This document discusses various image segmentation techniques. It begins by defining image segmentation as dividing an image into constituent regions or objects. It then describes several segmentation algorithms, including clustering in color space, thresholding, region growing, region splitting, and split and merge. Thresholding techniques discussed include basic global thresholding of bimodal histograms, adaptive thresholding for uneven illumination, and multilevel thresholding for multimodal histograms. The document provides examples of applying these techniques and discusses applications of image segmentation such as in 3D medical imaging.

1. Image Segmentation
CIS 601 Fall 2004
Longin Jan Latecki

2. Image Segmentation
• Segmentation divides an image into its
constituent regions or objects.
• Segmentation of images is a difficult task in
image processing. Still under research.
• Segmentation allows to extract objects in
images.
• Segmentation is unsupervised learning.
• Model based object extraction, e.g.,
template matching, is supervised learning.

3. What it is useful for
• After a successful segmenting the image, the contours of
objects can be extracted using edge detection and/or
border following techniques.
• Shape of objects can be described.
• Based on shape, texture, and color objects can be
identified.
• Image segmentation techniques are extensively used in
similarity searches, e.g.:
http://elib.cs.berkeley.edu/photos/blobworld/

4. Segmentation Algorithms
• Segmentation algorithms are based on one of
two basic properties of color, gray values, or
texture: discontinuity and similarity.
• First category is to partition an image based on
abrupt changes in intensity, such as edges in an
image.
• Second category are based on partitioning an
image into regions that are similar according to a
predefined criteria. Histogram thresholding
approach falls under this category.

5. Domain spaces
spatial domain (row-column (rc) space)
histogram spaces
color space
texture space
other complex feature space

6. Clustering in Color Space
1. Each image point is mapped to a point in a color
space, e.g.:
Color(i, j) = (R (i, j), G(i, j), B(i, j))
It is many to one mapping.
2. The points in the color space are grouped to clusters.
3. The clusters are then mapped back to regions in the
image.

7. Examples
Mnp: 30, percent 0.05, cluster number 4
Mnp : 20, percent 0.05, cluster number 7
Original pictures segmented pictures

8. Displaying objects in the
Segmented Image
• The objects can be distinguished by
assigning an arbitrary pixel value or
average pixel value to the pixels belonging
to the same clusters.

9. Thus, one needs clustering algorithms
for image segmentation.
Homework 8:
Implement in Matlab and test on some example images
the clustering in the color space.
Use Euclidean distance in RGB color space.
You can use k-means, PAM, or some other clustering
algorithm.
Links to k-means, PAM, data normalization
Test images: rose, plane, car, tiger, landscape

10. Segmentation by Thresholding
• Suppose that the gray-level histogram
corresponds to an image f(x,y) composed of
dark objects on the light background, in such a
way that object and background pixels have
gray levels grouped into two dominant modes.
One obvious way to extract the objects from the
background is to select a threshold ‘T’ that
separates these modes.
• Then any point (x,y) for which f(x,y) < T is called
an object point, otherwise, the point is called a
background point.

11. Gray Scale Image Example
Image of a Finger Print with light background

12. Histogram

13. Segmented Image
Image after Segmentation

14. In Matlab histograms for images can be
constructed using the imhist command.
I = imread('pout.tif');
figure, imshow(I);
figure, imhist(I) %look at the hist to get a threshold, e.g., 110
BW=roicolor(I, 110, 255); % makes a binary image
figure, imshow(BW) % all pixels in (110, 255) will be 1 and white
% the rest is 0 which is black
roicolor returns a region of interest selected as those pixels in I that
match the values in the gray level interval.
BW is a binary image with 1's where the values of I match the values
of the interval.

15. Thresholding Bimodal Histograms
• Basic Global Thresholding:
1)Select an initial estimate for T
2)Segment the image using T. This will produce two
groups of pixels. G1 consisting of all pixels with gray
level values >T and G2 consisting of pixels with values
<=T.
3)Compute the average gray level values mean1 and
mean2 for the pixels in regions G1 and G2.
4)Compute a new threshold value
T=(1/2)(mean1 +mean2)
5)Repeat steps 2 through 4 until difference in T in
successive iterations is smaller than a predefined
parameter T0.

16. Gray Scale Image - bimodal
Image of rice with black background

17. Segmented Image
Image after segmentation
Image histogram of rice

18. Basic Adaptive Thresholding:
Images having uneven illumination makes it difficult
to segment using histogram,
this approach is to divide the original image
into sub images
and use the thresholding process
to each of the sub images.

19. Multimodal Histogram
• If there are three or more dominant modes in the
image histogram, the histogram has to be
partitioned by multiple thresholds.
• Multilevel thresholding classifies a point (x,y) as
belonging to one object class
if T1 < (x,y) <= T2,
to the other object class
if f(x,y) > T2
and to the background
if f(x,y) <= T1.

20. Thresholding multimodal histograms
• A method based on
Discrete Curve Evolution
to find thresholds in the histogram.
• The histogram is treated as a polyline
and is simplified until a few vertices remain.
• Thresholds are determined by vertices that are local
minima.

21. Discrete Curve Evolution (DCE)
u
v
w u
v
w
It yields a sequence: P=P0, ..., Pm
Pi+1 is obtained from Pi by deleting the vertices of Pi
that have minimal relevance measure
K(v, Pi) = |d(u,v)+d(v,w)-d(u,w)|
>

22. Gray Scale Image - Multimodal
Original Image of lena

23. Multimodal Histogram
Histogram of lena

24. Segmented Image
Image after segmentation – we get a outline of her face, hat, shadow etc

25. Color Image - bimodal
Colour Image having a bimodal histogram

26. Histogram
Histograms for the three colour spaces

27. Segmented Image
Segmented image, skin color is shown

28. Split and Merge
• The goal of Image Segmentation is to find
regions that represent objects or
meaningful parts of objects. Major
problems of image segmentation are result
of noise in the image.
• An image domain X must be segmented in
N different regions R(1),…,R(N)
• The segmentation rule is a logical
predicate of the form P(R)

29. Introduction
• Image segmentation with respect to
predicate P partitions the image X into
subregions R(i), i=1,…,N such that
X = i=1,..N U R(i)
R(i) ∩ R(j) = 0 for I ≠ j
P(R(i)) = TRUE for i = 1,2,…,N
P(R(i) U R(j)) = FALSE for i ≠ j

30. Introduction
• The segmentation property is a logical
predicate of the form P(R,x,t)
• x is a feature vector associated with region
R
• t is a set of parameters (usually
thresholds). A simple segmentation rule
has the form:
P(R) : I(r,c) < T for all (r,c) in R

31. Introduction
• In the case of color images the feature
vector x can be three RGB image
components (R(r,c),G(r,c),B(r,c))
• A simple segmentation rule may have the
form:
P(R) : (R(r,c) <T(R)) && (G(r,c)<T(G))&&
(B(r,c) < T(B))

32. Region Growing (Merge)
• A simple approach to image segmentation
is to start from some pixels (seeds)
representing distinct image regions and to
grow them, until they cover the entire
image
• For region growing we need a rule
describing a growth mechanism and a rule
checking the homogeneity of the regions
after each growth step

33. Region Growing
• The growth mechanism – at each stage k
and for each region Ri(k), i = 1,…,N, we
check if there are unclassified pixels in the
8-neighbourhood of each pixel of the
region border
• Before assigning such a pixel x to a region
Ri(k),we check if the region homogeneity:
P(Ri(k) U {x}) = TRUE , is valid

34. Region Growing Predicate
The predicate
P: |m(R1) – m(R2)| < k*min{std(R1), std(R2)},
is used to decide if the merging
of the two regions R1, R2 is allowed, i.e.,
if |m(R1) – m(R2)| < k*min{std(R1), std(R2)},
two regions R1, R2 are merged.
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region R having n =|R| pixels:
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m
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35. Split
• The opposite approach to region growing is
region splitting.
• It is a top-down approach and it starts with the
assumption that the entire image is
homogeneous
• If this is not true, the image is split into four sub
images
• This splitting procedure is repeated recursively
until we split the image into homogeneous
regions

36. Split
• If the original image is square N x N, having
dimensions that are powers of 2(N = 2n):
• All regions produced but the splitting algorithm
are squares having dimensions M x M , where
M is a power of 2 as well.
• Since the procedure is recursive, it produces an
image representation that can be described by a
tree whose nodes have four sons each
• Such a tree is called a Quadtree.

37. Split
Quadtree
R0 R1
R2
R3
R0
R1
R00 R01 R02 R04

38. Split
• Splitting techniques disadvantage, they
create regions that may be adjacent and
homogeneous, but not merged.
• Split and Merge method is an iterative
algorithm that includes both splitting and
merging at each iteration:

39. Split / Merge
• If a region R is inhomogeneous
(P(R)= False) then is split into four sub
regions
• If two adjacent regions Ri,Rj are
homogeneous (P(Ri U Rj) = TRUE), they
are merged
• The algorithm stops when no further
splitting or merging is possible

40. Split / Merge
• The split and merge algorithm produces
more compact regions than the pure
splitting algorithm

41. Applications
• 3D – Imaging : A basic task in 3-D image
processing is the segmentation of an image
which classifies voxels/pixels into objects or
groups. 3-D image segmentation makes it
possible to create 3-D rendering for multiple
objects and perform quantitative analysis for the
size, density and other parameters of detected
objects.
• Several applications in the field of Medicine like
magnetic resonance imaging (MRI).

42. Results – Region grow

43. Results – Region Split

44. Results – Region Split and
Merge