The aim of image analysis is to extract features from it or to recognize shapes within it. Image analysis includes multiple and diversified application areas such as: biomedical imaging, satelite imaging, material analyzing, automatic control, robot vision... This topic has been developped a lot those past few years, from an application point of vue as well as the methods which are used.
Our approach towards image analysis is typically digital and is based on discrete structures. More precisly, we are involved in the study of the application of discrete topology to the design of algorithms to perform image processing and image analysis. The fundamental notions of topology like neighbors and continuity are a very pertinent and relevant paradigm for the processing of spatial data.
A part of our work concerns the study of transformations which preserve the topology of the image. In this context, we introduced a new characterization of simple points. An object point is simple if its removal does not change the topology of the object. We proposed several skeletonization algorithms based on this definition. We also proposed an algorithm which removes the simple points in parallel.
Another part of our work is the study of the transformations which may change selectively the topology of an object or an image. An example of such transformation is the "Hole Closing" of a 3D object (in the sense that a plain torus has one hole). We introduced such a transformation which performs a so called "topological filtering" of an object.
We also worked on the application of topological notions to digital images processing (grey level images). The principle of our approach is to define the topological equivalence between two digital images from the topological equivalence between the binary images produced by the slices (or thresholds) of the digital image at different levels. We proposed several original algorithms as well as a segmentation method without any parameters.
We have experimented these methods in the fields of microscopic imaging of materials and cells, as well as medical imaging 2D and 3D.