Wavelets for a vision
Mallat S; Proceedings Of The IEEE, Vol. 84, No. 4, April 1996
Multiscale processing is hardly avoidable to develop efficient image recognition algorithms. Before wavelets were called “wavelets,” researchers such as Burt and Adelson , Koenderink , M m , Witkin , and Rosenfeld 1301 had established the necessity to extract multiscale image information. Some of these ideas have later been formalized and refined by the wavelet theory. In parallel, psychophysics, and physiological experiments [ 1 11 have shown that multiscale transforms seem to appear in the visual cortex of mammals. This was an important motivation to further study the application of such transforms to image analysis. To explain the impact of wavelets for lowlevel vision, we concentrate on three major applications: multiresolution processing, multiscale edge detection, and texture discrimination.
Multiresolution algorithms modify the image resolution to process as little data as possible, for any particular visual task. Coarse to fine searches process first a low resolution image and zoom selectively into finer scale information, if necessary. Applications to stereo vision and optical flow measurements are described.
Local image contrasts are often more informative than light intensity values. A wavelet transform measures gray level image variations at different scales. Contours of image structures correspond to sharp contrasts and can be detected from the local maxima of a wavelet transform. Their importance is illustrated by our ability to recognize complex scenes from a drawing that outlines edges. The wavelet theory relates the behavior of multiscale edges to local image properties. It also opens the door to reconstruction algorithms which recover images from multiscale edges. Among low-level vision problems, texture discrimination is certainly one of the most difficult. Despite the fact that textures are quickly preattentively discriminated by a human observer 1211, there is still no appropriate model for textures. The perception of textures as opposed to edges depends upon local but not pointwise properties. However, there is no predefined neighborhood size over which textures can be analyzed. This has motivated the use of wavelet transforms that measure the image properties over domains of varying sizes. Local frequency measurements derived from a directional wavelet transform appear to be important for texture discrimination , , . Yet no comprehensive theory guides texture segmentations from wavelet coefficients.
When studying the application of wavelets to computer vision, the major difficulties arise at the interface between low-level algorithms and higher level visual models. Multiresolution search strategies must depend upon prior knowledge on the world. Similarly, edges detection can not be restricted to a pointwise processing as it shown by our perception of illusory contours . Texture discrimination also requires the elaboration of prior models which guide the grouping procedures for image segmentations. We discuss these issues in more details.
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