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The suitability of polar representation for quantitative image processing tasks is investigated. The classical colour polar-based representations (HLS, HSV, etc.) lead to brightness and saturation with nonconsistent properties. Af...
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The suitability of polar representation for quantitative image processing tasks is investigated. The classical colour polar-based representations (HLS, HSV, etc.) lead to brightness and saturation with nonconsistent properties. After a short critical analysis of the gamma correction, a new polar representation using the L_1 norm is proposed. It satisfies several quantitative requirements. The relevance of this representation is demonstrated by means of luminance/saturation histograms, which exhibit typical alignments. Their physical interpretation leads to a model for light reception in terms of linearly regionalized spectra. A full example illustrates the application of the histogram approach. Colour images are multivariable functions, and for segmenting them one must go through a reducing step. It is classically obtained by calculating a gradient module, which is then segmented as a grey tone image. An alternative solution is proposed. It is based on separated segmentations, followed by a final merging into a unique partition. The generalisation of the top-hat transformation for extracting colour details is also considered. These new marginal colour operators take advantage of an adaptive combination of the chromatic and the achromatic (or the spectral and the spatio-geometric) colour components.
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Les représentations polaires classiques de la couleur, du type (HSV, HLS, ...) conduisent à des brillances et des saturations aux propiétés incohérentes. Il leur est substitué des paramètres d'intensité (brillance et satur...
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Les représentations polaires classiques de la couleur, du type (HSV, HLS, ...) conduisent à des brillances et des saturations aux propiétés incohérentes. Il leur est substitué des paramètres d'intensité (brillance et saturation) qui sont des normes, dont L_1 et max-min. Deux exemples illustrent la pertinence d'une norme convenable. Le premier porte sur les histogrammes luminance/saturation. Construits dans le cadre des diverses normes introduites plus haut, ils mettent en évidence des alignements dans le cas de la norme L_1, alignements dont les points caractérisent des zones d'ombres ou de reflets dans l'image. Un modèle de comportement régionalisé linéairement des flux lumineux est proposé pour l'interprétation physique de ce phénomène. Le second exemple porte sur la segmentation d'images en couleur, à partir de représentations polaires. L'idée qui préside ici est de faire jouer à la saturation un rôle d'équilibrage entre luminance et teinte. Chacune des trois composantes luminance, saturation et teinte est traitée indépendamment des autres selon une technique classique de segmentation pour les fonctions numériques. Dans les classes de haute valeur de la saturation on retient alors la teinte comme paramètre significatif, et dans celles de basses saturation, la luminance. À nouveau, la norme L_1 présente des avantages par rapport aux autres représentations.
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We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (ⅰ...
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We study some basic morphological operators acting on the lattice of all subgraphs of an arbitrary (unweighted) graph G. To this end, we consider two dual adjunctions between the edge set and the vertex set of G. This allows us (ⅰ) to recover the classical notion of a dilation/erosion of a subset of the vertices of G and (ⅱ) to extend it to subgraphs of G. Afterward, we propose several new openings, closings, granulometries and alternate filters acting (ⅰ) on the subsets of the edge and vertex set of G and (ⅱ) on the subgraphs of G. The proposed framework is then extended to functions that weight the vertices and edges of a graph. We illustrate with applications to binary and grayscale image denoising, for which, on the provided images, the proposed approach outperforms the usual one based on structuring elements.
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DNA microarrays are an experimental technology which consists in arrays of thousands of discrete DNA sequences that are printed on glass microscope slides. Image analysis is an important aspect of microarray experiments. The aim o...
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DNA microarrays are an experimental technology which consists in arrays of thousands of discrete DNA sequences that are printed on glass microscope slides. Image analysis is an important aspect of microarray experiments. The aim of this step is to reduce an image of spots into a able with a measure of the intensity for each spot. Efficient, accurate and automatic analysis of DNA spot images is essential in order to use this technology in laboratory routines. We present an automatic non-supervised set of algorithms for a fast and accurate spot data extraction from DNA microarrays using morphological operators which are robust to both intensity variation and artefacts. The approach can be summarised as follows. Initially, a gridding algorithm yields the automatic segmentation of the microarray image into spot quadrants which are later individually analysed. Then the analysis of the spot quadrant images is achieved in five steps. First, a prequantification, the spot size distribution law is calculated. Second, the background noise extraction is performed using a morphological filtering by area. Third, an orthogonal grid provides the first approach to the spot locus. Fourth, the spot segmentation or spot boundaries definition is carried out using the watershed transformation. And fifth, the outline of detected spots allows the signal quantification or spot intensities extraction; in this respect, a noise model has been investigated. The performance of the algorithm has been compared with two packages: ScanAlyze and Genepix, showing its robustness and precision.
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This paper introduces a new fusion paradigm that reorders the contours of an input hierarchy of segmentations utilizing any external function. Ground truth partitions, markers, numerical functions, and other additional sources are...
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This paper introduces a new fusion paradigm that reorders the contours of an input hierarchy of segmentations utilizing any external function. Ground truth partitions, markers, numerical functions, and other additional sources are used to obtain a new reordered hierarchy. This transformation aids in combining sets, functions, and partitions in different ways, resulting in a hierarchy of partitions. This result is shown to be a lattice whose infimum operation is the Jordan net opening. Applications are demonstrated over hierarchies and ground truths from the Berkeley dataset. Experiments include hierarchy transformation by proximity to ground truth, fusion of two hierarchies, measuring structural changes produced by said transformations. We also demonstrate how intrinsic properties of the Jordan curves, like curvature, can be used to produce directional openings on contours of the partitions and reorder the hierarchy, in particular the L-opening over Quadtree partitions.
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The present study deals with the analysis of three-dimensional binary objects whose structure is not obvious nor generally clearly visible. Our approach is illustrated through three examples taken from biological microscopy. In on...
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The present study deals with the analysis of three-dimensional binary objects whose structure is not obvious nor generally clearly visible. Our approach is illustrated through three examples taken from biological microscopy. In one of our examples, we need to extract the osteocytes contained in sixty confocal sections. The cells are not numerous, but are characterized by long branches, hence they will be separated using a directional wavefront The two other objects are more complex and will be analysed by means of a spherical wavefront In the first case, a kidney of a rat embryo, the tissue grows like a tree, where we want to detect the branches, their extremities,and their spatial arrangement. The wavefront method enables us to define precisely branches and extremities, and gives flexible algorithms. The last example deals with the embryonic growth of the chicken shinbone. The central part of the bone (or shaft) is structured as a series of nested cylinders following the same axis, and connected by more or less long bridges. Using wavefronts, we show that it is possible to separate the cylinders,and to extract and count the bridges that connect them.
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Atherosclerotic and medial vascular calcifications are frequent in chronic renal failure patiens and predict their increased cardiovascular mortality. Experimental models for mice have been recently developed in order to study the...
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Atherosclerotic and medial vascular calcifications are frequent in chronic renal failure patiens and predict their increased cardiovascular mortality. Experimental models for mice have been recently developed in order to study these disorders. The aim of this paper is to present the morphological image processing algorithms developed for the semi-automated measurement of calcification from sections of aorta stained using von Kossa's silver nitrate procedure and acquired at low magnification power (x 2.5) on colour images. The approach is separated into two sequential phases. First, the segmentation is aimed to extract the calcification structures and on the other hand to demarcate the region of the atherosclerotic lesion within the tissue. The segmentation yields the image data which is the input to the second phase, the quantification. Calcified structures are measured inside and outside the lesion using a granulometric curve which allows the calculation of statistical parameters of size. The same operator computes the shape of the lesion. The relative proportion of the area of calcification is also calculated respectively for the atherosclerotic lesion area and the area outside such lesions. In conclusion, the here developed method allows quantification of vascular calcified deposits in mouse aorta. This method will be useful for the quantitative assessment of pathological vascular changes in animals and man.
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There are various ways to define digital convexity in Z~n. The proposed approach focuses on structuring elements (and not the sets under study), whose digital versions should allow to construct hierarchies of operators satisfying ...
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There are various ways to define digital convexity in Z~n. The proposed approach focuses on structuring elements (and not the sets under study), whose digital versions should allow to construct hierarchies of operators satisfying Matheron semi-groups law γ_λγ_μ = γ_(max(λ-μ)) where λ. is a size factor. In R~n the convenient class is the Steiner one. Its elements are Minkowski sums of segments. We prove that it admits a digital equivalent when the segments of Z~n are Bezout. The conditions under which the Steiner sets are convex in Z~n, and are connected, are established. The approach is then extended to structuring elements that vary according to the law of perspective, and also to anamorphoses, so that the digital Steiner class and its properties can extend to digital spaces as a sphere or a torus.
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This lecture comprises two parts. Firstly, after a formal definition of segmentation as the largest partition of the space according to a criterion a and a function /, the notion of a morphological connection is reminded. It is us...
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This lecture comprises two parts. Firstly, after a formal definition of segmentation as the largest partition of the space according to a criterion a and a function /, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 7), that identifies segmentation with some classes of connections. Just as connections, the segmentations can then be regrouped by suprema and infima. The generality of the theorem makes it valid for all functions from any space to any other one. Two propositions make precise the AND and OR combinations of connective criteria. The segmentation classes turn out to be independent of their location in the measuring held, assuming that a convenient neighbourhood is experimentally accessible. The second part studies the notion of a connected operator, in a more restricted framework than previously. It provides segmentations with more flexibility, and allows us to make them depend- on parameters. Hierarchies of connected filters are built, whose the partitions increase when going up in the pyramid, and where the various levels are structured as semi-groups.
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The use of mathematical morphology in the CIE L*a*b* colour space is discussed. It is possible to impose a total order on the colour vectors in this space by using a weighting function and lexicographical order. An order analogous...
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The use of mathematical morphology in the CIE L*a*b* colour space is discussed. It is possible to impose a total order on the colour vectors in this space by using a weighting function and lexicographical order. An order analogous to one by colour saturation is suggested by making use of a weighting function based on an electrostatic potential. This weighting function assigns a lower weight to colour vectors near the colours with maximum chroma, and higher weights to colour vectors near the lightness axis. The use of morphological operators with the colour vector order imposed by this function is demonstrated. Finally, a top-hat operator making use of the Euclidean colour distance in the L*a*b* space is introduced.
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