In this paper, a unified computational framework is presented for facilitating edge detection both in untextured as well as textured two-dimensional (2-D) images. The framework is based on a complete set of difference operators which are easily configurable from a set of orthogonal polynomials. The widely known Roberts, Sobel, Prewitt, and Marr's LOG edge operators can easily be represented in terms of these operators. For detection of untextured or textured edges, the proposed operators are employed to separate out the responses toward edge or texture and noise. Untextured edges are detected by maximizing signal-to-noise ratio (SNR) or identifying the zero crossings in the second directional derivatives. Textured edges are detected in two stages. First, the significance of responses toward texture is computed statistically in order to test the presence of microtexture and compute a local descriptor called "pronum" for its representation. Finally, a global descriptor for texture called "prospectrum" is obtained by observing the frequency of occurrence of pronums. The textured edges are detected at the second stage by applying the methods of detection of untextured edges on these prospectrums. The results are encouraging.

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A new orthogonal polynomials based transform coding scheme has been presented in this paper. A class of orthogonal polynomial functions for obtaining polynomial operators with different sizes is proposed. The statistical design of experiments paradigm has been used to separate out the spatial variation within the image region due to discriminable low level features from the spatial variation due to unexplained sources called noise. The degree of this separationability can be controlled by speTransformation [SI have been studied and reported for effective transform coding of monochrome images. In this paper we present a new orthogonal polynomials based transform coding for monochrome image data compression. In the transformed domain, statistical tests have been used to characterize the signal and noise parts of an image. Compression is achieved by retaining the singal parts alone, followed by a bit allocation scheme. This eliminates the intuitive notion of retaining only lower frequency components as used in other transform coding schemes.cifying the level of signal-to-noise ratio. The process of separation of signals during polynomial transform coding is based on the proposed statistical hypothesis testing 2 The orthogonal polynomial opprocedures. The results are encouraging. erator