Geometric Approaches for 3D Shape Denoising and Retrieval

A key issue in developing an accurate 3D shape recognition system is to design an efficient shape descriptor for which an index can be built, and similarity queries can be answered efficiently. While the overwhelming majority of prior work on 3D shape analysis has concentrated primarily on rigid shape retrieval, many real objects such as articulated motions of humans are nonrigid and hence can exhibit a variety of poses and deformations. Motivated by the recent surge of interest in content-based analysis of 3D objects in computeraided design and multimedia computing, we develop in this thesis a unified theoretical and computational framework for 3D shape denoising and retrieval by incorporating insights gained from algebraic graph theory and spectral geometry. We first present a regularized kernel diffusion for 3D shape denoising by solving partial differential equations in the weighted graph-theoretic framework. Then, we introduce a computationally fast approach for surface denoising using the vertexcentered finite volume method coupled with the mesh covariance fractional anisotropy. Additionally, we propose a spectral-geometric shape skeleton for 3D object recognition based on the second eigenfunction of the Laplace-Beltrami operator in a bid to capture the global and local geometry of 3D shapes. To further enhance the 3D shape retrieval accuracy, we introduce a graph matching approach by assigning geometric features to each endpoint of the shape skeleton. Extensive experiments are carried out on two 3D shape benchmarks to assess the performance of the proposed shape retrieval framework in comparison with state-of-the-art methods. The experimental results show that the proposed shape descriptor delivers best-in-class shape retrieval performance

Extracting curve-skeletons from digital shapes using occluding contours

Curve-skeletons are compact and semantically relevant shape descriptors, able to summarize both topology and pose of a wide range of digital objects. Most of the state-of-the-art algorithms for their computation rely on the type of geometric primitives used and sampling frequency. In this paper we introduce a formally sound and intuitive definition of curve-skeleton, then we propose a novel method for skeleton extraction that rely on the visual appearance of the shapes. To achieve this result we inspect the properties of occluding contours, showing how information about the symmetry axes of a 3D shape can be inferred by a small set of its planar projections. The proposed method is fast, insensitive to noise, capable of working with different shape representations, resolution insensitive and easy to implement

MonoPerfCap: Human Performance Capture from Monocular Video

We present the first marker-less approach for temporally coherent 3D performance capture of a human with general clothing from monocular video. Our approach reconstructs articulated human skeleton motion as well as medium-scale non-rigid surface deformations in general scenes. Human performance capture is a challenging problem due to the large range of articulation, potentially fast motion, and considerable non-rigid deformations, even from multi-view data. Reconstruction from monocular video alone is drastically more challenging, since strong occlusions and the inherent depth ambiguity lead to a highly ill-posed reconstruction problem. We tackle these challenges by a novel approach that employs sparse 2D and 3D human pose detections from a convolutional neural network using a batch-based pose estimation strategy. Joint recovery of per-batch motion allows to resolve the ambiguities of the monocular reconstruction problem based on a low dimensional trajectory subspace. In addition, we propose refinement of the surface geometry based on fully automatically extracted silhouettes to enable medium-scale non-rigid alignment. We demonstrate state-of-the-art performance capture results that enable exciting applications such as video editing and free viewpoint video, previously infeasible from monocular video. Our qualitative and quantitative evaluation demonstrates that our approach significantly outperforms previous monocular methods in terms of accuracy, robustness and scene complexity that can be handled.Comment: Accepted to ACM TOG 2018, to be presented on SIGGRAPH 201

Correcting curvature-density effects in the Hamilton-Jacobi skeleton

The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method