### Browsing by Author "Ran, X."

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Item Fast Algorithms for 2-D Circular Convolutions and Number Theoretic Transforms Based on Polynomial Transforms over Finite Rings(1992) Ran, X.; Liu, K.J. Ray; ISRIn this paper, we develop new fast algorithms for 2-D integer circular convolutions and 2-D Number Theoretic Transforms (NTT). These new algorithms, which offers improved computational complexity, are constructed based on polynomial transforms over Zp; these transforms are Fourier-like transforms over Zp [x ] which is the integral domain of polynomial forms over Zp. Having defined such polynomial transforms over Zp, we prove several necessary and sufficient conditions for their existence. We then apply the existence conditions to recognize two applicable polynomial transforms over Zp: One is for p equal to Mersenne numbers and the other for Fermat numbers. Based on these two transforms, referred to as Mersenne Number Polynomial Transforms (MNPT) and Fermat Number Polynomial Transforms (FNPT), we develop fast algorithms for 2-D integer circular convolutions, 2-D Mersenne Number Transforms, and 2-D Fermat Number Transforms. As compared to the conventional row-column computation of 2-D NTT for 2-D integer circular convolutions and 2-D NTTs, the new algorithms give rise to reduced computational complexities by saving more than 25% or 42% in numbers of operations for multiplying 2i, i 1; these percentages of savings also grow with the size of the 2-D integer circular convolutions or the 2-D NTTs.Item Low Bit-Rate Image Coding Using a Three-Component Image Model(1992) Ran, X.; Farvardin, Nariman; ISRIn this paper the use of a perceptually-motivated image model in the context of image compression is investigated. The model consists of a so-called primary component which contains the strong edge information of the image, a smooth component which represents the background slow-intensity variations and a texture component which contains the textures. The primary component, which is known to be perceptually important, is encoded separately by encoding the intensity and geometric information of the strong edge brim contours. Two alternatives for coding the smooth and texture components are studied: Entropy-coded adaptive DCT and entropy-coded subband coding. It is shown via extensive simulations that the proposed schemes, which can be thought of as a hybrid of waveform coding and featurebased coding techniques, result in both subjective and objective performance improvements over several other image coding schemes and, in particular, over the JPEG continuous-tone image compression standard. These improvements are especially noticeable at low bit rates. Furthermore, it is shown that a perceptual tuning based on the contrast-sensitivity of the human visual system can be used in the DCT-based scheme, which in conjunction with the 3- component model, leads to additional subjective performance improvements.Item A Perceptually Motivated Three-Component Image Model(1992) Ran, X.; Farvardin, Nariman; ISRIn this paper, results of phychovisual studies of the human visual system are discussed and interpreted in a mathematical framework. The formation of the perception is described by appropriate minimization problems and the edge information is found to be of primary importance in visual perception. Having introduced the concept of edge strength, it is demonstrated that strong edges are of higher perceptual importance than weaker edges (textures). We have also found that smooth areas of an image influence our perception together with the edge information, and that this influence can be mathematically described via a minimization problem. Based on this study, we have proposed to decompose the image into three components: (i) primary, (ii) smooth and (iii) texture, which contain, respectively, the strong edges, the background and the textures. An algorithm is developed to generate the three-component image model and an example is provided in which the resulting three components demonstrate the specific properties as expected. finally, it is shown that the primary component provides a superior representation of the strong edge information as compared with the Laplacian-Gaussian Operator scheme which is a popular edge extraction method.Item A Three-Component Image Model Based on Human Visual Perception and Its Applications in Image Coding and Processing(1992) Ran, X.; Farvardin, N.; ISRIn this work, results of psychovisual studies of the human visual system are discussed and interpreted in a mathematical framework. the formation of the perception is described by appropriate minimization problems and the edge information is found to be of primary importance in the visual perception. Having introduced the concept of edge strength, it is demonstrated that strong edges are of higher perceptual importance than weaker edges (textures). We have also found that smooth areas of an image influence the human visual perception together with the edge information, and that this influence can be mathematically described via a minimization problem. Based on this study, we have proposed to decompose the image into three components: (i) primary, (ii) smooth and (iii) texture, which contain, respectively, the strong edges, the background and the textures. An algorithm is developed to generate the three-component images model.Then, the use of this perceptually-motivated image model in the context of image compression is investigated. The primary component is encoded separately by encoding the intensity and geometric information of the strong edge brim contours. Two alternatives for coding the smooth and texture components are studied: Entropy-coded adaptive DCT and entropy-coded subband coding. It is shown via extensive simulations that the proposed schemes, which can be thought of as a hybrid of waveform coding and feature-based coding techniques, result in both subjective and objective performance improvements over several other image coding schemes and, in particular, over the JPEG continuous-tone image compression standard. These improvements are especially noticeable at low bit rates. Furthermore, it is shown that a perceptual tuning based on the contrast-sensitivity of the human visual system can be used in the DCT-based scheme, which in conjunction with the three-component model, leads to additional subjective performance improvements.

Finally, a scheme for structurally representing planar curves is developed based on the ideas for the three-component image model. This scheme does not have the ambiguity problem associated with the scale-space-based schemes.