Evaluation of Image Segmentation algorithms

ByDr. Rajeev Srivastava

Contents

• Introduction• Image segmentation algorithms• Evaluation Metrics• Result for segmentation

Introduction• Segmentation subdivides the image into its constituents

region or objects.• The level to which the subdivides is carried depends on the

problem being solved.• Segmentation should stop when the object of interest in an

application 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 the intensities. -In second category partition an image into certain

region 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 scanning the image pixel by pixel an labelling each pixel as object or background depending on whether the gray level of that pixel is greater or less than the value of T.

• Algorithm1 Select an initial estimate for T2 Segment the image using T . This will produce two groups of pixels : consisting of all the pixels with gray-levels > T and consist of pixels < T.

Otsu segmentation

3 Compute the average gray level of and for the pixels in the region and 4 Compute a new threshold value 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 the detecting the meaningful discontinuities in gray level. 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 an image.

• The sign of second derivative can be used to determine whether an edge pixel lies on the dark or 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

Edge Detection

• Sobel mask

-1 -2 -1

0 0 0

1 2 1

-1 0 1

-2 0 2

-1 0 1

Region Growing

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

• The basic approach is to start with a set of seed points and from these grow regions by appending to each seed those neighbouring pixels that have properties similar to the seeds.

• When a priori information is not available the procedure is to compute at every pixels the same set of properties that ultimately will be used to assign pixels to region during the growing process.

Region splitting and merging

• The procedure to subdivide an image initially into a set of arbitrary disjointed regions and then 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 segmenting R is to subdivide it successively into smaller and smaller quadrant regions so that for any region 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 ( ) where each observation is a d-dimensional real vector K-means clustering aims to partition the n observation into k sets (k≤n) S={ ,………………….., } so as to minimize the within-cluster sum of squares

Where is the mean of points in

K-means

• Algorithm– Assignment step :

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

Where each is assigned to exactly one even if it could be assigned to two or more of them.

– Update StepCalculate the new means to be the centroids of the observation 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 belonging to clusters as in fuzzy logic rather than belonging completely to just one cluster. Thus points on the edge of 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 the centroid of a cluster is the mean of all points weighted by their degree of belonging to the cluster :

FuzzyCmeans

• Algorithm1 Choose a number of clusters2 Assign randomly to each point coefficient for being in the clusters.3 Repeat until the algorithm has converged

Evaluation metrics

• Layout Entropy(HlofE)-: E is a evaluation function based on information theory and the Minimum Description length Principle (MDL).

• Hl is defined as the entropy of the pixels in a segmentation layout. Segmentation layout is an image used to describe the result of segmentation.

• According to the Minimum description Length principle if we balance the trade-off between the uniformity of the individual regions with the complexity of the segmentation the minimum description length corresponds to the best segmentation.

Layout Entropy• Layout entropy measures the segmentation complexity. Layout

entropy also gives indicates the number of bits (or Harleys when using a base-10 logarithm) per pixel needed to specify a region id of each pixel for a particular segmentation I.

• Again, when viewed using a coding theory framework, one can view pj = Sj/SI as the probability that a each pixel in the image belongs to region j under a probabilistic assumption that each pixel is independently selected to be in region j with probability pj.

Gray level uniformity

• It is based on the colour error of the region and it helps in describing the inter region uniformity. The algorithm which generate the uniform images have better boundary separating different various regions.

• The is known as square colour error which we can define as

Gray level uniformity

𝐸𝑖𝑛𝑡𝑟𝑎𝑜𝑓 𝐸𝑐𝑤• Evaluation method Ecw uses E inter to measure the

inter-region colour difference, which is defined as the weighted proportion of pixels whose colour difference between its original colour and the average region colour in the other region is less that a pre-defined threshold.

• Note that, for a segmented image, a large value of intra-region visual error means plenty of pixels may be mistakenly merged and this image could have been undersegmented.

𝐸𝑖𝑛𝑡𝑟𝑎𝑜𝑓 𝐸𝑐𝑤

• Where

𝐷 ( 𝐼 )𝑜𝑓 𝐹𝑟𝑐• Intra region disparity quantifies the homogeneity of

each region in the image. The global intra-region disparity is proportional to the number of pixels ri of each region Ri.

• The more a rcgion has an important number of pixels, the more it has an infiuence in the global intra.-region disparity. The region containing two different primitives must have a high intra-region disparity compared to the same region composed of one primitive.

𝐷 ( 𝐼 )𝑜𝑓 𝐹𝑟𝑐• . It measure how far one region differ from

one-another .It is criteria which quantifies the quality of segmentation result.

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

• denotes the square colour error for region j

F(I)

• The evaluation function F(I) is defined as

• where I is the image to be segmented, R, the number of regions in the segmented image, A, the area, or the number of pixels of the I th region, and e, the colour error of region .

• , is defined as the sum of the Euclidean distance of the colour vectors between the original image and the segmented 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 assigned an 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 assigned an appropriate feature (colour). The smaller the value of F, the better is the segmentation result.

Discrepancy

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

• The measure proposed was the sum of the squared differences between gray levels of corresponding points in the original and smoothed pictures.

• If we assume that the image consists of objects and background, each having a specified distribution of gray levels, then we can compute, for any given threshold t, the Probability of misclassifying an object point 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 is performed on mammographic images databases (such as DDISM) and texture image database.

• In order to evaluate various segmentation algorithms first we applied various segmentation algorithms on the images and evaluate various metrics based on the segmentation images.

Result and Discussion

• Texture image segmentation algorithm will require larger number 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-segmented

images.• Region growing shows the higher value of disparity value

which suggest that segmented images produce by region growing are of better quality.

DDISMDatabase

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 0.6727Gray-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 0.52022000528 2007256 2007457 2231478 3004150 2587649 7906856 2536798125217 125453 125354 138856 172883 166398 338919 151671

Discrepancy 15061 13057 16789 23518 21703 21816 33521 21460

Result and Discussion

• 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.

Result and Discussion

• 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.

Result and Discussion• Fuzzy-C-means produce the better

segmentation result.• Active Contour segmentation algorithm has

largest value of discrepancy value which suggest that large number of background pixels are considered as object pixels.