Local energy, the pre-envelope, and filter resolution

We examine the construction of new filters for computing local energy, and compare these filters with the Gabor filters and the three-point-filter of Venkatesh [l]. Further, we demonstrate that the effect of convolution with complex Gabor filters is to band-pass (with some differentiating effect) and compute the local energy of the result. The magnitude of the resulting local energy is then used to detect features [2], [3] (step features, texture etc.), and the phase is used to classify the detected features [l], [4] or provide disparity information for stereo [5] and motion work [6], [7]. Each of these types of information can be obtained at multiple resolutions, enabling the use of course to fine strategies for computing disparity, and allowing the discrimination of image textures on the basis of which parts of the Fourier domain they dominate [8], [9].