introduction to Segmentation

Image Segmentation
The segmentation process intends to subdivide an image into distinct regions that
Are supposed to correlate strongly with objects or features of interest in the image. In general, two conditions should be fulfilled in image segmentation:
Pixels that are grouped together ( that belong to the same region) must have similar attributes.
Generated regions (groups of pixels) should be meaningful.
Definition of Segmentation
Segmentation of an image I using an homogeneity predicate P is defined as a partition S = R ¬, R , …R of I that verifies the following conditions:
1. i=1,2,…n
2. R is connected, i=1,2,…n
3. P(R )=TRUE, i=1,2,…n
4. P(R R )= FALSE i ? j, for all adjacent regions R , R .
Condition (1) asserts that every pixel should belong to a region .that is the segmentation is complete.
Condition (2) is to say that regions are composed of continuous pixels.
Condition (3) confirms that every region is homogenous and verifies the similarity criteria.
Condition (4) affirms that region could not be extended any more.
Image Segmentation Algorithms
The image segmentation methods attempt to convert the information contained in
the variation of gray scales into information about the contents of the image.
An image of length M and width N having L gray level values can be viewed as a numeric function f such that:
F(x,y) = k x=0, 1, …M-1; y = 0, 1, …N-1; k = 0, 1, … L-1
Four classical approaches to image segmentation will be shortly presented.
1- Thresholding.
2- Edged-Based Methods.
3- Region-Based Methods.
4- Hybrid Methods.
1-Thresholding
The thresholding technique is very popular in image processing operations, one of which is the segmentation. Thresholding transforms a dataset containing values that vary over some range into a new dataset containing values that vary over smaller range. The simplest case is when the destination dataset contains only two values; a threshold is applied to the input data so that values falling below the threshold are replaced by one of the values in the output dataset; input values at or above the threshold are replaced by the other output value.
Threshold techniques in image processing are based on the threshold values, which are usually selected from the image histogram. This operation encounters no problems if either the portion of the image area occupied by the objects is known or the gray level ranges of objects and background are well separated ( the gray level histogram has deep valley between two peaks)
Thresholding is defined as an operation that involves tests against a numeric function T of the form

Where p(x,y) denotes some local property of the point (x,y).
The resulting thresholded image g(x,y) is then defined as:
g(x,y) = …(1)
In general, asingle threshold value is not enough to detect all the objects in a
complicated image, such as natural outdoor images. It is more efficient to use multiple thresholds rather than a single threshold.
Multiple thresholding is an operation that involves tests against a D-dimensional
function T.
(T , T , …, T )= T{x,y,p(x,y),f(x,y)} With 0The resulting thresholded image g(x,y) uses D+1 values (V , V , …, V ) to map the D+1 classes in the image defined by the D threshols.
g(x,y) =

f versus the output gray level as illustrated in figure (1).
g g
V


V
1
V

0 0
T f T T … T f
Figure (1) single and multiple thresholding



Notes
– Three kinds of thresholding are distinguished:
1- Global thresholding : if T depends only on f(x,y)
2- Local thresholding : if T depends on p(x,y) and f(x,y)
3- Dynamic thresholding: if T depends on p(x,y), f(x,y) and (x,y).
Efficiency of the thresholding technique resides entirely on the selection of appropriate thresholds. In fact, if the threshold level is too high there will be loss of information and.
Ex.\

Original "smhouse" Segmented Contours





Original "hand" Segmented Contours