Mathematical morphology and texture analysis

This talk presents our researches on the application of mathematical morphology, which is a mathematical framework of quatitative image manipulations, to the characterization and manipulation of textures. A texture is considered as a repetitive arrangement of homothetic magnifications of a small object called primitive. The shape and arrangement of the primitive are estimated by a method based on the morphological size distribution. A method of the filter optimization for textures using the estimated primitive is also presented. Morphological texture description Texture in the context of image processing is an image structure whose characteristics are given by the size, shape, and arrangement of its parts. Various methods of texture analysis, for example the cooccurrence matrix method and the spatial frequency method, have been proposed. These methods measure global or statistical characteristics of a texture based on its randomness. We have proposed a model of texture description, called “Primitive, Grain and Point Configuration (PGPC)” texture model and parameter estimation methods [1]. The PGPC texture model is based on the following observation of the texture suggested by Gestalt psychology: A repetitive appearance of similar objects of a moderate size is organized to be a meaningful structure by the human cognitive process. This observation suggests that a texture is neither completely deterministic nor completely random, but is often locally deterministic and globally random or regular, and that an appropriate texture description model has to be locally deterministic as well as globally deterministic or stochastic. Our model assumes that a texture is composed by arranging grains regularly or randomly on an image, and a grain is defined as a locally extended object actually appearing in a texture. The grains in the PGPC model are regarded to be derived from one primitive by some shape modifications, since the texture is regarded to be composed by the arrangement of similar small objects, as explained in the above observation. The primitive is a model parameter estimated from a texture, and its shape determines local deterministic characteristics of the texture. The grain arrangement determines global characteristics of the texture. The primitive and grain arrangement are estimated using an optimization process based on the morphological granulometry and skeletonization. We have also presented that the primitive estimation method is applicable to the optimization of image filtering based on morphological opening [2]. Opening is one of the most important image operations in the context of mathematical morphology. Opening presents the composition of an image by the repetitive arrangement of a structuring element, which is a small object used as a probe. The significance of opening is its quantitativeness in the sizes of image objects. For example, a quantitative noise removal in images is achieved by opening in the sense that noise objects smaller than the structuring element are removed exactly. Since the shape of structuring element appears directly in the result of opening, the opening using the structuring element resembling objects contained in the target image preserves the visual appearance of the whole image. Of course it is not generally possible to determine one typical object resembling various objects contained in an image. However, if the target image is restricted to a texture, we can derive a typical object representing the whole texture. It is this typical object that is presented as the estimated primitive in PGPC texture model here. Our current activity We recently established a research group on mathematical morphology, le Club des Morphologistes Mathématiques du Japon [3]. This group will organize a symposium on mathematical morphology in the next IEICE General Conference.