Abstract-Image compression systems commonly operate by transforming the input signal into a new representation whose elements are independently quantized. The success of such a system depends on two properties of the representation. First, the coding rate is minimized only if the elements of the representation are statistically independent. Second, the perceived coding distortion is minimized only if the errors in a reconstructed image arising from quantization of the different elements of the representation are perceptually independent. We argue that linear transforms cannot achieve either of these goals, and propose instead an adaptive non-linear image representation in which each coefficient of a linear transform is divided by a weighted sum of coefficient amplitudes in a generalized neighborhood. We then show that the divisive operation greatly reduces both the statistical and the perceptual redundancy amongst representation elements. We develop an efficient method of inverting this transformation, and we demonstrate through simulations that the dual reduction in dependency can greatly improve the visual quality of compressed images.

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Curve discrimination is an important task in engineering and other sciences. We propose several shape descriptors for classifying functional data, inspired by form analysis from the image analysis field: statistical moments, coefficients of the components of independent component analysis (ICA) and two mathematical morphology descriptors (morphological covariance and spatial size distributions). They are applied to three problems: an artificial problem, a speech recognition problem and a biomechanical application. Shape descriptors are compared with other methods in the literature, obtaining better or similar performances.

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