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

A bayesian approach to simultaneously recover camera pose and non-rigid shape from monocular images

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we bring the tools of the Simultaneous Localization and Map Building (SLAM) problem from a rigid to a deformable domain and use them to simultaneously recover the 3D shape of non-rigid surfaces and the sequence of poses of a moving camera. Under the assumption that the surface shape may be represented as a weighted sum of deformation modes, we show that the problem of estimating the modal weights along with the camera poses, can be probabilistically formulated as a maximum a posteriori estimate and solved using an iterative least squares optimization. In addition, the probabilistic formulation we propose is very general and allows introducing different constraints without requiring any extra complexity. As a proof of concept, we show that local inextensibility constraints that prevent the surface from stretching can be easily integrated. An extensive evaluation on synthetic and real data, demonstrates that our method has several advantages over current non-rigid shape from motion approaches. In particular, we show that our solution is robust to large amounts of noise and outliers and that it does not need to track points over the whole sequence nor to use an initialization close from the ground truth.Peer ReviewedPostprint (author's final draft

Towards recovery of complex shapes in meshes using digital images for reverse engineering applications

When an object owns complex shapes, or when its outer surfaces are simply inaccessible, some of its parts may not be captured during its reverse engineering. These deficiencies in the point cloud result in a set of holes in the reconstructed mesh. This paper deals with the use of information extracted from digital images to recover missing areas of a physical object. The proposed algorithm fills in these holes by solving an optimization problem that combines two kinds of information: (1) the geometric information available on the surrounding of the holes, (2) the information contained in an image of the real object. The constraints come from the image irradiance equation, a first-order non-linear partial differential equation that links the position of the mesh vertices to the light intensity of the image pixels. The blending conditions are satisfied by using an objective function based on a mechanical model of bar network that simulates the curvature evolution over the mesh. The inherent shortcomings both to the current holefilling algorithms and the resolution of the image irradiance equations are overcom

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

Intrinsic Dynamic Shape Prior for Fast, Sequential and Dense Non-Rigid Structure from Motion with Detection of Temporally-Disjoint Rigidity

While dense non-rigid structure from motion (NRSfM) has been extensively studied from the perspective of the reconstructability problem over the recent years, almost no attempts have been undertaken to bring it into the practical realm. The reasons for the slow dissemination are the severe ill-posedness, high sensitivity to motion and deformation cues and the difficulty to obtain reliable point tracks in the vast majority of practical scenarios. To fill this gap, we propose a hybrid approach that extracts prior shape knowledge from an input sequence with NRSfM and uses it as a dynamic shape prior for sequential surface recovery in scenarios with recurrence. Our Dynamic Shape Prior Reconstruction (DSPR) method can be combined with existing dense NRSfM techniques while its energy functional is optimised with stochastic gradient descent at real-time rates for new incoming point tracks. The proposed versatile framework with a new core NRSfM approach outperforms several other methods in the ability to handle inaccurate and noisy point tracks, provided we have access to a representative (in terms of the deformation variety) image sequence. Comprehensive experiments highlight convergence properties and the accuracy of DSPR under different disturbing effects. We also perform a joint study of tracking and reconstruction and show applications to shape compression and heart reconstruction under occlusions. We achieve state-of-the-art metrics (accuracy and compression ratios) in different scenarios