Behavior of Normalized Moments under Distortion and Optimization

Abstract

Various types of moments have been used to recognize planar shapes. The algorithms are mostly based upon extracting moment features and train the machine to match these features with a database of templates. The shape could be represented by a polygon whose vertices lie on the boundary. The computational complexity of algorithm is a function of number of vertices of polygon. In this paper, we first present one such algorithm for hand drawn shapes. Vertices are picked up randomly as the user draws the shape with the help of mouse on a monitor. We have used a database of four templates for training the machine. The robustness of the algorithm based upon the moment features has been exhibited by matching a test shape that is a distortion of one of template stored in the database. In the second part of paper we have proposed an optimization technique that discards most of the redundant vertices of the polygon representing the shapes, thus reducing significantly the complexity. Integral square error norm is used to calculate optimal vertices and nearest – neighbor (NN) classifier for classifying the shapes. Empirical results have been presented for extracting the moment feature vectors.