Operators-Based on Second Derivative double derivative Laplacian operator Laplacian Operator Laplacian Of Gaussian (LOG) Operator LOG

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1 Operators-Based on Second Derivative The principle of edge detection based on double derivative is to detect only those points as edge points which possess local maxima in the gradient values. Laplacian operator is the most commonly used second derivative-based edge operator. Laplacian Operator The Laplacian operator is expressed by Laplacian Of Gaussian (LOG) Operator To reduce the noise, Laplacian of Gaussian (LOG) operator can be used. LOG first performs the Gaussian smoothing, which is followed by the Laplacian operation. Difference of Gaussian (DOG) operator It is possible to approximate the LOG filter by taking the difference of two differently sized Gaussians. The DOG operator is implemented by convolving an image with a mask which is obtained by subtracting two Gaussian masks with two different sigma values

2 Limitations of Edge-Based Segmentation [page 143] The principal limitations of edge detection methods are: (a) The edges extracted using the classical methods often do not necessarily correspond to boundary objects. In many low-quality images, captured using low quality imaging devices, some of the conventional methods produce spurious edges and gaps. (b) The edge detection techniques depend on the information contained in the local neighborhood of the image. Most of the edge detection techniques do not consider model-based information embedded in an image. (c) In most of the cases the edge detection strategies ignore the higher order organization which may be meaningfully present in the image. (d) After the edge points are extracted from the image, these points are linked in order to determine boundaries. This is usually done by first associating edge elements into edge segments and then by associating segments into boundaries. The edge linking process sometimes lead to discontinuities and gaps in the image. (e) The edge linking methods used arbitrary interpolation in order to complete boundary gaps. (f) It is often difficult to identify and classify spurious edges. IMAGE THRESHOLDING TECHNIQUES The thresholding operation involves identification of a set of optimal thresholds, based on which the image is partitioned into several meaningful regions. Bi-level Thresholding Bi-level thresholding is employed on images which have bimodal histograms. In bi-level thresholding, the object and background form two different groups with distinct gray levels In bimodal thresholding all gray values greater than threshold T are assigned the object label and all other gray values are assigned the background label, thus separating the object pixels from the background pixels. Thresholding thus is a transformation of an input image A into a segmented output image B as follows: (a) bij, = 1 for aij >= T. (b) bij = 0 for at, < T, where T is the threshold Multilevel thresholding

3 In Multilevel thresholding, the image is partitioned into different segments using multiple threshold values. The histograms in such cases are multimodal, with valleys in between. Entropy-Based Thresholding Entropy based thresholding is widely used in bilevel thresholding. Entropy is a measure of information in an image defined by Shannon. The variants of Shannon s entropy have been effectively used for estimation of thresholds in image segmentation. In entropy-based thresholding, the entropy of foreground (object) and background regions are used for optimal selection of thresholds. In Kapur s thresholding technique, the foreground and background region entropies are where the foreground gray values range from 0 to T and background pixels lie in [T + 1, L 1] n an L-level gray image. In Eqs. 7.5 and 7.6, p( g ) is the probability mass function where h(g) is the histogram of gray value g and N is the total number of pixels. The foreground and background area probability values are The gray level value that maximizes the entropy for the sum of H f and H b is used as the threshold. The thresholding strategy maximizes the total entropy of both the foreground and the background regions. Renyi s entropy has also been used for image thresholding.the Renyi s entropy for foreground and background regions are In this thresholding technique, the total entropy of foreground and background regions is computed for various p and appropriate p value is chosen that yields the best thresholding results. REGION GROWING Region growing refers to the procedure that groups pixels or subregions into larger regions. Starting with a set of seed points, the regions are grown from these points by including to each seed point those neighboring pixels that have similar attributes like intensity, gray level texture, color, etc Region Adjacency Graph

4 The adjacency relation among the regions in a scene can be represented by a region adjacency graph (RAG). The regions in the scene are represented by a set of nodes N = { N1, N2,..., N,} in the RAG, where node Ni, represent the region Ri, in the scene and properties of the region Ri, is stored in the node data structure Ni,. The edge eij between Ni, and Nj represent the adjacency between the regions Ri, and Rj. Two regions Ri, and Rj are adjacent if there exist a pixel in region Ri, and a pixel in region Rj which are adjacent to each other. The adjacency can be either 4-connected or 8connected. The adjacency relation is reflexive and symmetric, but not necessarily transitive. In Figure 7.17, we show the adjacency graph of a scene. Region Merging and Splitting A segmentation algorithm can produce too many small regions because of fragmentation of a single large region in the scene. In such a situation, the smaller regions need to be merged based on similarity and compactness of the smaller regions. A simple region merging algorithm is presented below. Step 1: Segment the image into R1, R2,..., Rm, using a set of thresholds. Step 2: Create a region adjacency graph (RAG) from the segmented description of the image. Step 3: For every Ri, i = 1, 2,..., m, identify all Rj, j # i from the RAG such that Ri is adjacent to Rj. Step 4: Compute an appropriate similarity measure Sij between Ri, and Rj,for all i and j. Step 5 : If Sij > T, then merge Ri, and Rj,. Step 6: Repeat steps 3 to 5 until there is no region to be merged according to the similarity criteria. Clustering Based Segmentation Data driven segmentation techniques can be histogram-oriented or cluster oriented. Histogram-oriented segmentation produces an individual segmentation for each feature of the multifeature data, and then overlaps the segmentation results from each

5 feature to produce more fragmented regions. Cluster oriented segmentation uses the multidimensional data to partition the image pixels into clusters. Cluster-oriented techniques may be more appropriate than histogram-oriented ones in segmenting images, where each pixel has several attributes and is represented by a vector. Each clustering configuration is assigned a value or cost to measure its goodness. An appropriate cost function measures the goodness of a cluster. Usually, the cost for a cluster configuration is its squared error, i.e., the sum of squared Euclidean distances of each point to its cluster center. Thus low values of such a cost indicate better clustering results. It is found that this cost surface is complicated in nature with many poor local minima. K-means is a popular cluster based segmentation method where each pixel is iteratively assigned to the nearest cluster and the cluster center position is recalculated. After each iteration the cost will decrease until the cluster configuration converges at a stable state, at which point the cost is at a local minimum.