New Geometric Data Structures for Collision Detection

We present new geometric data structures for collision detection and more, including: Inner Sphere Trees - the first data structure to compute the peneration volume efficiently. Protosphere - an new algorithm to compute space filling sphere packings for arbitrary objects. Kinetic AABBs - a bounding volume hierarchy that is optimal in the number of updates when the objects deform. Kinetic Separation-List - an algorithm that is able to perform continuous collision detection for complex deformable objects in real-time. Moreover, we present applications of these new approaches to hand animation, real-time collision avoidance in dynamic environments for robots and haptic rendering, including a user study that exploits the influence of the degrees of freedom in complex haptic interactions. Last but not least, we present a new benchmarking suite for both, peformance and quality benchmarks, and a theoretic analysis of the running-time of bounding volume-based collision detection algorithms

Proceedings of the EAA Spatial Audio Signal Processing symposium: SASP 2019

International audienc

Doctor of Philosophy

dissertationThe statistical study of anatomy is one of the primary focuses of medical image analysis. It is well-established that the appropriate mathematical settings for such analyses are Riemannian manifolds and Lie group actions. Statistically defined atlases, in which a mean anatomical image is computed from a collection of static three-dimensional (3D) scans, have become commonplace. Within the past few decades, these efforts, which constitute the field of computational anatomy, have seen great success in enabling quantitative analysis. However, most of the analysis within computational anatomy has focused on collections of static images in population studies. The recent emergence of large-scale longitudinal imaging studies and four-dimensional (4D) imaging technology presents new opportunities for studying dynamic anatomical processes such as motion, growth, and degeneration. In order to make use of this new data, it is imperative that computational anatomy be extended with methods for the statistical analysis of longitudinal and dynamic medical imaging. In this dissertation, the deformable template framework is used for the development of 4D statistical shape analysis, with applications in motion analysis for individualized medicine and the study of growth and disease progression. A new method for estimating organ motion directly from raw imaging data is introduced and tested extensively. Polynomial regression, the staple of curve regression in Euclidean spaces, is extended to the setting of Riemannian manifolds. This polynomial regression framework enables rigorous statistical analysis of longitudinal imaging data. Finally, a new diffeomorphic model of irrotational shape change is presented. This new model presents striking practical advantages over standard diffeomorphic methods, while the study of this new space promises to illuminate aspects of the structure of the diffeomorphism group

Inverse problem theory in shape and action modeling

In this thesis we consider shape and action modeling problems under the perspective of inverse problem theory. Inverse problem theory proposes a mathematical framework for solving model parameter estimation problems. Inverse problems are typically ill-posed, which makes their solution challenging. Regularization theory and Bayesian statistical methods, which are proposed in the context of inverse problem theory, provide suitable methods for dealing with ill-posed problems. Regarding the application of inverse problem theory in shape and action modeling, we first discuss the problem of saliency prediction, considering a model proposed by the coherence theory of attention. According to coherence theory, salience regions emerge via proto-objects which we model using harmonic functions (thin-membranes). We also discuss the modeling of the 3D scene, as it is fundamental for extracting suitable scene features, which guide the generation of proto-objects. The next application we consider is the problem of image fusion. In this context, we propose a variational image fusion framework, based on confidence driven total variation regularization, and we consider its application to the problem of depth image fusion, which is an important step in the dense 3D scene reconstruction pipeline. The third problem we encounter regards action modeling, and in particular the recognition of human actions based on 3D data. Here, we employ a Bayesian nonparametric model to capture the idiosyncratic motions of the different body parts. Recognition is achieved by comparing the motion behaviors of the subject to a dictionary of behaviors for each action, learned by examples collected from other subjects. Next, we consider the 3D modeling of articulated objects from images taken from the web, with application to the 3D modeling of animals. By decomposing the full object in rigid components and by considering different aspects of these components, we model the object up this hierarchy, in order to obtain a 3D model of the entire object. Single view 3D modeling as well as model registration is performed, based on regularization methods. The last problem we consider, is the modeling of 3D specular (non-Lambertian) surfaces from a single image. To solve this challenging problem we propose a Bayesian non-parametric model for estimating the normal field of the surface from its appearance, by identifying the material of the surface. After computing an initial model of the surface, we apply regularization of its normal field considering also a photo-consistency constraint, in order to estimate the final shape of the surface. Finally, we conclude this thesis by summarizing the most significant results and by suggesting future directions regarding the application of inverse problem theory to challenging computer vision problems, as the ones encountered in this work