To the Graduate Council: I am submitting herewith a thesis written by ...

Chapter 2: Literature Review 14is from Hu [Hu, 1962]. He used the work of nineteenth century mathematicians onimages for pattern recognition.p qmpq = x y f ( x, y ), p,q = 0 , 1,2....x y(2.4)Lower-order geometric moments from Equation 2.4 are easy to compute and aresufficient for representing simple shapes. Algebraic moments [Taubin and Cooper,1991] and [Taubin and Cooper, 1992] on the other hand are based on the centralmoments of predetermined matrices that can be constructed for any order and areinvariant to affine transformations. Teague [Teague, 1980] defines orthogonalmoments by replacing the x p y q term by the Zernike polynomials. Moment shapedescriptors are concise, robust, and easy to compute and match. The disadvantage ofmoment methods is that it is difficult to correlate higher-order moments with theshape’s physical features.Among the many moment shape descriptors, Zernike moments [Jeannin, 2000] are themost desirable for shape description. Due to the incorporation of a sinusoid functioninto the kernel, they have similar properties of spectral features, which are wellunderstood. Although Zernike moment descriptors have a robust performance, theyhave several shortcomings. First, the kernel of Zernike moments is complex tocompute, and the shape has to be normalized into a unit disk before deriving themoment features. Second, the radial features and circular features captured by Zernikemoments are not consistent, one is in the spatial domain and the other is in spectraldomain. This approach does not allow multi-resolution analysis of a shape in the radialdirection. Third, the circular spectral features are not captured evenly at each other andcan result in loss of significant features which are useful for shape description.To overcome these shortcomings, a generic Fourier descriptor (GFD) has beenproposed by Zhang and Lu [Zhang and Lu, 2002]. The GFD is acquired by applying a2D Fourier transform on a polar-raster sampled image using the Equation 2.5.PF ( ρ,φ ) =2 r 2πif ( r, θi)expj2π( ρ + ϕ Rr i T(2.5)Zhang and Lu show that GFD outperforms contour shape descriptors such as curvaturescale spaces, Fourier descriptors and moment-based descriptors.The grid shape descriptor proposed by [Lu and Sajjanhar, 1999] has been used in[Chakrabarti et al., 2000] and [Safar et al., 2000]. Basically, a grid of cells is overlaidon a shape; the grid is then scanned from left to right and top to bottom. The result issaved as a bitmap. The cells covered by the shape are assigned one and those notcovered by the shape are assigned zero. The shape can then be represented as a binary