Finite Element Based Tracking of Deforming Surfaces

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object's surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.Comment: additional experiment

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

Learning the dynamics and time-recursive boundary detection of deformable objects

We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object

Localization from semantic observations via the matrix permanent

Most approaches to robot localization rely on low-level geometric features such as points, lines, and planes. In this paper, we use object recognition to obtain semantic information from the robot’s sensors and consider the task of localizing the robot within a prior map of landmarks, which are annotated with semantic labels. As object recognition algorithms miss detections and produce false alarms, correct data association between the detections and the landmarks on the map is central to the semantic localization problem. Instead of the traditional vector-based representation, we propose a sensor model, which encodes the semantic observations via random finite sets and enables a unified treatment of missed detections, false alarms, and data association. Our second contribution is to reduce the problem of computing the likelihood of a set-valued observation to the problem of computing a matrix permanent. It is this crucial transformation that allows us to solve the semantic localization problem with a polynomial-time approximation to the set-based Bayes filter. Finally, we address the active semantic localization problem, in which the observer’s trajectory is planned in order to improve the accuracy and efficiency of the localization process. The performance of our approach is demonstrated in simulation and in real environments using deformable-part-model-based object detectors. Robust global localization from semantic observations is demonstrated for a mobile robot, for the Project Tango phone, and on the KITTI visual odometry dataset. Comparisons are made with the traditional lidar-based geometric Monte Carlo localization

A Generic Framework for Tracking Using Particle Filter With Dynamic Shape Prior

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.894244Tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time. Tracking algorithms using Kalman filters or particle filters (PFs) have been proposed for tracking such objects, but these have limitations due to the lack of dynamic shape information. In this paper, we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter. The PF also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and backgroun

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

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

Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery

One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions

Physics-Based Modeling of Nonrigid Objects for Vision and Graphics (Dissertation)

This thesis develops a physics-based framework for 3D shape and nonrigid motion modeling for computer vision and computer graphics. In computer vision it addresses the problems of complex 3D shape representation, shape reconstruction, quantitative model extraction from biomedical data for analysis and visualization, shape estimation, and motion tracking. In computer graphics it demonstrates the generative power of our framework to synthesize constrained shapes, nonrigid object motions and object interactions for the purposes of computer animation. Our framework is based on the use of a new class of dynamically deformable primitives which allow the combination of global and local deformations. It incorporates physical constraints to compose articulated models from deformable primitives and provides force-based techniques for fitting such models to sparse, noise-corrupted 2D and 3D visual data. The framework leads to shape and nonrigid motion estimators that exploit dynamically deformable models to track moving 3D objects from time-varying observations. We develop models with global deformation parameters which represent the salient shape features of natural parts, and local deformation parameters which capture shape details. In the context of computer graphics, these models represent the physics-based marriage of the parameterized and free-form modeling paradigms. An important benefit of their global/local descriptive power in the context of computer vision is that it can potentially satisfy the often conflicting requirements of shape reconstruction and shape recognition. The Lagrange equations of motion that govern our models, augmented by constraints, make them responsive to externally applied forces derived from input data or applied by the user. This system of differential equations is discretized using finite element methods and simulated through time using standard numerical techniques. We employ these equations to formulate a shape and nonrigid motion estimator. The estimator is a continuous extended Kalman filter that recursively transforms the discrepancy between the sensory data and the estimated model state into generalized forces. These adjust the translational, rotational, and deformational degrees of freedom such that the model evolves in a consistent fashion with the noisy data. We demonstrate the interactive time performance of our techniques in a series of experiments in computer vision, graphics, and visualization