Dense 3D Face Correspondence

We present an algorithm that automatically establishes dense correspondences between a large number of 3D faces. Starting from automatically detected sparse correspondences on the outer boundary of 3D faces, the algorithm triangulates existing correspondences and expands them iteratively by matching points of distinctive surface curvature along the triangle edges. After exhausting keypoint matches, further correspondences are established by generating evenly distributed points within triangles by evolving level set geodesic curves from the centroids of large triangles. A deformable model (K3DM) is constructed from the dense corresponded faces and an algorithm is proposed for morphing the K3DM to fit unseen faces. This algorithm iterates between rigid alignment of an unseen face followed by regularized morphing of the deformable model. We have extensively evaluated the proposed algorithms on synthetic data and real 3D faces from the FRGCv2, Bosphorus, BU3DFE and UND Ear databases using quantitative and qualitative benchmarks. Our algorithm achieved dense correspondences with a mean localisation error of 1.28mm on synthetic faces and detected $14$ anthropometric landmarks on unseen real faces from the FRGCv2 database with 3mm precision. Furthermore, our deformable model fitting algorithm achieved 98.5% face recognition accuracy on the FRGCv2 and 98.6% on Bosphorus database. Our dense model is also able to generalize to unseen datasets.Comment: 24 Pages, 12 Figures, 6 Tables and 3 Algorithm

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas

Deformable meshes for shape recovery: models and applications

With the advance of scanning and imaging technology, more and more 3D objects become available. Among them, deformable objects have gained increasing interests. They include medical instances such as organs, a sequence of objects in motion, and objects of similar shapes where a meaningful correspondence can be established between each other. Thus, it requires tools to store, compare, and retrieve them. Many of these operations depend on successful shape recovery. Shape recovery is the task to retrieve an object from the environment where its geometry is hidden or implicitly known. As a simple and versatile tool, mesh is widely used in computer graphics for modelling and visualization. In particular, deformable meshes are meshes which can take the deformation of deformable objects. They extend the modelling ability of meshes. This dissertation focuses on using deformable meshes to approach the 3D shape recovery problem. Several models are presented to solve the challenges for shape recovery under different circumstances. When the object is hidden in an image, a PDE deformable model is designed to extract its surface shape. The algorithm uses a mesh representation so that it can model any non-smooth surface with an arbitrary precision compared to a parametric model. It is more computational efficient than a level-set approach. When the explicit geometry of the object is known but is hidden in a bank of shapes, we simplify the deformation of the model to a graph matching procedure through a hierarchical surface abstraction approach. The framework is used for shape matching and retrieval. This idea is further extended to retain the explicit geometry during the abstraction. A novel motion abstraction framework for deformable meshes is devised based on clustering of local transformations and is successfully applied to 3D motion compression

Slippage Features

In this report, we present a novel feature detection technique for unstructured point clouds. We introduce a generalized concept of geometric features that detects locally uniquely identifiable keypoints as centroids of area with locally minimal slippage. We extend the concept to multiple scales and extract features using multi-scale mean shift clustering. In order to validate matches between feature points, we employ a two stage technique that first sorts out unlikely matches, followed by an approximate alignment between remaining features by a rotational cross-correlation analysis and a local iterative closest point (ICP) registration. The resulting residuals are then used as final similarity measure. The proposed combination of techniques results in a robust and reliable correspondence detection technique that yields registration results in situations where previous techniques are not able to detect usable feature correspondences. We provide a detailed empirical analysis of the method, and apply the technique to global registration, symmetry detection and deformable matching problems

Multi-scale and multi-spectral shape analysis: from 2d to 3d

Shape analysis is a fundamental aspect of many problems in computer graphics and computer vision, including shape matching, shape registration, object recognition and classification. Since the SIFT achieves excellent matching results in 2D image domain, it inspires us to convert the 3D shape analysis to 2D image analysis using geometric maps. However, the major disadvantage of geometric maps is that it introduces inevitable, large distortions when mapping large, complex and topologically complicated surfaces to a canonical domain. It is demanded for the researchers to construct the scale space directly on the 3D shape. To address these research issues, in this dissertation, in order to find the multiscale processing for the 3D shape, we start with shape vector image diffusion framework using the geometric mapping. Subsequently, we investigate the shape spectrum field by introducing the implementation and application of Laplacian shape spectrum. In order to construct the scale space on 3D shape directly, we present a novel idea to solve the diffusion equation using the manifold harmonics in the spectral point of view. Not only confined on the mesh, by using the point-based manifold harmonics, we rigorously derive our solution from the diffusion equation which is the essential of the scale space processing on the manifold. Built upon the point-based manifold harmonics transform, we generalize the diffusion function directly on the point clouds to create the scale space. In virtue of the multiscale structure from the scale space, we can detect the feature points and construct the descriptor based on the local neighborhood. As a result, multiscale shape analysis directly on the 3D shape can be achieved

Shape basis interpretation for monocular deformable 3D reconstruction

© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper, we propose a novel interpretable shape model to encode object non-rigidity. We first use the initial frames of a monocular video to recover a rest shape, used later to compute a dissimilarity measure based on a distance matrix measurement. Spectral analysis is then applied to this matrix to obtain a reduced shape basis, that in contrast to existing approaches, can be physically interpreted. In turn, these pre-computed shape bases are used to linearly span the deformation of a wide variety of objects. We introduce the low-rank basis into a sequential approach to recover both camera motion and non-rigid shape from the monocular video, by simply optimizing the weights of the linear combination using bundle adjustment. Since the number of parameters to optimize per frame is relatively small, specially when physical priors are considered, our approach is fast and can potentially run in real time. Validation is done in a wide variety of real-world objects, undergoing both inextensible and extensible deformations. Our approach achieves remarkable robustness to artifacts such as noisy and missing measurements and shows an improved performance to competing methods.Peer ReviewedPostprint (author's final draft