Principle of a Parallel Vision System Adapted to Textures

Abstract

A number of methods for classifying textures and for segmentation of textured images make use of multichannel filtering techniques because of their computational simplicity. On the other hand, biological experiments have shown the existence and the properties of visual channels and make it possible for us to select the "best" filter bank. In a performing artificial vision system, three important problems are to be solved: the rigorous sampling of the spatial frequencies, the scale related problem and parallel processing. This paper presents a mathematical solution to the logarithmic 1-D sampling of the spatial frequencies of a signal characterized by its energy spectrum. This solution obeys the signal theory. It is then extended to the 2-D sampling of the output energy image generated by what we call a "homothetic filter bank". While verifying the Shannon theorem, our system is compatible with the visual cells' sensitivities to frequencies and orientations. Scale problems are often encountered in computer vision, especially in methods using multichannel filtering. Our approach gives us a representation of an input textured image with a continuous multiresolution. With this representation, an interpretation of the information content of the image, invariant to scale and to orientation, is made possible. Any scale change in the image is represented by a simple translation along a logarithmic frequency-axis. In the same manner, a rotation corresponds to a translation along a linear orientation-axis. In our "homothetic visual-filter bank" (HFB) theory, it is shown that the frequency-filter function can be changed according to the application under consideration. In cases where texture discrimination is difficult, e.g. if two different textures have the same power spectrum, the solution may be to extract phase information using a classical complex Gabor function. But, we have shown that in order to design a parallel vision system, it is more pertinent to use the differences of Gaussian functions (DOG) which are real functions.