Real-time 3D reconstruction of non-rigid shapes with a single moving camera

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper describes a real-time sequential method to simultaneously recover the camera motion and the 3D shape of deformable objects from a calibrated monocular video. For this purpose, we consider the Navier-Cauchy equations used in 3D linear elasticity and solved by finite elements, to model the time-varying shape per frame. These equations are embedded in an extended Kalman filter, resulting in sequential Bayesian estimation approach. We represent the shape, with unknown material properties, as a combination of elastic elements whose nodal points correspond to salient points in the image. The global rigidity of the shape is encoded by a stiffness matrix, computed after assembling each of these elements. With this piecewise model, we can linearly relate the 3D displacements with the 3D acting forces that cause the object deformation, assumed to be normally distributed. While standard finite-element-method techniques require imposing boundary conditions to solve the resulting linear system, in this work we eliminate this requirement by modeling the compliance matrix with a generalized pseudoinverse that enforces a pre-fixed rank. Our framework also ensures surface continuity without the need for a post-processing step to stitch all the piecewise reconstructions into a global smooth shape. We present experimental results using both synthetic and real videos for different scenarios ranging from isometric to elastic deformations. We also show the consistency of the estimation with respect to 3D ground truth data, include several experiments assessing robustness against artifacts and finally, provide an experimental validation of our performance in real time at frame rate for small mapsPeer ReviewedPostprint (author's final draft

Geometry-Aware Network for Non-Rigid Shape Prediction from a Single View

We propose a method for predicting the 3D shape of a deformable surface from a single view. By contrast with previous approaches, we do not need a pre-registered template of the surface, and our method is robust to the lack of texture and partial occlusions. At the core of our approach is a {\it geometry-aware} deep architecture that tackles the problem as usually done in analytic solutions: first perform 2D detection of the mesh and then estimate a 3D shape that is geometrically consistent with the image. We train this architecture in an end-to-end manner using a large dataset of synthetic renderings of shapes under different levels of deformation, material properties, textures and lighting conditions. We evaluate our approach on a test split of this dataset and available real benchmarks, consistently improving state-of-the-art solutions with a significantly lower computational time.Comment: Accepted at CVPR 201

Tracking an elastic object with an RGB-D sensor for a pizza chef robot

This paper presents a method to track in real-time a 3D object which undergoes large deformations such as elastic ones, and fast rigid motions, using the point cloud data provided by a RGB-D sensor. This solution would contribute to robotic humanoid manipulation purposes. Our framework relies on a prior visual segmentation of the object in the image. The segmented point cloud is then registered first in a rigid manner and then by non-rigidly fitting the mesh, based on the Finite Element Method to model elasticity and on geometrical point-to-point correspondences to compute external forces exerted on the mesh. The real-time performance of the system is demonstrated on real data involving challenging deformations and motions, for a pizza dough to be ideally manipulated by a chef robot

Single View Augmentation of 3D Elastic Objects

International audienceThis paper proposes an efficient method to capture and augment highly elastic objects from a single view. 3D shape recovery from a monocular video sequence is an underconstrained problem and many approaches have been proposed to enforce constraints and resolve the ambiguities. State-of-the art solutions enforce smoothness or geometric constraints, consider specific deformation properties such as inextensibility or ressort to shading constraints. However, few of them can handle properly large elastic deformations. We propose in this paper a real-time method which makes use of a me chanical model and is able to handle highly elastic objects. Our method is formulated as a energy minimization problem accounting for a non-linear elastic model constrained by external image points acquired from a monocular camera. This method prevents us from formulating restrictive assumptions and specific constraint terms in the minimization. The only parameter involved in the method is the Young's modulus where we show in experiments that a rough estimate of its value is sufficient to obtain a good reconstruction. Our method is compared to existing techniques with experiments conducted on computer-generated and real data that show the effectiveness of our approach. Experiments in the context of minimally invasive liver surgery are also provided

Sequential non-rigid structure from motion using physical priors

© 20xx 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.We propose a new approach to simultaneously recover camera pose and 3D shape of non-rigid and potentially extensible surfaces from a monocular image sequence. For this purpose, we make use of the Extended Kalman Filter based Simultaneous Localization And Mapping (EKF-SLAM) formulation, a Bayesian optimization framework traditionally used in mobile robotics for estimating camera pose and reconstructing rigid scenarios. In order to extend the problem to a deformable domain we represent the object's surface mechanics by means of Navier's equations, which are solved using a Finite Element Method (FEM). With these main ingredients, we can further model the material's stretching, allowing us to go a step further than most of current techniques, typically constrained to surfaces undergoing isometric deformations. We extensively validate our approach in both real and synthetic experiments, and demonstrate its advantages with respect to competing methods. More specifically, we show that besides simultaneously retrieving camera pose and non-rigid shape, our approach is adequate for both isometric and extensible surfaces, does not require neither batch processing all the frames nor tracking points over the whole sequence and runs at several frames per second.Peer ReviewedPostprint (author's final draft

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

Real-time tracking of 3D elastic objects with an RGB-D sensor

This paper presents a method to track in real-time a 3D textureless object which undergoes large deformations such as elastic ones, and rigid motions, using the point cloud data provided by an RGB-D sensor. This solution is expected to be useful for enhanced manipulation of humanoid robotic systems. Our framework relies on a prior visual segmentation of the object in the image. The segmented point cloud is registered first in a rigid manner and then by non-rigidly fitting the mesh, based on the Finite Element Method to model elasticity, and on geometrical point-to-point correspondences to compute external forces exerted on the mesh. The real-time performance of the system is demonstrated on synthetic and real data involving challenging deformations and motions

Calipso: Physics-based Image and Video Editing through CAD Model Proxies

We present Calipso, an interactive method for editing images and videos in a physically-coherent manner. Our main idea is to realize physics-based manipulations by running a full physics simulation on proxy geometries given by non-rigidly aligned CAD models. Running these simulations allows us to apply new, unseen forces to move or deform selected objects, change physical parameters such as mass or elasticity, or even add entire new objects that interact with the rest of the underlying scene. In Calipso, the user makes edits directly in 3D; these edits are processed by the simulation and then transfered to the target 2D content using shape-to-image correspondences in a photo-realistic rendering process. To align the CAD models, we introduce an efficient CAD-to-image alignment procedure that jointly minimizes for rigid and non-rigid alignment while preserving the high-level structure of the input shape. Moreover, the user can choose to exploit image flow to estimate scene motion, producing coherent physical behavior with ambient dynamics. We demonstrate Calipso's physics-based editing on a wide range of examples producing myriad physical behavior while preserving geometric and visual consistency.Comment: 11 page

Modal space: a physics-based model for sequential estimation of time-varying shape from monocular video

The final publication is available at link.springer.comThis paper describes two sequential methods for recovering the camera pose together with the 3D shape of highly deformable surfaces from a monocular video. The nonrigid 3D shape is modeled as a linear combination of mode shapes with time-varying weights that define the shape at each frame and are estimated on-the-fly. The low-rank constraint is combined with standard smoothness priors to optimize the model parameters over a sliding window of image frames. We propose to obtain a physics-based shape basis using the initial frames on the video to code the time-varying shape along the sequence, reducing the problem from trilinear to bilinear. To this end, the 3D shape is discretized by means of a soup of elastic triangular finite elements where we apply a force balance equation. This equation is solved using modal analysis via a simple eigenvalue problem to obtain a shape basis that encodes the modes of deformation. Even though this strategy can be applied in a wide variety of scenarios, when the observations are denser, the solution can become prohibitive in terms of computational load. We avoid this limitation by proposing two efficient coarse-to-fine approaches that allow us to easily deal with dense 3D surfaces. This results in a scalable solution that estimates a small number of parameters per frame and could potentially run in real time. We show results on both synthetic and real videos with ground truth 3D data, while robustly dealing with artifacts such as noise and missing data.Peer ReviewedPostprint (author's final draft