evaluation of image segmentation algorithm1

8/16/2019 Evaluation of Image Segmentation Algorithm1

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Evaluation of Image Segmentation

algorithms

By

Dr. Rajeev Srivastava



Contents

• Introduction

• Image segmentation algorithms

•

Evaluation Metrics• Result for segmentation



Introduction

• Segmentation subdivides the image into its constituentsregion or objects.

• The level to which the subdivides is carried depends on theproblem being solved.

•Segmentation should stop when the object of interest in anapplication have been isolated.

• Segmentation method can be classified into two categories-:

- In first category approach is to partition the

images based on the abrupt changes in theintensities.

-In second category partition an image into certainregion which are similar according to certain criteria.



Image segmentation algorithm

We will discuss following segmentation

algorithm in the subsequent slides : Otsu,Edge

based segmentation ,K-means ,fuzzyc-means

,region-based method ,snakes , contour based

segmentation.



Otsu-segmentation

• Segmentation is then accomplished by scanningthe image pixel by pixel an labelling each pixel asobject or background depending on whether the

gray level of that pixel is greater or less than thevalue of T.

• Algorithm

1 Select an initial estimate for T

2 Segment the image using T . This will produce twogroups of pixels : consisting of all the pixels withgray-levels > T and 2 consist of pixels < T.



Otsu segmentation

3 Compute the average gray level of and 2 for

the pixels in the region and 2 . 4 Compute a new threshold value

2 2 .

5 Repeat steps 2 through 4 until the difference in T

in successive iterations is smaller than predefined

parameter .



Edge detection

• It is the most common approach for detecting thedetecting the meaningful discontinuities in graylevel. We will discuss the first and second order

for detecting the edges.• The magnitude of the first derivative can be used

to detect the presence of an edge at a point in animage.

• The sign of second derivative can be used todetermine whether an edge pixel lies on the darkor light side of an edge.



Edge Detection

• The two additional properties of second

derivative are-:

– It produces two value for every edge in an image.

– Imaginary straight line joining the extreme

positive and negative value of the second

derivative would cross zero near the midpoint of

the edge.• The zero-crossing property of the second derivative is

quite useful for locating the centres of thick edges.



Edge Detection

• The gradient of an image is a vector of and

.There are various operator to calculate

the gradient of an image.

• For an image 3x3 region where z represent the

gray level values-:



Edge Detection

• Robert mask

• Prewitt mask

-1 0

0 1

0 -1

1 0

-1 -1 -1

0 0 0

1 1 1

-1 0 1

-1 0 1

-1 0 1



Region Growing

• It is a procedure that groups pixels or sub regioninto larger regions based on predefined criteria.

• The basic approach is to start with a set of seedpoints and from these grow regions by appendingto each seed those neighbouring pixels that haveproperties similar to the seeds.

• When a priori information is not available theprocedure is to compute at every pixels the same

set of properties that ultimately will be used toassign pixels to region during the growingprocess.



Region splitting and merging

• The procedure to subdivide an image initiallyinto a set of arbitrary disjointed regions andthen merge and split the regions in an attempt

to satisfy the conditions.• Let R represent the entire image region and

select a predicate P. Approach for segmentingR is to subdivide it successively into smallerand smaller quadrant regions so that for anyregion P()=TRUE.



Region splitting and merging

• Algorithm -:

1. Split into four disjoint quadrants any region

for which

2. Merge any adjacent regions and for which

∪

3. Stop when no further merging or splitting is

possible.



K-means

• Given a set of observation (, 2, … … … . , )where each observation is a d-dimensionalreal vector K-means clustering aims to

partition the n observation into k sets (k≤n)S={, 2,………………….., } so as to minimizethe within-cluster sum of squares

armin −

Where is the mean of points in



K-means

• Algorithm – Assignment step :

Assign each observation to the cluster whose mean is closestto it (i.e partition the observations )

() ∶ () ≤ ()

Where each is assigned to exactly one () even if it couldbe assigned to two or more of them.

– Update Step

Calculate the new means to be the centroids of theobservation in the new clusters. (+) () ∈()

– The algorithm has converged when the assignment no longer change.



Fuzzy-C-means

• In fuzzy clustering each point has a degree of belongingto clusters as in fuzzy logic rather than belongingcompletely to just one cluster. Thus points on the edgeof a cluster may be in the cluster to a lesser degree

than points in the centre of cluster.• Any point x has set of coefficient giving the degree of

being in the k th cluster (). With fuzzy c-means thecentroid of a cluster is the mean of all points weighted

by their degree of belonging to the cluster :

()



FuzzyCmeans

• Algorithm

1 Choose a number of clusters

2 Assign randomly to each point coefficient for

being in the clusters.

3 Repeat until the algorithm has converged



Evaluation metrics

• Layout Entropy(Hl ofE )-: E is a evaluation function basedon information theory and the Minimum Descriptionlength Principle (MDL).

• Hl is defined as the entropy of the pixels in asegmentation layout. Segmentation layout is an imageused to describe the result of segmentation.

• According to the Minimum description Length principleif we balance the trade-off between the uniformity of

the individual regions with the complexity of thesegmentation the minimum description lengthcorresponds to the best segmentation.



Layout Entropy

• Layout entropy measures the segmentation complexity.Layout entropy also gives indicates the number of bits (orHarleys when using a base-10 logarithm) per pixel neededto specify a region id of each pixel for a particularsegmentation I.

•

= log

• Again, when viewed using a coding theory framework, one

can view pj = Sj/SI as the probability that a each pixel in theimage belongs to region j under a probabilistic assumptionthat each pixel is independently selected to be in region jwith probability pj.



Gray level uniformity

• It is based on the colour error of the regionand it helps in describing the inter regionuniformity. The algorithm which generate the

uniform images have better boundaryseparating different various regions.

•

()×

=

• The 2is known as square colour error which

we can define as



Gray level uniformity

• 2 ,∈

• Cx , ℎ ℎ

• Cx ℎ ℎ



• Evaluation method Ecw uses E inter to measurethe inter-region colour difference, which isdefined as the weighted proportion of pixels

whose colour difference between its originalcolour and the average region colour in the otherregion is less that a pre-defined threshold.

• Note that, for a segmented image, a large value

of intra-region visual error means plenty of pixelsmay be mistakenly merged and this image couldhave been undersegmented.



• ( −

∗∗−)∈

• Where 1 > 0 ℎ

0



• . It measure how far one region differ from one-another .It is criteria which quantifies the quality ofsegmentation result.

1

= 2()

• Where Sj denotes the number of pixels in region j andSi denotes the pixels in image I.

• 2() denotes the square colour error for region j



F(I)

• The evaluation function F(I) is defined as

2

=

• where I is the image to be segmented, R, the numberof regions in the segmented image, A, the area, or thenumber of pixels of the I th region, and e, the colourerror of region .

• , is defined as the sum of the Euclidean distance of

the colour vectors between the original image and thesegmented image of each pixel in the region



F(I)

• .The term

is a global measure which penalizes

small regions or regions with a large colour error.e, indicates whether or not a region is assignedan appropriate feature (colour).

• The term is a local measure which penalizes

small regions or regions with a large colour error.

e, indicates whether or not a region is assignedan appropriate feature (colour). The smaller thevalue of F, the better is the segmentation result.



Discrepancy

• A discrepancy measure was based on the differencebetween the original and smoothed pictures.

• The measure proposed was the sum of the squareddifferences between gray levels of corresponding

points in the original and smoothed pictures.

• If we assume that the image consists of objects andbackground, each having a specified distribution ofgray levels, then we can compute, for any given

threshold t, the Probability of misclassifying an objectpoint as background, or vice versa.



Discrepancy

• This probability can be regarded as a measure

of the discrepancy between the classifications

produced by the threshold and the "ideal"

classification.

((,)(,))



Result and Discussion

• The evaluation of segmentation algorithm isperformed on mammographic imagesdatabases (such as DDISM) and texture image

database.• In order to evaluate various segmentation

algorithms first we applied varioussegmentation algorithms on the images and

evaluate various metrics based on thesegmentation images.




• Texture image segmentation algorithm will require largernumber of bits to specify the region id per pixel for the

segmented image.

• Active contour produces the most uniform segmented images

• All the images generate the same degree of under-segmentedimages.

• Region growing shows the higher value of disparity value

which suggest that segmented images produce by region

growing are of better quality.

DDISM

Database

Otsu K-means Fuzzy-

C-means

Gaussian Active

Countour

Texture Region

Growing

GraphCut

Layout Entropy

0.633104

0.6732

0.6731

0.66403

0.6689

0.6798

0.6590

0.6727

Gray-level

Uniformity

58971 59459 58903 79765 104946 59690 60336 103416

E intra of Ecw 0.5202 0.5202 0.5202 0.5138 0.5199 0.5195 0.5136 0.5202

2000528

2007256

2007457

2231478

3004150

2587649

7906856

2536798

()

125217

125453

125354

138856

172883

166398

338919

151671

Discrepancy 15061

13057

16789

23518

21703

21816

33521

21460




• Otsu present better segmentation result.

• The higher value of discrepancy of region

growing suggest that larger number of

background pixel are considered as object

pixel.




• Fuzzy-c-means produces the most disorder segmented images

which suggest it will require the larger number of bits to specify the

region id per pixel.

• Region Growing produces the most uniform segmented images.

• All the segmented images produces the same degree of under-

segmented images.

• Active contour has largest disparity value which suggest that

segmented images produce by active contour is of better quality.




• Fuzzy-C-means produce the bettersegmentation result.

• Active Contour segmentation algorithm has

largest value of discrepancy value whichsuggest that large number of background

pixels are considered as object pixels.

evaluation of image segmentation algorithm1

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