A STUDY OF EDGE DETECTION FILTERS AND OPERATORS FOR TWO DIMENSIONAL IMAGE DATA

Abstract

The extraction of features such as edges, curves, boundaries etc. is useful for variety of purposes. Edges are useful in matching images, improving the quality of segmentation, texture analysis and in extracting shapes of objects in a given image. Our interest is centered on edge detection part of the image processing. Edge detection, in spatial- domain, can be classified into two broad classes viz, gradient operators and the second derivative operators In this disseration theoretical and computational aspects of various operators and filters have been considered. The classical edge detectors use the first derivative to find the intensity gradient at each point in image and the points of gradient optima corrosponds to the edge locations The classical operators which have been studied are Roberts, Laplacian, Prewitt, Sobel, Compass Gradient and Kirsch. The drawback of these operators is that they are very sensitive to noise. Further, the study has been extended to second derivative operators/The zero crossing technique uses the second derivative operators and is found to be very useful. The operators used are Laplacian and Directional derivative in the direction of the gradient/ The Gaussian lowpass filter is choosen for smoothing of data and its Laplacian gives Laplacian of Gaussion (LoG) filter. ii s This is convolved with image matrix and the zero crossings in the convolved image give the edge locations and orientations. Similarly the second derivative operator, to the direction of gradient with the Gaussian function gives directional derivative Qv of Gaussidn (DDoG) filter. Although the images and standard test edges used for the analysis are noise free it is straight forward to use additive noise with uniform Gaussian distribution or white noise and carryout the study. We have used LoG and DDoG operators in which the gaussian low pass filter is inherently incorporated. The Gaussian filter is normally used to mitigate the effect of noise and carryout smoothing of data. The effectiveness of both these operators over the classical operators is established In the noise free images which we have chossen for our study and in which the gaussian filter function is retained as it does not in any way affect the results. The results and further details are presented in subsequent chapters.