Résumé
This paper describes morphological tools that have been adapted to omnidirectional catadioptric images. The field of mathematical morphology contributes a wide range of operators to image processing, all based on a few simple mathematical concepts derived from set theory [1]. Two baseline operations in mathematical morphology are erosion and dilation — names illustrating their properties when applied to binary images. Morphological operations involve comparing the image with a kernel (also known as structuring element) so as to transform the image through expanding, contracting, analyzing , filtering, etc. Opening (dilation of an eroded image) and closing (erosion of a dilated image) are done to filter features smaller than the structuring element. When comparing a dilation to an erosion of an image, the resulting image shows the boundaries of the projected objects — this operation is called morphological gradient. Classical mathematical morphology has been based on Boolean set theory and therefore requires binary images and binary kernels. Different extensions have been proposed to provide a coherent set of operations able to process grey-level images and functional kernels. In [2], Isabelle Bloch proposed to divide these different extensions into three families: • grey-level mathematical morphology with binary struc-turing elements and functional images, • functional mathematical morphology with functional structuring elements and binary images, • the fuzzy mathematical morphology where both images and structuring elements are assumed to be functional. Fuzzy set theory generalization fits our intuitive knowledge concerning diffuse localization of projected objects in an image due to noise, discretization, digitalization and instris-tic modelling imprecision. Fuzzy sets can represent both im-precision and uncertainty from the signal level to the highest decision level. The ability of morphological tools to provide transformations that are suitable for real projective images is related to the potential for positioning the camera and the objects to be analyzed in such a manner that a regular mesh on the objects projects regular mesh on the image. Therefore, a morphological modification of the image is the projection of an equivalent morphological operation on the object. Otherwise, due to perspective effects, a morphological operation in the image is not the projection of an equivalent morphological operation on the objects to be analyzed. Figure 1 illustrates this inadequacy: an erosion does not uniformly alter the lines of a grid pattern.