Tree-based shape spaces : definition and applications in image processing and computer vision

Abstract : In a large number of applications, the processing relies on objects or area of interests, and the pixel-based image representation is notwell adapted. These applications would benefit from a region-based processing. Early examples of region-based processing can be found in the area of image segmentation, such as the quad tree. Recently, in mathematical morphology, the connected operators have received much attention. They are region-based filtering tools that act by merging flat zones. They have good contour preservation properties in the sense that they do not create any new boundaries, neither do they shift the existing ones. One popular implementation for connected operators relies on tree-based image representations, notably threshold decomposition representations and hierarchical representations. Those tree-based image representations are widely used in many image processing and computer vision applications. Tree-based connected operators consist in constructing a set of nested or disjoint connected components, followed by a filtering of these connected components based on an attribute function characterizing each connected component. Finally, the filtered image is reconstructed from the simplified tree composed of the remaining connected components. In the work presented in this thesis, we propose to expand the ideas of tree-based connected operators. We introduce the notion of tree-based shape spaces, built from tree-based image representations. Many state-of-the-art methods relying on tree-based image representations consist of analyzing this shape space. A first consequence of this change of point of view is our proposition of a local feature detector, called the tree-based Morse regions (TBMR). It can be seen as a variant of the MSER method. The selection of TBMRs is based on topological information, and hence it extracts the regions independently of the contrast, which makes it truly contrast invariant and quasi parameters free. The accuracy and robustness of the TBMR approach are demonstrated by the repeatability test and by applications to image registration and 3D reconstruction, as compared to some state-of-the-art methods. The basic idea of the main proposition in this thesis is to apply connected filters on the shape space. Such a processing is called the framework of shape-based morphology. It is a versatile framework that deals with region-based image representations. It has three main consequences. 1) For filtering purpose, it is a generalization of the existing tree-based connected operators. Indeed, the framework encompasses classical existing connected operators by attributes. Besides, It also allows us to propose two classes of novel connected operators: shape-based lower/upper levelings and shapings. 2) This framework can be used to object detection/segmentation by selecting relevant points in the shape space. 3) We can also use this framework to transform the hierarchies using the extinction values, so that a hierarchical simplification or segmentation is obtained. Some applications are developed using the framework of shape-based morphology to demonstrate its usefulness. The applications of the shape-based filtering to retinal image analysis show that a mere filtering step that we compare to more evolved processings, achieves state-of-the-art results. An efficient shaping used for image simplification is proposed by minimizing Mumford-Shah functional subordinated to the topographic map. For object detection/segmentation, we proposed a context-based energy estimator that is suitable to characterize object meaningfulness. Last, we extend the hierarchy of constrained connectivity using the aspect of hierarchy transformation of constrained connectivity using the aspect ofhierarchy transformation.
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Yongchao Xu. Tree-based shape spaces : definition and applications in image processing and computer vision. Other [cs.OH]. Université Paris-Est, 2013. English. ⟨NNT : 2013PEST1175⟩. ⟨tel-00965890v2⟩

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