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ment. The objective of segmentation is to classify each RGB pixel in a given image as having a color in the specified range or not [16, 20]. In order to perform this comparison, it is necessary to have a measure of similarity. One of the simplest measure is the Euclidean distance.. Because the distances are positive and monotonic, we can work with the distance squared instead, thus avoiding square root computation. To subdivide the data set into membership functions it needs some procedure to establish fuzzy thresholds between classes of data. We can determine a threshold line with an entropy minimization screening methods; they start the segmentation process first into two classes. By partitioning the first two classes one more time, we can have three different classes.

 

Therefore a repeated partitioning with threshold value calculations will allow us to partition the data set into a no of classes or fuzzy sets, depending on the shape used to describe the membership in each set. Membership function generation is based on a partitioning or analog screening concept, which draws a threshold line between two classes of sample data. The main idea behind drawing the threshold line is to classify the samples while minimizing the entropy for an optimum partitioning.

 

Clustering refers to identifying the number of subclasses of c clusters in a data universe X comprised of n data samples and partitioning X into C clusters (2 < c < n), c=1 denotes rejection of the hypothesis that there are clusters in the data, where c=n constitutes the trivial case where each sample is in a cluster by itself. There are two kinds of c partitions of data; hard (or crisp) and soft (or fuzzy). Two important issues to consider in this regard are how to measure the similarity between pairs of observations and how to evaluate the partitions once they are formed. One of the simplest similarity measures is distance between pairs of feature vectors in the feature space. If one can determine suitable distance measure and compute the distance between all pairs of observations, them one may expect that the distance between points in the same cluster will be considerably less than the distance between points the different clusters.

 

Considering all of these, the segmentation process is done. Then calculate the mean value of each region and they calculate the mean value of nonshadow region. Take pixels whose values are larger than the mean value of region i as the nonshadow background. Then subtract the minimum channel from the maximum channel. This value is denoted as Xi. Then this value is binarized based on the assumption that shadows are often darker than the mean value of Xi, which is denoted as T. Then mark all pixels less than T. indicate the pixel on the red, green and blue channel and integrate them. To obtain this select the suitable values for m and n. For obtaining more accurate values some coefficient are selected. By integrating the pixels values of red, green and blue the final shadow is obtained.

 

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