Generating Second Order (Co)homological Information within AT-Model Context

In this paper we design a new family of relations between (co)homology classes, working with coefficients in a field and starting from an AT-model (Algebraic Topological Model) AT(C) of a finite cell complex C These relations are induced by elementary relations of type “to be in the (co)boundary of” between cells. This high-order connectivity information is embedded into a graph-based representation model, called Second Order AT-Region-Incidence Graph (or AT-RIG) of C. This graph, having as nodes the different homology classes of C, is in turn, computed from two generalized abstract cell complexes, called primal and dual AT-segmentations of C. The respective cells of these two complexes are connected regions (set of cells) of the original cell complex C, which are specified by the integral operator of AT(C). In this work in progress, we successfully use this model (a) in experiments for discriminating topologically different 3D digital objects, having the same Euler characteristic and (b) in designing a parallel algorithm for computing potentially significant (co)homological information of 3D digital objects.Ministerio de Economía y Competitividad MTM2016-81030-PMinisterio de Economía y Competitividad TEC2012-37868-C04-0

Automatic skeletonization and skin attachment for realistic character animation.

The realism of character animation is associated with a number of tasks ranging from modelling, skin defonnation, motion generation to rendering. In this research we are concerned with two of them: skeletonization and weight assignment for skin deformation. The fonner is to generate a skeleton, which is placed within the character model and links the motion data to the skin shape of the character. The latter assists the modelling of realistic skin shape when a character is in motion. In the current animation production practice, the task of skeletonization is primarily undertaken by hand, i.e. the animator produces an appropriate skeleton and binds it with the skin model of a character. This is inevitably very time-consuming and costs a lot of labour. In order to improve this issue, in this thesis we present an automatic skeletonization framework. It aims at producing high-quality animatible skeletons without heavy human involvement while allowing the animator to maintain the overall control of the process. In the literature, the tenn skeletonization can have different meanings. Most existing research on skeletonization is in the remit of CAD (Computer Aided Design). Although existing research is of significant reference value to animation, their downside is the skeleton generated is either not appropriate for the particular needs of animation, or the methods are computationally expensive. Although some purpose-build animation skeleton generation techniques exist, unfortunately they rely on complicated post-processing procedures, such as thinning and pruning, which again can be undesirable. The proposed skeletonization framework makes use of a new geometric entity known as the 3D silhouette that is an ordinary silhouette with its depth information recorded. We extract a curve skeleton from two 3D silhouettes of a character detected from its two perpendicular projections. The skeletal joints are identified by down sampling the curve skeleton, leading to the generation of the final animation skeleton. The efficiency and quality are major performance indicators in animation skeleton generation. Our framework achieves the former by providing a 2D solution to the 3D skeletonization problem. Reducing in dimensions brings much faster performances. Experiments and comparisons are carried out to demonstrate the computational simplicity. Its accuracy is also verified via these experiments and comparisons. To link a skeleton to the skin, accordingly we present a skin attachment framework aiming at automatic and reasonable weight distribution. It differs from the conventional algorithms in taking topological information into account during weight computation. An effective range is defined for a joint. Skin vertices located outside the effective range will not be affected by this joint. By this means, we provide a solution to remove the influence of a topologically distant, hence highly likely irrelevant joint on a vertex. A user-defined parameter is also provided in this algorithm, which allows different deformation effects to be obtained according to user's needs. Experiments and comparisons prove that the presented framework results in weight distribution of good quality. Thus it frees animators from tedious manual weight editing. Furthermore, it is flexible to be used with various deformation algorithms

Occlusion Reasoning for Skeleton Extraction of Self-Occluded Tree Canopies

In this work, we present a method to extract the skeleton of a self-occluded tree canopy by estimating the unobserved structures of the tree. A tree skeleton compactly describes the topological structure and contains useful information such as branch geometry, positions and hierarchy. This can be critical to planning contact interactions for agricultural manipulation, yet is difficult to gain due to occlusion by leaves, fruits and other branches. Our method uses an instance segmentation network to detect visible trunk, branches, and twigs. Then, based on the observed tree structures, we build a custom 3D likelihood map in the form of an occupancy grid to hypothesize on the presence of occluded skeletons through a series of minimum cost path searches. We show that our method outperforms baseline methods in highly occluded scenes, demonstrated through a set of experiments on a synthetic tree dataset. Qualitative results are also presented on a real tree dataset collected from the field.Comment: 7 pages, 10 figures, submitted to ICRA 202

A Homologically Persistent Skeleton is a fast and robust descriptor of interest points in 2D images

2D images often contain irregular salient features and interest points with non-integer coordinates. Our skeletonization problem for such a noisy sparse cloud is to summarize the topology of a given 2D cloud across all scales in the form of a graph, which can be used for combining local features into a more powerful object-wide descriptor. We extend a classical Minimum Spanning Tree of a cloud to a Homologically Persistent Skeleton, which is scale-and-rotation invariant and depends only on the cloud without extra parameters. This graph (1) is computable in time O(nlogn) for any n points in the plane; (2) has the minimum total length among all graphs that span a 2D cloud at any scale and also have most persistent 1-dimensional cycles; (3) is geometrically stable for noisy samples around planar graphs

Vascular Complexity Evaluation Using a Skeletonization Approach and 3D LED-Based Photoacoustic Images

Vasculature analysis is a fundamental aspect in the diagnosis, treatment, outcome evaluation and follow-up of several diseases. The quantitative characterization of the vascular network can be a powerful means for earlier pathologies revealing and for their monitoring. For this reason, non-invasive and quantitative methods for the evaluation of blood vessels complexity is a very important issue. Many imaging techniques can be used for visualizing blood vessels, but many modalities are limited by high costs, the need of exogenous contrast agents, the use of ionizing radiation, a very limited acquisition depth, and/or long acquisition times. Photoacoustic imaging has recently been the focus of much research and is now emerging in clinical applications. This imaging modality combines the qualities of good contrast and the spectral specificity of optical imaging and the high penetration depth and the spatial resolution of acoustic imaging. The optical absorption properties of blood also make it an endogenous contrast agent, allowing a completely non-invasive visualization of blood vessels. Moreover, more recent LED-based photoacoustic imaging systems are more affordable, safe and portable when compared to a laser-based systems. In this chapter we will confront the issue of vessel extraction techniques and how quantitative vascular parameters can be computed on 3D LED-based photoacoustic images using an in vitro vessel phantom model