In The Name Of God

Digital Image ProcessingDigital Image Processing

Lecture8:

Image Segmentation

By: M. Ghelich OghliM. Ghelich OghliE-mail: E-mail: m.g31_mesu@yahoo.comm.g31_mesu@yahoo.com

Fall 2012

Image Segmentation

• Description: Subdividing image into its constituent regions or objects

•There is not any absolute theory of image segmentation.

Rather, there are a collection of methods that have received some degree of popularity.

Detection of Discontinuity

• Point Detection

Detection of Discontinuity

• Line Detection

Example of Line Detection

Detection of Discontinuity

• Edge Detection: detection of discontinuity in image• Edge Model

Edge Detection• using first order derivatives• using second order derivatives

Noise effect in Edge Detection

Result: noise filtering is required especially in second order derivatives

Gradient operators

Edge Detection (first order derivatives)

Edge Detection (Second order derivatives)

• Laplacian

• Laplacian of Gaussian (LoG)

Edge Detection (LoG)

Image Segmentation

1. Hard segmentationA pixel belongs to object or background

Image Segmentation

2. Soft (Fuzzy) segmentation

First class Second class Third class

Image Segmentation

Image Segmentation methods

•Pixel based methods

•Region based methods

•Clustering segmentation methods

•Boundary detection

•Texture segmentation

Image Segmentation

Pixel based methodsConceptually, the simplest approach we can take for

segmentation.

But, it is not the best method.

The most sensible example of this category:

Thresholding

Thresholding

• Foundation:

Thresholding

• In A: light objects in dark background

• To extract the objects:

– Select a T that separates the objects from the background

– i.e. any (x,y) for which f(x,y)>T is an object point.

• A thresholded image:

(objects)

(background)

Thresholding

• In B: a more general case of this approach (multilevel thresholding)

• So: (x,y) belongs:

– To one object class if T1<f(x,y)≤T2

– To the other if f(x,y)>T2

– To the background if f(x,y)≤T1

Global Thresholding

Multi level Thresholding

Adaptive Thresholding

Advantage: Alleviates the illumination problem

Method: Divides the original image to subimages and applies threshold to each subimage individually

Adaptive Thresholding

Image Segmentation

Region based methodsRegion based methods doesn’t include one of the most

important disadvantage of pixel-based techniques and it is

ignoring pixel relationships and connectivity.

An object consists of not independent and not isolated

pixels.

A robust segmentation method should consider this fact.

Region Growing

In this method neighboring pixels of similar amplitude

are grouped together to form a segmented region.

Image segmentation partitions the set X into the subsets R(i), i=1,

…,N having the following properties

• 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

Region Growing by Pixel Aggregation

• 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

Region Growing by Pixel Aggregation

• 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

Gray Space map

Compute the seed gray level (V) and look for pixels have the same gray level and over lap the seed

Then define a set of gray levels from “V-D” to “V+D”

Region Growing by Pixel Aggregation

Ghelich Oghli, M., Fallahi, A., Pooyan, M. Automatic Region Growing Method using GSmap and Spatial Information on Ultrasound Images. In: 18th Iranian Conference on Electrical Engineering, May 11-13, pp. 35-38 (2010)

At each iteration we increase the difference D by 1

Region Growing by Pixel Aggregation

Ghelich Oghli, M., Fallahi, A., Pooyan, M. Automatic Region Growing Method using GSmap and Spatial Information on Ultrasound Images. In: 18th Iranian Conference on Electrical Engineering, May 11-13, pp. 35-38 (2010)

Image Segmentation

Clustering segmentation methodsSubdividing data's into classes based on some criteria's.

K-Means Clustering

1. Set ic (iteration count) to 1

2. Choose randomly a set of K means m1(1), …, mK(1) (Center

of Classes).

3. For each pixel compute D(xi , mk(ic)), k=1,…K and assign

xi to the cluster Cj with nearest mean.

4. Increment ic by 1, update the means to get m1(ic),…,mK(ic).

5. Repeat steps 3 and 4 until Ck(ic) = Ck(ic+1) for all k.

K-Means Clustering

In some applications (Specially medical application)

because of effect of other slices, absolutely assigning a

pixel to a class is not logically true.

So, we should classify data's by a fuzziness view.

And we should use:

Fuzzy C-Means (FCM)

algorithm

Fuzzy C-Means (FCM)

•A membership function exists for each class at every pixel location

0; if the pixel does not belong to the class

1; if the pixel belongs, with absolute certainty, to the class

0-1; degree of belonging a pixel to a class

at any pixel location the sum of the membership functions

of all the classes must be 1

The fuzzy membership function reflects the similarity

between the data value at that pixel and the value of the

class centroid.

Fuzzy C-Means (FCM)

Fuzzy C-Means (FCM)

Boundary Detectionor

Curve Fitting • It is possible to segment an image into regions of common

attribute by detecting the boundary of each region for which there is a significant change in attribute across the boundary.

• Methodology

Initial guess

Iteratively deforming curves according to the minimization of

internal and external energy functional and controls the smoothness of the curve.

Boundary Detectionor

Curve Fitting

Boundary Detectionor

Curve Fitting

Drawback(Speckle Noise)

Example

Deformable models– Parametric Deformable models (Snake)

– Geometric Deformable models (Level set)

Boundary Detectionor

Curve Fitting

LevelsetThis figure illustrates several important ideas about the level set method.

A bounded regionBoundary=zero level set

Graph of a level set function

Changing (Evolving) in Region…

Moving X-Y plane through …