Catálogo de publicaciones - libros

Random closed sets (RACS) in the —dimensional Euclidean space are considered, whose realizations belong to the extended convex ring. A family of nonparametric estimators is investigated for the simultaneous estimation of the vector of all specific Minkowski functionals (or, equivalently, the specific intrinsic volumes) of stationary RACS. The construction of these estimators is based on a representation formula for the expected local connectivity number of stationary RACS intersected with spheres, whose radii are small in comparison with the size of the whole sampling window. Asymptotic properties of the estimators are given for unboundedly increasing sampling windows. Numerical results are provided as well.

A novel method of texture characterization, called of grain occurrences, is proposed. This idea is based on a model of texture description, called “Primitive, Grain and Point Configuration (PGPC)” texture model. This model assumes that a texture is composed by arranging , which are locally extended objects appearing actually in a texture. The grains in the PGPC model are regarded to be derived from one by the homothetic magnification, and the size of grain is defined as the degree of magnification. The intersize correlation is the correlation between the occurrences of grains of different sizes located closely to each other. This is introduced since homothetic grains of different sizes often appear repetitively and the appearance of smaller grains depends on that of larger grains. Estimation methods of the primitive and grain arrangement of a texture are presented. A method of estimating the intersize correlation and its application to texture regeneration are presented with experimental results. The regenerated texture has the same intersize correlation as the original while the global arrangement of large-size grains are completely different. Although the appearance of the resultant texture is globally different from the original, the semi-local appearance in the neighborhood of each largesize grain is preserved.

Texture segmentation based on local morphological pattern spectra provides an attractive alternative to linear scale spaces as the latter suffer from blurring and do not preserve the shape of image features. However, for successful segmentation, pattern spectra derived using a number of structuring elements, often at different orientations, are required. This paper addresses this problem by using area morphology to generate a single pattern spectrum, consisting of a local granulometry and anti-granulometry, at each pixel position. As only one spectrum is produced, segmentation is performed by directly using the spectrum as the feature vector instead of taking pattern spectrum moments. Segmentation results for a simulated image of Brodatz textures and test images from the Outex texture database show the potential of the new approach.

We investigate the use of the standard morphological texture characterisation methods, the granulometry and the variogram, in the task of texture classification. These methods are applied to both colour and greyscale texture images. We also introduce a method for minimising the effect of different illumination conditions and show that its use leads to improved classification. The classification experiments are performed on the publically available Outex 14 texture database. We show that using the illumination invariant variogram features leads to a significant improvement in classification performance compared to the best results reported for this database.

The extension of lattice based operators to color images is still a challenging task in mathematical morphology. The first choice of a well-defined color space is crucial and we propose to work on a lum/sat/hue representation in norm . We then introduce an unified framework to consider different ways of defining morphological color operators either using the classical formulation with total orderings by means of lexicographic cascades or developing new transformations which takes advantage of an adaptive combination of the chromatic and the achromatic (or the spectral and the spatio-geometric) components. More precisely, we prove that the presented saturation-controlled operators cope satisfactorily with the complexity of color images. Experimental results illustrate the performance and the potential applications of the new algorithms.

Motivated by the unsuitability of the image extrema paradigm for processing multiphase or multichannel images, we propose a solution in the context of image simplification based on a combination of the flat zone and seeded region growing paradigms. Concepts and results are illustrated on satellite images.

The operators of greyscale morphology rely on the notions of maximum and minimum which regrettably are not directly available for tensor-valued data since the straightforward component-wise approach fails.

This paper aims at the extension of the maximum and minimum operations to the tensor-valued setting by employing the Loewner ordering for symmetric matrices. This prepares the ground for matrix-valued analogs of the basic morphological operations. The novel definitions of maximal/minimal matrices are rotationally invariant and preserve positive semidefiniteness of matrix fields as they are encountered in DT-MRI data. Furthermore, they depend continuously on the input data which makes them viable for the design of morphological derivatives such as the Beucher gradient or a morphological Laplacian. Experiments on DT-MRI images illustrate the properties and performance of our morphological operators.

Magnetic resonance angiography (MRA) provides 3-dimensional data of vascular structures by finding the flowing blood signal. Classically, algorithms dedicated to vessel segmentation detect the cerebral vascular tree by only seeking the high intensity blood signal in MRA. We propose here to use both cerebral MRA and MRI and to integrate a priori anatomical knowledge to guide the segmentation process. The algorithm presented here uses mathematical morphology tools (watershed segmentation and grey-level operators) to carry out a simultaneous segmentation of both blood signal in MRA and blood and wall signal in MRI. It is dedicated to the superior sagittal sinus segmentation but similar strategies could be considered for segmentation of other vascular structures. The method has been performed on 6 cases composed of both MRA and MRI. The results have been validated and compared to other results obtained with a region growing algorithm. They tend to prove that this method is reliable even when the vascular signal is inhomogeneous or contains artefacts.

In this paper we propose an original method of segmentation of the portal network in the liver. For this, we combine two applications of the grey scale hit-or- miss transform. The automatic segmentation is performed in two steps. In the first step, we detect the shape of the entrance of the portal vein in the liver by application of a grey scale hit-or-miss transform. This gives the seed or starting point of the region-growing algorithm. In a second step, we apply a region- growing algorithm by using a criterion still based on a hit-or-miss. Our method performs better than a previous method based on region-growing algorithm with a single threshold criterion.

In this study, a segmentation method is presented for the images of microscopic peripheral blood which mainly contain red blood cells, some of which contain parasites, and some white blood cells. The method uses several operators based on mathematical morphology. The cell area information which is estimated using the area granulometry (area pattern spectrum) is used for several steps in the method. A modified version of the original watershed algorithm [31] called minimum area watershed transform is developed and employed as an initial segmentation operator. The circle Radon transform is applied to the labelled regions to locate the cell centers (markers). The final result is produced by applying the original marker controlled watershed transform to the Radon transform output with its markers obtained from the regional maxima. The proposed method can be applied to similar blob object segmentation problems by adapting red blood cell characteristics for the new blob objects. The method has been tested on a benchmark set and scored a successful correct segmentation rate of 95.40%.