Shape and Image Analysis using Neural Networks Fractals and Wavelets

Abstract

REPORT DOCUMENTATION PAGEForm ENCY USE ONLY (Leave blank)2. REPORT DATE May 7, 2000 REPORT TYPE AND DATES COVEREDFinal en A-firQk-~&1 Mpur OQ LE AND SUBTITLEShape and Image Analysis using Neural Networks, Fractals and Wavelets. THOR(S)C.R. Rao S.R.T. Kumara FUNDING NUMBERS DAAH04-96-1-0082 ^FORMING ORGANIZATION NAMES(S) AND ADDRESS(ES)The e views, opinions and/or findings contained in this report are those of the author(s) and should not be construed as official Department of the Army position, policy or decision, unless so designated by other documentation.'ISTRIBUTION / AVAILABILITY STATEMENT >proved for public release; distribution unlimited. b. DISTRIBUTION CODE ISTRACT (Maximum 200 words)A general theory and appropriate statistical analysis are developed for discrimination of objects by shape, i.e., by using features which are invariant to location, scale and orientation, in particular to reflection also. In the case of landmark data, features such as Euclidean distances between landmarks or angles of triangles after suitable triangulation are considered. When the objects do not have recognizable landmarks, as in the case of closed boundaries, we can use topological properties of points on the boundary at intervals of constant length as features. To deal with such cases, a new geometry of circular vectors with a suitably defined metric is developed. This enables the use of distance methods such as k-NN rule in pattern recognition. We have also concentrated on the extraction of features for representing shapes. As a generalization we have considered the signals from machining process and studied characterization using chaos and fractal analysis. We extended this work to represent shapes using wavelets, Fourier descriptors, fractal image compression and iterated functional systems. We have conducted a comparative analysis. In the contemporary internet world search engines need sophisticated techniques to search for images of interest based on shapes. We proposed a preliminary model and web bot based upon our shape analysis study to develop an image search engine for the www. IBJECT TERMS Statement of the Problems Studied Technical Objectives and MotivationDiscriminant analysis based on multiple measurements is a fundamental tool in several practical applications ranging from disputed paternity and authorship of a manuscript to medical diagnosis character recognition, and detection and identification of signals. In many situations, the measurements made on an object depend on its location, scale and orientation. The technical problem involved is to extract features of objects which are invariant to the above transformations, which are called shape measurements and develop the statistical methodology for discrimination by shape.Multifractal image analysis dealing with image representation and image compression is a problem of paramount importance in activities, and will assume tremendous importance in the future due to proliferation of new techniques such as remote and virtual collaboration in the internet. T...