CONTRIBUTION TO THE STUDY OF OPTIMAL EDGE DETECTION FILTERS AND OPERATORS IN TWO DIMENSIONAL NOISY IMAGES

Abstract

It is an application oriented thesis with the aim of developing new edge detection algorithms within the frame work of image analysis, an application area of digital image processing. Image Analysis primarily centers on extracting features or specific information of interest. In general, it enables one to examine natural and artificial features both in order to extract relevant features of interest. Our interest is centered in the analysis of imagery, specifically noisy images, where we endevour to locate and identify different types of so called edges, commonly defined as sudden intensity changes in gray levels. Such edges may be of step, ramp, roof, pulse or general irregular curves, lines etc., for example, rivers, canals, agricultural fields etc., whose boundaries could be located as precisely as possible. With the incorporation of appropriate filter theory along with a suitable operator, it is shown that the detection of such edges should be considered to have matured atleast to a practical extent. The whole problem can be divided into two parts, the first being the study of existing algorithms, propose and develop new algorithms in the global formulation of the problem. This study involves optimization theory, discontinuous signals, operators, random phenomenon and processing of two dimensional space signals suggesting, by and large an interdisciplinary approach for the problem. In the other part, the computational aspects have been examined. The processing techniques like convolution, DFT etc., have been executed in the usual common manner. However, since our interest of research was centered more towards the adequacy of results, we did not give much weightage/attention for the improvement of execution time or even to the storage capacity required. Within the frame work of the image matrix available, the storage of DEC-2050 and PC is sufficient for us to obtain the results consistent with the theory. Even for large image matrices we have used window, say, 11 x 11 to be centered at each point in space to perform the processing. In order to minimise the effects of noise, a filtering step is thus required. We have used Prolate and Gaussian filters and compared the results with other filters too. The operators are LOG and Directional Derivatives in the direction of gradient. Our main feature has been centered on the scaling of the derivative in 2D, so that, the S/N ratio and location, both could give optimum results, i.e., a precise location of zero-crossings. Although we have mentioned, first differential and template matching technique in this thesis, we are mainly concerned with the second derivative, in order to apply Zero-Crossing technique for the location of edges. Apart from the standard edges like, step, pulse, ramp, roof, etc., we have considered irregular curves, both in the form of edges and lines and made an attempt to establish the effectiveness of the technique employed. In all above cases, addition noise has also been considered to examine its effects on the location and S/N performance. It has been, therefore, the aim of this thesis to detect and locate edges in noisy images, which is our prime concern.

There are numerous applications of the edge detection techniques. Recent efforts have to a great extent been able to suggest and justify that such operators as used for edge detection, are directly applicable to the entire field of computer vision. How a computer should see an object or an edge ?. Answer to such questions can be provided more conviniently, within the framework of the edge detection theory, as the operators used for image detection also participate in computer vision, so as to give correct location and identification. In another very popular application, which is that of biological visionyit. turns out that the Human Visual System is also utilising such operators for edge detection and passing the information to the brain, for further processing. Both the fields of computer vision and Human Visual System are relating to a new and a huge amount of life long work for either developing a computer vision chain, including Robot vision or setting up new models for Human Visual System, opens completly a new dimension of vision research. In the end, it will only be appropriate to point out that the author forsees the emergence of new commercial software packages, for systems for edge detection or a galaxy of number of expert systems, related to vision-computer or biological.