Robust Structure and Motion Recovery Based on Augmented Factorization

This paper proposes a new strategy to promote the robustness of structure from motion algorithm from uncalibrated video sequences. First, an augmented affine factorization algorithm is formulated to circumvent the difficulty in image registration with noise and outliers contaminated data. Then, an alternative weighted factorization scheme is designed to handle the missing data and measurement uncertainties in the tracking matrix. Finally, a robust strategy for structure and motion recovery is proposed to deal with outliers and large measurement noise. This paper makes the following main contributions: 1) An augmented factorization algorithm is proposed to circumvent the difficult image registration problem of previous affine factorization, and the approach is applicable to both rigid and nonrigid scenarios; 2) by employing the fact that image reprojection residuals are largely proportional to the error magnitude in the tracking data, a simple outliers detection approach is proposed; and 3) a robust factorization strategy is developed based on the distribution of the reprojection residuals. Furthermore, the proposed approach can be easily extended to nonrigid scenarios. Experiments using synthetic and real image data demonstrate the robustness and efficiency of the proposed approach over previous algorithms.22289016157335

Robust and Accurate Structure from Motion of Rigid and Nonrigid Objects

As a central theme in computer vision, the problem of 3D structure and motion recovery from image sequences has been widely studied during the past three decades, and considerable progress has been made in theory, as well as in prac- tice. However, there are still several challenges remaining, including algorithm robustness and accuracy, especially for nonrigid modeling. The thesis focuses on solving these challenges and several new robust and accurate algorithms have been proposed. The first part of the thesis reviews the state-of-the-art techniques of structure and motion factorization. First, an introduction of structure from motion and some mathematical background of the technique is presented. Then, the general idea and different formulations of structure from motion for rigid and nonrigid objects are discussed. The second part covers the proposed quasi-perspective projection model and its application to structure and motion factorization. Previous algorithms are based on either a simplified affine assumption or a complicated full perspective projection model. The affine model is widely adopted due to its simplicity, whereas the extension to full perspective suffers from recovering projective depths. A quasi-perspective model is proposed to fill the gap between the two models. It is more accurate than the affine model from both theoretical analysis and experimental studies. More geometric properties of the model are investigated in the context of one- and two-view geometry. Finally, the model was applied to structure from motion and a framework of rigid and nonrigid factorization under quasi-perspective assumption is established. The last part of the thesis is focused on the robustness and three new al- gorithms are proposed. First, a spatial-and-temporal-weighted factorization algorithm is proposed to handle significant image noise, where the uncertainty of image measurement is estimated from a new perspective by virtue of repro- jection residuals. Second, a rank-4 affine factorization algorithm is proposed to avoid the difficulty of image alignment with erroneous data, followed by a robust factorization scheme that can work with missing and outlying data. Third, the robust algorithm is extended to nonrigid scenarios and a new augmented nonrigid factorization algorithm is proposed to handle imperfect tracking data. The main contributions of the thesis are as follows: The proposed quasi- perspective projection model fills the gap between the simplicity of the affine model and the accuracy of the perspective model. Its application to structure and motion factorization greatly increases the efficiency and accuracy of the algorithm. The proposed robust algorithms do not require prior information of image measurement and greatly improve the overall accuracy and robustness of previous approaches. Moreover, the algorithms can also be applied directly to structure from motion of nonrigid objects

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

Deformable 3-D Modelling from Uncalibrated Video Sequences

Submitted for the degree of Doctor of Philosophy, Queen Mary, University of Londo

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