corresponding histogram Département GE - TI - Olivier Bernard

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Histogram based


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Region-based segmentation Region transformation based methods Step that consists on splitting an image into subsets Ri called regions


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Region-based segmentation Region transformation based methods Methods based on a similarity criterion P and an elementary partition One has to define a test function that allows to validate the similarity criterion


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Region-based segmentation Region transformation based methods Similarity criterion in segmentation: region Ri is homogeneous Test function used to verify the previous similarity criterion Region contrast

P ( Ri ) = true ⇔ max Ri [ I ( x, y )] − min Ri [ I ( x, y ) ] < σ


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Region-based segmentation Region transformation based methods Similarity criterion in segmentation: region Ri is homogeneous Test function used to verify the previous similarity criterion Region standard deviation P( Ri ) = true ⇔ where

1 N

2 ( I ( x , y ) − m ) 0 ) if ( in1(i-1,j) > 0 ) out(i-1,j) = 255; count = count + end if ( in1(i+1,j) > 0 ) out(i+1,j) = 255; count = count + end if ( in1(i,j-1) > 0 ) out(i,j-1) = 255; count = count + end if ( in1(i,j+1) > 0 ) out(i,j+1) = 255; count = count + end end end end k = k + 1; end Département GE - TI - Olivier Bernard

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