Quick Construction of Efficient Morphological Operators by Computational Learning

The author introduces a new technique to construct generic morphological operators quickly and automatically using input-output pairs of images as training samples. This process can be modeled as generalized PAC (Probably Approximately Correct) learning. He also introduces a new representation for morphological operators, much more efficient than the traditional one. Introduction: Mathematical Morphology is one of the techniques used in Image Processing. We must solve two problems to use Mathematical Morphology in practice. The first problem is the construction of the desired morphological operator, that is, the choice of the most adequate operator among a great number of candidates. Barrera et al. [1] represent the desired operator as input-output pairs of images. In that work, the user has to obtain some typical input images of the application with corresponding output images. These images feed a system that constructs automatically the desired morphological operator. But the algorithms described in [1] are too slow and they are for binary images only. In this letter, we present a new algorithm that constructs automatically generic operators (binary, gray-level and color). Moreover, in some practical tests, when used to construct binary operators, the new algorithm was 11000 times faster than the old ones, spending 3 times less memory (see table 1). Automatic construction of morphological operators can be modeled as a generalized PAC learning (see [2]). The second problem is the need of complex operators, frequently composed of hundreds of thousands of elementary operators, to process gray-scale and color images. Using conventional techniques, we spend a lot of computational time to apply such a complex operator. An elementary morphological operator, such as an erosion, spends some seconds to process an image with, for example, 512 × 480 pixels. To apply 100000 erosions to that image, we would spend at least 1 day. New algorithm can apply 100000 sup-generators (the infimum of an erosion and an antidilation and consequently more powerful than a simple erosion) in only 15 seconds.