Segmentation algorithms By Dr Rajeev Srivastava Contents Introduction Image segmentation algorithms Evaluation Metrics Result for segmentation Introduction Segmentation subdivides the image into its constituents region or objects ID: 509599
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Slide1
Evaluation of Image
Segmentation
algorithms
By
Dr.
Rajeev
SrivastavaSlide2
Contents
Introduction
Image segmentation algorithms
Evaluation Metrics
Result for segmentationSlide3
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.Slide4
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.Slide5
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.
Algorithm
1 Select an initial estimate for T
2 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.
Slide6
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 tha
n predefined parameter
.
Slide7
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.Slide8
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.Slide9
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-:
Slide10
Edge Detection
Robert mask
Prewitt mask
-1
0
0
1
0
-1
10-1-1 -100011 1
-1
0
1
-1
0
1
-1
0
1Slide11
Edge Detection
Sobel
mask
-1
-2
-1
0
0
012
1
-1
01-202-101Slide12
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.Slide13
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.
Slide14
Region splitting and merging
Algorithm -:
Split into four disjoint quadrants any region
for which
Merge any adjacent regions
and
for which
Stop when no further merging or splitting is possible.
Slide15
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
Slide16
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 Step
Calculate the new means to be the centroids of the observation in the new clusters.
The algorithm has converged when
the assignment
no longer change.
Slide17
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 :
Slide18
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
Slide19
Evaluation metrics
Layout Entropy(
H
l
ofE
)-:
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. Slide20
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
.
Slide21
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
Slide22
Gray
level uniformity
Slide23
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
.Slide24
Where
Slide25
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.Slide26
. 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
Slide27
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 Slide28
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.
Slide29
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.Slide30
Discrepancy
This probability can be regarded as a measure of the discrepancy between the classifications produced by the threshold and the "ideal" classification.
Slide31
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. Slide32
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.
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
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
21460Slide33
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.Slide34
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.Slide35
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.