Efficient Distance Transformation for Path-based Metrics

In many applications, separable algorithms have demonstrated their efficiency to perform high performance volumetric processing of shape, such as distance transformation or medial axis extraction. In the literature, several authors have discussed about conditions on the metric to be considered in a separable approach. In this article, we present generic separable algorithms to efficiently compute Voronoi maps and distance transformations for a large class of metrics. Focusing on path-based norms (chamfer masks, neighborhood sequences...), we propose efficient algorithms to compute such volumetric transformation in dimension $n$. We describe a new $O(n\cdot N^n\cdot\log{N}\cdot(n+\log f))$ algorithm for shapes in a $N^n$ domain for chamfer norms with a rational ball of $f$ facets (compared to $O(f^{\lfloor\frac{n}{2}\rfloor}\cdot N^n)$ with previous approaches). Last we further investigate an even more elaborate algorithm with the same worst-case complexity, but reaching a complexity of $O(n\cdot N^n\cdot\log{f}\cdot(n+\log f))$ experimentally, under assumption of regularity distribution of the mask vectors

Features extraction based on the Discrete Hartley Transform for closed contour

In this paper the authors propose a new closed contour descriptor that could be seen as a Feature Extractor of closed contours based on the Discrete Hartley Transform (DHT), its main characteristic is that uses only half of the coefficients required by Elliptical Fourier Descriptors (EFD) to obtain a contour approximation with similar error measure. The proposed closed contour descriptor provides an excellent capability of information compression useful for a great number of AI applications. Moreover it can provide scale, position and rotation invariance, and last but not least it has the advantage that both the parameterization and the reconstructed shape from the compressed set can be computed very efficiently by the fast Discrete Hartley Transform (DHT) algorithm. This Feature Extractor could be useful when the application claims for reversible features and when the user needs and easy measure of the quality for a given level of compression, scalable from low to very high quality

Quantification of the plant endoplasmic reticulum

One of the challenges of quantitative approaches to biological sciences is the lack of understanding of the interplay between form and function. Each cell is full of complex-shaped objects, which moreover change their form over time. To address this issue, we exploit recent advances in confocal microscopy, by using data collected from a series of optical sections taken at short regular intervals along the optical axis to reconstruct the Endoplasmic Reticulum (ER) in 3D, obtain its skeleton, then associate to each of its edges key geometric and dynamic characteristics obtained from the original filled in ER specimen. These properties include the total length, surface area, and volume of the ER specimen, as well as the length surface area, and volume of each of its branches. In a view to benefit from the well established graph theory algorithms, we abstract the obtained skeleton by a mathematical entity that is a graph. We achieve this by replacing the inner points in each edge in the skeleton by the line segment connecting its end points. We then attach to this graph the ER geometric properties as weights, allowing therefore a more precise quantitative characterisation, by thinning the filled in ER to its essential features. The graph plays a major role in this study and is the final and most abstract quantification of the ER. One of its advantages is that it serves as a geometric invariant, both in static and dynamic samples. Moreover, graph theoretic features, such as the number of vertices and their degrees, and the number of edges and their lengths are robust against different kinds of small perturbations. We propose a methodology to associate parameters such as surface areas and volumes to its individual edges and monitor their variations with time. One of the main contributions of this thesis is the use of the skeleton of the ER to analyse the trajectories of moving junctions using confocal digital videos. We report that the ER could be modeled by a network of connected cylinders (0.87μm±0.36 in diameter) with a majority of 3-way junctions. The average length, surface area and volume of an ER branch are found to be 2.78±2.04μm, 7.53±5.59μm2 and 1.81±1.86μm3 respectively. Using the analysis of variance technique we found that there are no significant differences in four different locations across the cell at 0.05 significance level. The apparent movement of the junctions in the plant ER consists of different types, namely: (a) the extension and shrinkage of tubules, and (b) the closing and opening of loops. The average velocity of a junction is found to be 0.25μm/sec±0.23 and lies in the range 0 to 1.7μm/sec which matches the reported actin filament range

Multi-scale active shape description in medical imaging

Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed

Décomposition volumique d'images pour l'étude de la microstructure de la neige

Les avalanches de neige sont des phénomènes naturels complexes dont l'occurrence s'explique principalement par la structure et les propriétés du manteau neigeux. Afin de mieux comprendre les évolutions de ces propriétés au cours du temps, il est important de pouvoir caractériser la microstructure de la neige, notamment en termes de grains et de ponts de glace les reliant. Dans ce contexte, l'objectif de cette thèse est la décomposition d'échantillons de neige en grains individuels à partir d'images 3-D de neige obtenues par microtomographie X. Nous présentons ici deux méthodes de décomposition utilisant des algorithmes de géométrie discrète. Sur la base des résultats de ces segmentations, certains paramètres, comme la surface spécifique et la surface spécifique de contact entre grains sont ensuite estimés sur des échantillons de neiges variées. Ces méthodes de segmentation ouvrent de nouvelles perspectives pour la caractérisation de la microstructure de la neige, de ses propriétés, ainsi que de leur évolution au cours du temps.Snow avalanches are complex natural phenomena whose occurrence is mainly due to the structure and properties of the snowpack. To better understand the evolution of these properties over time, it is important to characterize the microstructure of snow, especially in terms of grains and ice necks that connect them. In this context, the objective of this thesis is the decomposition of snow samples into individual grains from 3-D images of snow obtained by X-ray microtomography. We present two decomposition methods using algorithms of discrete geometry. Based on the results of these segmentations, some parameters such as the specific surface area and the specific contact area between grains are then estimated from samples of several snow types. These segmentation methods offer new outlooks for the characterization of the microstructure of snow, its properties, and its time evolution