Unsupervised morphological segmentation for images

This paper deals with a morphological approach to unsupervised image segmentation. The proposed technique relies on a multiscale Top-Down approach allowing a hierarchical processing of the data ranging from the most global scale to the most detailed one. At each scale, the algorithm consists of four steps: image simplification, feature extraction, contour localization and quality estimation. The main emphasis of this paper is to discuss the selection of a simplification filter for segmentation. Morphological filters based on reconstruction proved to be very efficient for this purpose. The resulting unsupervised algorithm is very robust and can deal with very different type of images.Peer ReviewedPostprint (published version

Generalized connected operators

This paper deals with the notion of connected operators These operators are becoming popular in image processing because they have the fundamental property of simplifying the signal while preserving the contour information In a rst step we recall the basic notions involved in binary and gray level connected operators. Then we show how one can extend and generalize these operators We focus on two important issues the connectivity and the simplication criterion We will show in particular how to create connectivities that are either more or less strict than the usual ones and how to build new criteriaPeer ReviewedPostprint (published version

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version

Digital Morphometry : A Taxonomy Of Morphological Filters And Feature Parameters With Application To Alzheimer\u27s Disease Research

In this thesis the expression digital morphometry collectively describes all those procedures used to obtain quantitative measurements of objects within a two-dimensional digital image. Quantitative measurement is a two-step process: the application of geometrical transformations to extract the features of interest, and then the actual measurement of these features. With regard to the first step the morphological filters of mathematical morphology provide a wealth of suitable geometric transfomations. Traditional radiometric and spatial enhancement techniques provide an additional source of transformations. The second step is more classical (e.g. Underwood, 1970; Bookstein, 1978; and Weibull, 1980); yet here again mathematical morphology is applicable - morphologically derived feature parameters. This thesis focuses on mathematical morphology for digital morphometry. In particular it proffers a taxonomy of morphological filters and investigates the morphologically derived feature parameters (Minkowski functionals) for digital images sampled on a square grid. As originally conceived by Georges Matheron, mathematical morphology concerns the analysis of binary images by means of probing with structuring elements [typically convex geometric shapes] (Dougherty, 1993, preface). Since its inception the theory has been extended to grey-level images and most recently to complete lattices. It is within the very general framework of the complete lattice that the taxonomy of morphological filters is presented. Examples are provided to help illustrate the behaviour of each type of filter. This thesis also introduces DIMPAL (Mehnert, 1994) - a PC-based image processing and analysis language suitable for researching and developing algorithms for a wide range of image processing applications. Though DIMPAL was used to produce the majority of the images in this thesis it was principally written to provide an environment in which to investigate the application of mathematical morphology to Alzheimer\u27s disease research. Alzheimer\u27s disease is a form of progressive dementia associated with the degeneration of the brain. It is the commonest type of dementia and probably accounts for half the dementia of old age (Forsythe, 1990, p. 21 ). Post mortem examination of the brain reveals the presence of characteristic neuropathologic lesions; namely neuritic plaques and neurofibrillary tangles. They occur predominantly in the cerebral cortex and hippocampus. Quantitative studies of the distribution of plaques and tangles in normally aged and Alzheimer brains are hampered by the enormous amount of time and effort required to count and measure these lesions. Here in a morphological algorithm is proposed for the automatic segmentation and measurement of neuritic plaques from light micrographs of post mortem brain tissue

N-ary Mathematical Morphology

International audienceMathematical morphology on binary images can be fully de-scribed by set theory. However, it is not sucient to formulate mathe-matical morphology for grey scale images. This type of images requires the introduction of the notion of partial order of grey levels, together with the denition of sup and inf operators. More generally, mathemati-cal morphology is now described within the context of the lattice theory. For a few decades, attempts are made to use mathematical morphology on multivariate images, such as color images, mainly based on the no-tion of vector order. However, none of these attempts has given fully satisfying results. Instead of aiming directly at the multivariate case we propose an extension of mathematical morphology to an intermediary situation: images composed of a nite number of independent unordered categories

Morphological Three-Dimensional Analysis

This paper presents the main results of our research on mathematical morphology for three-dimensional images. The first issue is to decide which grid must be used. The face-centred cubic grid and the centred cubic grid seem to be more suitable than the cubic grid in terms of possible rotations. For these two grids we derive the formulae for the basic Minkovski measures. Then we show through several examples that extension from 2D to 3D is straightforward for most transformations. The efficiency of direct 3D processing is illustrated by applications to filtering, overlapping particle separation and grey-scale image segmentation