BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes

We present Basis Restricted Elastic Shape Analysis (BaRe-ESA), a novel Riemannian framework for human body scan representation, interpolation and extrapolation. BaRe-ESA operates directly on unregistered meshes, i.e., without the need to establish prior point to point correspondences or to assume a consistent mesh structure. Our method relies on a latent space representation, which is equipped with a Riemannian (non-Euclidean) metric associated to an invariant higher-order metric on the space of surfaces. Experimental results on the FAUST and DFAUST datasets show that BaRe-ESA brings significant improvements with respect to previous solutions in terms of shape registration, interpolation and extrapolation. The efficiency and strength of our model is further demonstrated in applications such as motion transfer and random generation of body shape and pose.Comment: 13 pages, 7 figures, 3 table

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

Computing weak distances between the 2-sphere and its nonsmooth approximations

A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute distances between them using the Fourier transform on the ambient space. In particular, the inhomogeneous Sobolev norms of negative order are approximated from data in the frequency space, which amounts to comparing measures after appropriate smoothing. Such Fourier-based distances allow several advantages including high accuracy due to fast-converging numerical quadrature rules, acceleration by the nonuniform fast Fourier transform, parallelization on massively parallel architectures. In numerical experiments, the 2-sphere, which is an example whose Fourier transform is explicitly known, is compared with its icosahedral discretization, and it is observed that the piecewise linear approximations converge to the smooth object at the quadratic rate up to small truncations.Comment: 14 pages, 4 figure

Topology-Aware Surface Reconstruction for Point Clouds

We present an approach to inform the reconstruction of a surface from a point scan through topological priors. The reconstruction is based on basis functions which are optimized to provide a good fit to the point scan while satisfying predefined topological constraints. We optimize the parameters of a model to obtain likelihood function over the reconstruction domain. The topological constraints are captured by persistence diagrams which are incorporated in the optimization algorithm promote the correct topology. The result is a novel topology-aware technique which can: 1.) weed out topological noise from point scans, and 2.) capture certain nuanced properties of the underlying shape which could otherwise be lost while performing surface reconstruction. We showcase results reconstructing shapes with multiple potential topologies, compare to other classical surface construction techniques, and show the completion of real scan data

Surface Remeshing and Applications

Due to the focus of popular graphic accelerators, triangle meshes remain the primary representation for 3D surfaces. They are the simplest form of interpolation between surface samples, which may have been acquired with a laser scanner, computed from a 3D scalar field resolved on a regular grid, or identified on slices of medical data. Typical methods for the generation of triangle meshes from raw data attempt to lose as less information as possible, so that the resulting surface models can be used in the widest range of scenarios. When such a general-purpose model has to be used in a particular application context, however, a pre-processing is often worth to be considered. In some cases, it is convenient to slightly modify the geometry and/or the connectivity of the mesh, so that further processing can take place more easily. Other applications may require the mesh to have a pre-defined structure, which is often different from the one of the original general-purpose mesh. The central focus of this thesis is the automatic remeshing of highly detailed surface triangulations. Besides a thorough discussion of state-of-the-art applications such as real-time rendering and simulation, new approaches are proposed which use remeshing for topological analysis, flexible mesh generation and 3D compression. Furthermore, innovative methods are introduced to post-process polygonal models in order to recover information which was lost, or hidden, by a prior remeshing process. Besides the technical contributions, this thesis aims at showing that surface remeshing is much more useful than it may seem at a first sight, as it represents a nearly fundamental step for making several applications feasible in practice