Approches multivaluées et supervisées en morphologie mathématique et applications en analyse d'image

Abstract : This dissertation contains a summary of research activities in mathematical morphology done in LSIIT (UMR 7005 CNRS–UDS) since 2003. Mathematical morphology is a theory introduced more than 40 years ago by two french researchers, Georges Matheron and Jean Serra. Since then, it has been widely used in the fields of image analysis and processing, due to its ability to analyse spatial structures (most often by means of a neighbourhood called structuring element) in a non-linear framework. Its application to binary and greylevel images is straightforward, relying on the set theory or preferably the lattice theory. However, its extension to multivalued images (where each pixel is represented by a vector instead of a scalar) is not trivial and is still an open problem. Thus, we focused on vectorial morphological approaches based on (theoretically sound) total orderings, and we have try to alleviate their high asymetric behavior with various quantification methods in order to rely on the whole set of available data. We have also studied another strategy which avoids the explicit need of a vectorial ordering by decomposing the image into a set of binary or greyscale components, which are then processed independently or jointly. Regardless of image type, building a morphological image analysis system requires most often some domain expertise and very precise knowledge about the problem under consideration in order to select, combine, and set up adequately the morphological operators to be involved. Thus, morphological methods cannot usually be reused in a different context from the one for which they have been designed, and do not ensure the genericity property expected in image analysis. This problem is of course not limited at all to mathematical morphology (it is frequently encountered in image processing), and we have addressed it following two principal directions. On the one side, we have studied how knowledge could be formalised within structuring elements in the context of object detection. On the other side, we have relied on techniques from supervised classication (where learning sets are provided by the expert) or unsupervised classification or clustering (where only the number of objects or classes of interest is known) wihtin the process of image segmentation. The overall objective is to obtain multivalued and supervised morphological approaches, able to process every kind of data, in any context. So we have applied these works in several fields, in particular colour image analysis (with the aim of content-based image annotation and retrieval), remote sensing (at very high spatial resolution), and astronomical imaging (where data can be very noisy). These application fields, where images are multivalued and knowledge integration to drive image processing techniques is necessary, are relevant since spatial information is crucial (thus mathematical morphology is worth being used). Recurring problems we were dealing with in these fields are object detection, image segmentation and description. Complementary to these mathematical morphology-related works, we also present the PELICAN project, which is a generic and extensible framework for image processing. This dissertation ends with indicating a few research directions for future works in the context of several collaborative projects. Ensuring invariance and uncertainty within mathematical morphology would help solving biomedical imaging-related problems. Using mathematical morphology for video sequence analysis and design of local image descriptors would offer some alternative solutions for multimedia indexing. Finally, since mathematical morphology is by no way limited to image data, its application to other types of data should be carefully studied.
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Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00515901
Contributor : Sébastien Lefèvre <>
Submitted on : Wednesday, September 8, 2010 - 11:22:34 AM
Last modification on : Thursday, January 11, 2018 - 6:22:39 AM
Long-term archiving on : Tuesday, October 23, 2012 - 3:45:11 PM

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Sébastien Lefèvre. Approches multivaluées et supervisées en morphologie mathématique et applications en analyse d'image. Interface homme-machine [cs.HC]. Université de Strasbourg, 2009. ⟨tel-00515901⟩

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