Image Segmentation

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Image Segmentation

• CIS 601 Fall 2004
• Longin Jan Latecki

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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.

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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/

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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.

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• Domain spaces
• spatial domain (row-column (rc) space)
• histogram spaces
• color space
• texture space
• other complex feature space

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

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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) lt T is
  called an object point, otherwise, the point is
  called a background point.

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Gray Scale Image Example
Image of a Finger Print with light background
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Histogram
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Segmented Image
Image after Segmentation
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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 BWroicolor(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.
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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 gtT and G2 consisting of
  pixels with values ltT.
• 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.

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Gray Scale Image - bimodal
Image of rice with black background
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Segmented Image
Image after segmentation
Image histogram of rice
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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.
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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 lt (x,y) lt T2,
• to the other object class
• if f(x,y) gt T2
• and to the background
• if f(x,y) lt T1.

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Thresholding multimodal histograms

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

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Discrete Curve Evolution (DCE)
It yields a sequence PP0, ..., Pm Pi1 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)
v
v
gt
w
w
u
u
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Gray Scale Image - Multimodal
Original Image of lena
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Multimodal Histogram
Histogram of lena
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Segmented Image
Image after segmentation we get a outline of
her face, hat, shadow etc
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Color Image - bimodal
Colour Image having a bimodal histogram
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Histogram
Histograms for the three colour spaces
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Segmented Image
Segmented image, skin color is shown
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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)

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Introduction

• Image segmentation with respect to predicate P
  partitions the image X into subregions R(i),
  i1,,N such that
• X i1,..N U R(i)
• R(i) n 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

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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) lt T for all (r,c) in R

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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) ltT(R)) (G(r,c)ltT(G))
• (B(r,c) lt T(B))

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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

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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

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Region Growing Predicate
The arithmetic mean m and standard deviation std
of a region R having n R pixels

• The predicate
• P m(R1) m(R2) lt kminstd(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) lt kminstd(R1), std(R2),
• two regions R1, R2 are merged.

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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

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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.

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Split

• Quadtree

R0
R1
R0
R3
R1
R2
R00
R01
R02
R04
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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

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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

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Split / Merge

• The split and merge algorithm produces more
  compact regions than the pure splitting algorithm

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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).

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Results Region grow
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Results Region Split
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Results Region Split and Merge