Curvature for Fourier Heat Transformation Method: A Shape based Object Recognition

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Studies in System Science (SSS) Volume 2, 2014 www.as‐se.org/sss

Curvature for Fourier Heat Transformation Method: A Shape based Object Recognition M. Radhika Mani1, Dr. G.P.S. Varma2, Dr. Potukichi DM3, Dr. Ch. Satyanarayana*4 1

Pragati Engg. College, Surampalem, A.P., India‐533437

2

SRKR Engg. College, Bhimavaram, A.P., India‐534204

3

JNT University Kakinada, Kakinada, A.P., India‐533003

4

JNT University Kakinada, Kakinada, A.P., India‐533003

1

radhika_madireddy@yahoo.com; 2gpsvarma@yahoo.com; 3potukuchidm@yahoo.com; chsatyanarayana@yahoo.com

*4

Abstract In Shape based Object Recognition processes, heat transformations are widely used. Elegance for the computation of it with Fourier transformation is presented. Generic involvement of Cartesian coordinates for the computation is discussed. A novel method that utilizes the features of curvature of the object in the computation of heat transformation, CFHT is proposed. An invariant feature vector is generated with the help of Fourier transformation. New distance measure is used for the computation of shape similarity. The proposed CFHT method is testified over MPEG CE‐1 set B database. The results and the analysis infer relative efficiency for the present method than those with normal Cartesian coordinate method. Keywords Polar Coordinates; Distance Measure; Heat Kernel; Feature Vector; Fourier Transform

Introduction Shape based methods is widely used in the image processing and pattern recognition process recently [1]. The shape based approach consists of different stages viz., shape representation, shape description and shape toning. The shape representation stage identifies the effective representative points of an object. There are two categories of shape representation methods viz., boundary based and region based methods [2, 3]. Moment Invariants [4], Zernike Moments [5, 6] , Krawtchouk moments [7], Chebyshev moments [8, 9] represent some other types of popular moments used for region based descriptors. However, the region based shape representation methods involves the procedures as the medial axis transform [10, 11, 12], grid method [13], and generic Fourier transform [14] etc. Recently, the inelastic deformations that involved with the shape of an object are described by geodesic geometry [15, 16, 17] , inner distances with dynamic programming [18, 19], Laplacian transforms [20, 21] and heat diffusion [22, 23]. Currently, the heat flow equation [24, 25] is successfully applied in different fields. The diffusion process is tested in a more generalized perspective which can be connected to other analogus processes. Nevertheless, Fourier transformation can efficiently describe [26] the intrinsic features of the given object. Based on the shape representation points, shape signature [26, 27] would be constructed and it can be used as an input to the Fourier transformation to generate the shape characteristic feature vector. In the wake of the necessity (i) to conceive the fineness of shape information mediated by details of curvature information and (ii) overcome the problem of mis coverage finer detail information of sharp bends; the existing heat equation based methods needs a more efficient, but simpler method which includes the curvature of the object. Hence, the authors intend to propose a novel curvature based Fourier Heat Transformation method for Shape based Object Recognition. The paper is organized in 3‐sections. Introduction to heat equation based shape description methods is briefed in Section‐I. The details of methodology implemented presently and the relevance is detailed in section‐II. Results of implementing the novel algorithm designed by curvature approach to the standard databases and their analysis with relevant discussion is presented in Section‐III. Methodology An innovative Curvature based Fourier Heat Transformation (CFHT) method for object recognition process is presently proposed. The proposal consists of 4 successive steps viz., (i) Shape representation with contour (ii) CFHT construction (iii) Shape description by using Fourier Transform and (iv) Shape similarity and ranking, respectively. The first step involves the contour representation of the shape surface. Surface is sampled by a finite number of

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