Doctor of Philosophy

dissertationShape analysis is a well-established tool for processing surfaces. It is often a first step in performing tasks such as segmentation, symmetry detection, and finding correspondences between shapes. Shape analysis is traditionally employed on well-sampled surfaces where the geometry and topology is precisely known. When the form of the surface is that of a point cloud containing nonuniform sampling, noise, and incomplete measurements, traditional shape analysis methods perform poorly. Although one may first perform reconstruction on such a point cloud prior to performing shape analysis, if the geometry and topology is far from the true surface, then this can have an adverse impact on the subsequent analysis. Furthermore, for triangulated surfaces containing noise, thin sheets, and poorly shaped triangles, existing shape analysis methods can be highly unstable. This thesis explores methods of shape analysis applied directly to such defect-laden shapes. We first study the problem of surface reconstruction, in order to obtain a better understanding of the types of point clouds for which reconstruction methods contain difficulties. To this end, we have devised a benchmark for surface reconstruction, establishing a standard for measuring error in reconstruction. We then develop a new method for consistently orienting normals of such challenging point clouds by using a collection of harmonic functions, intrinsically defined on the point cloud. Next, we develop a new shape analysis tool which is tolerant to imperfections, by constructing distances directly on the point cloud defined as the likelihood of two points belonging to a mutually common medial ball, and apply this for segmentation and reconstruction. We extend this distance measure to define a diffusion process on the point cloud, tolerant to missing data, which is used for the purposes of matching incomplete shapes undergoing a nonrigid deformation. Lastly, we have developed an intrinsic method for multiresolution remeshing of a poor-quality triangulated surface via spectral bisection

Deep Learning-based Methods for Sequential 3D Point Cloud Upsampling

Point cloud is a fundamental 3D representation that has received increasing attention from the computer vision community due to the recent popularity of Light Detection and Ranging (LIDAR) sensors and RGB-D cameras. However, analyzing and understanding 3D point clouds with deep networks is challenging since the raw point cloud data captured by scanning devices always suffers from sparsity and irregular data structure. To cope with this problem, several studies have been proposed to perform restoration by upsampling the input sparse point clouds via deep neural networks (DNN). Despite the successes achieved by these studies, they cannot generate satisfying results due to the insufficient geometry contexts from the input single point cloud snapshot. Considering that the 3D sensors usually capture point cloud sequences instead of each single point cloud snapshot, in this thesis, I propose three sequential point cloud sampling algorithms to significantly improve the performance of the previous single frame-based methods by exploiting temporal dependencies. In the first method, I propose a recurrent framework for sequential point cloud upsampling (SPU), which leverages multi-scale long-/short-term temporal dependencies to recover the point cloud of the current frame. To improve the efficiency and generalizability, in the second method, I extend the sequential point cloud upsampling framework to a patch-based version, namely the VPU framework. Lastly, to address the patch-misalignment issue from VPU, I propose a sequential point cloud upsampling framework built upon progressive multi-level refinement (PMR-Net), including three different refinement stages at the frame level, shape level, and detail level, respectively. Comprehensive experiments on multiple point cloud sequence datasets demonstrate the effectiveness of our proposed frameworks SPU, VPU, and PMRNet for sequential point cloud upsampling

A survey on deep geometry learning: from a representation perspective

Researchers have achieved great success in dealing with 2D images using deep learning. In recent years, 3D computer vision and geometry deep learning have gained ever more attention. Many advanced techniques for 3D shapes have been proposed for different applications. Unlike 2D images, which can be uniformly represented by a regular grid of pixels, 3D shapes have various representations, such as depth images, multi-view images, voxels, point clouds, meshes, implicit surfaces, etc. The performance achieved in different applications largely depends on the representation used, and there is no unique representation that works well for all applications. Therefore, in this survey, we review recent developments in deep learning for 3D geometry from a representation perspective, summarizing the advantages and disadvantages of different representations for different applications. We also present existing datasets in these representations and further discuss future research directions

Differentiable Subdivision Surface Fitting

In this paper, we present a powerful differentiable surface fitting technique to derive a compact surface representation for a given dense point cloud or mesh, with application in the domains of graphics and CAD/CAM. We have chosen the Loop subdivision surface, which in the limit yields the smooth surface underlying the point cloud, and can handle complex surface topology better than other popular compact representations, such as NURBS. The principal idea is to fit the Loop subdivision surface not directly to the point cloud, but to the IMLS (implicit moving least squares) surface defined over the point cloud. As both Loop subdivision and IMLS have analytical expressions, we are able to formulate the problem as an unconstrained minimization problem of a completely differentiable function that can be solved with standard numerical solvers. Differentiability enables us to integrate the subdivision surface into any deep learning method for point clouds or meshes. We demonstrate the versatility and potential of this approach by using it in conjunction with a differentiable renderer to robustly reconstruct compact surface representations of spatial-temporal sequences of dense meshes

Non-Rigid Registration meets Surface Reconstruction

International audienceNon rigid registration is an important task in computer vision with many applications in shape and motion modeling. A fundamental step of the registration is the data association between the source and the target sets. Such association proves difficult in practice, due to the discrete nature of the information and its corruption by various types of noise, e.g. outliers and missing data. In this paper we investigate the benefit of the implicit representations for the non-rigid registration of 3D point clouds. First, the target points are described with small quadratic patches that are blended through partition of unity weighting. Then, the discrete association between the source and the target can be replaced by a continuous distance field induced by the interface. By combining this distance field with a proper deformation term, the registration energy can be expressed in a linear least square form that is easy and fast to solve. This significantly eases the registration by avoiding direct association between points. Moreover, a hierarchical approach can be easily implemented by employing coarse-to-fine representations. Experimental results are provided for point clouds from multi-view data sets. The qualitative and quantitative comparisons show the outperformance and robustness of our framework

A Survey of Surface Reconstruction from Point Clouds

International audienceThe area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of the original shape, recent work has taken on more specialized priors to address significantly challenging data imperfections, where the reconstruction can take on different representations – not necessarily the explicit geometry. We survey the field of surface reconstruction, and provide a categorization with respect to priors, data imperfections, and reconstruction output. By considering a holistic view of surface reconstruction, we show a detailed characterization of the field, highlight similarities between diverse reconstruction techniques, and provide directions for future work in surface reconstruction