Rigid Structure

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Hongdong Li - One of the best experts on this subject based on the ideXlab platform.

  • 3DV - Multi-Body Non-Rigid Structure-from-Motion
    2016 Fourth International Conference on 3D Vision (3DV), 2016
    Co-Authors: Suryansh Kumar, Hongdong Li
    Abstract:

    In this paper, we present the first multi-body non-Rigid Structure-from-motion (SFM) method, which simultaneously reconstructs and segments multiple objects that are undergoing non-Rigid deformation over time. Under our formulation, 3D trajectories for each non-Rigid object can be well approximated with a sparse affine combination of other 3D trajectories from the same object. The resultant optimization is solved by the alternating direction method of multipliers (ADMM). We demonstrate the efficacy of the proposed method through extensive experiments on both synthetic and real data sequences. Our method outperforms other alternative methods, such as first clustering the 2D feature tracks to groups and then doing non-Rigid reconstruction in each group or first conducting 3D reconstruction by using single subspace assumption and then clustering the 3D trajectories into groups.

  • a simple prior free method for non Rigid Structure from motion factorization
    International Journal of Computer Vision, 2014
    Co-Authors: Hongdong Li, Mingyi He
    Abstract:

    This paper proposes a simple "prior-free" method for solving the non-Rigid Structure-from-motion (NRSfM) factorization problem. Other than using the fundamental low-order linear combination model assumption, our method does not assume any extra prior knowledge either about the non-Rigid Structure or about the camera motions. Yet, it works effectively and reliably, producing optimal results, and not suffering from the inherent basis ambiguity issue which plagued most conventional NRSfM factorization methods. Our method is very simple to implement, which involves solving a very small SDP (semi-definite programming) of fixed size, and a nuclear-norm minimization problem. We also present theoretical analysis on the uniqueness and the relaxation gap of our solutions. Extensive experiments on both synthetic and real motion capture data (assuming following the low-order linear combination model) are conducted, which demonstrate that our method indeed outperforms most of the existing non-Rigid factorization methods. This work offers not only new theoretical insight, but also a practical, everyday solution to NRSfM.

  • a simple prior free method for non Rigid Structure from motion factorization
    Computer Vision and Pattern Recognition, 2012
    Co-Authors: Hongdong Li, Mingyi He
    Abstract:

    This paper proposes a simple “prior-free” method for solving non-Rigid Structure-from-motion factorization problems. Other than using the basic low-rank condition, our method does not assume any extra prior knowledge about the nonRigid scene or about the camera motions. Yet, it runs reliably, produces optimal result, and does not suffer from the inherent basis-ambiguity issue which plagued many conventional nonRigid factorization techniques. Our method is easy to implement, which involves solving no more than an SDP (semi-definite programming) of small and fixed size, a linear Least-Squares or trace-norm minimization. Extensive experiments have demonstrated that it outperforms most of the existing linear methods of nonRigid factorization. This paper offers not only new theoretical insight, but also a practical, everyday solution, to non-Rigid Structure-from-motion.

Vladislav Golyanik - One of the best experts on this subject based on the ideXlab platform.

  • neural dense non Rigid Structure from motion with latent space constraints
    European Conference on Computer Vision, 2020
    Co-Authors: Vladislav Golyanik, Vikramjit Sidhu, Edgar Tretschk, Antonio Agudo, Christian Theobalt
    Abstract:

    We introduce the first dense neural non-Rigid Structure from motion (N-NRSfM) approach, which can be trained end-to-end in an unsupervised manner from 2D point tracks. Compared to the competing methods, our combination of loss functions is fully-differentiable and can be readily integrated into deep-learning systems. We formulate the deformation model by an auto-decoder and impose subspace constraints on the recovered latent space function in a frequency domain. Thanks to the state recurrence cue, we classify the reconstructed non-Rigid surfaces based on their similarity and recover the period of the input sequence. Our N-NRSfM approach achieves competitive accuracy on widely-used benchmark sequences and high visual quality on various real videos. Apart from being a standalone technique, our method enables multiple applications including shape compression, completion and interpolation, among others. Combined with an encoder trained directly on 2D images, we perform scenario-specific monocular 3D shape reconstruction at interactive frame rates. To facilitate the reproducibility of the results and boost the new research direction, we open-source our code and provide trained models for research purposes (http://gvv.mpi-inf.mpg.de/projects/Neural_NRSfM/).

  • scalable dense non Rigid Structure from motion
    2020
    Co-Authors: Vladislav Golyanik
    Abstract:

    THE focus of this chapter lies on scalable NRSfM methods. In the recent years, the scalability in NRSfM has gained increased attention. Thus, the goal is not only obtaining accurate reconstructions but also the results have to remain consistently accurate with the different number of input point tracks and for as many different scenarios as possible.

  • shape priors in dense non Rigid Structure from motion
    2020
    Co-Authors: Vladislav Golyanik
    Abstract:

    THIS chapter is devoted to two NRSfM methods with shape priors obtained on-the-fly. Both static and dynamic shape priors are investigated. Static shape prior refers to a single prior 3D state, and dynamic shape prior refers to a series of states.

  • intrinsic dynamic shape prior for fast sequential and dense non Rigid Structure from motion with detection of temporally disjoint Rigidity
    arXiv: Computer Vision and Pattern Recognition, 2019
    Co-Authors: Vladislav Golyanik, Didier Stricker, Andre Jonas, Christian Theobalt
    Abstract:

    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.

  • WACV - Dense Batch Non-Rigid Structure from Motion in a Second
    2017 IEEE Winter Conference on Applications of Computer Vision (WACV), 2017
    Co-Authors: Vladislav Golyanik, Didier Stricker
    Abstract:

    In this paper, we show how to minimise a quadratic function on a set of orthonormal matrices using an efficient semidefinite programming solver with application to dense non-Rigid Structure from motion. Thanks to the proposed technique, a new form of the convex relaxation for the Metric Projections (MP) algorithm is obtained. The modification results in an efficient single-core CPU implementation enabling dense factorisations of long image sequences with tens of thousands of points into camera pose and non-Rigid shape in seconds, i.e., at least two orders of magnitude faster than the runtimes reported in the literature so far. The proposed implementation can be useful for interactive or real-time robotic and other applications, where monocular non-Rigid reconstruction is required. In a narrow sense, our paper complements research on MP, though the proposed convex relaxation methodology can also be useful in other computer vision tasks. The experimental part providing runtime evaluation and qualitative analysis concludes the paper.

Yuchao Dai - One of the best experts on this subject based on the ideXlab platform.

  • dense non Rigid Structure from motion a manifold viewpoint
    arXiv: Computer Vision and Pattern Recognition, 2020
    Co-Authors: Suryansh Kumar, Luc Van Gool, Anoop Cherian, Carlos Eduardo Porto De Oliveira, Yuchao Dai
    Abstract:

    Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. Classical approaches to this problem assume a small number of feature points and, ignore the local non-linearities of the shape deformation, and therefore, struggles to reliably model non-linear deformations. Furthermore, available dense NRSfM algorithms are often hurdled by scalability, computations, noisy measurements and, restricted to model just global deformation. In this paper, we propose algorithms that can overcome these limitations with the previous methods and, at the same time, can recover a reliable dense 3D Structure of a non-Rigid object with higher accuracy. Assuming that a deforming shape is composed of a union of local linear subspace and, span a global low-rank space over multiple frames enables us to efficiently model complex non-Rigid deformations. To that end, each local linear subspace is represented using Grassmannians and, the global 3D shape across multiple frames is represented using a low-rank representation. We show that our approach significantly improves accuracy, scalability, and robustness against noise. Also, our representation naturally allows for simultaneous reconstruction and clustering framework which in general is observed to be more suitable for NRSfM problems. Our method currently achieves leading performance on the standard benchmark datasets.

  • scalable dense non Rigid Structure from motion a grassmannian perspective
    Computer Vision and Pattern Recognition, 2018
    Co-Authors: Suryansh Kumar, Anoop Cherian, Yuchao Dai
    Abstract:

    This paper addresses the task of dense non-Rigid Structure-front-motion (NRSfM) using multiple images. State-of-the-art methods to this problem are often hurdled by scalability, expensive computations, and noisy measurements. Further, recent methods to NRSfM usually either assume a small number of sparse feature points or ignore local non-linearities of shape deformations, and thus cannot reliably model complex non-Rigid deformations. To address these issues, in this paper, we propose a new approach for dense NRSfM by modeling the problem on a Grassmann manifold. Specifically, we assume the complex non-Rigid deformations lie on a union of local linear subspaces both spatially and temporally. This naturally allows for a compact representation of the complex non-Rigid deformation over frames. We provide experimental results on several synthetic and real benchmark datasets. The procured results clearly demonstrate that our method, apart from being scalable and more accurate than state-of-the-art methods, is also more robust to noise and generalizes to highly nonlinear deformations.

  • spatio temporal union of subspaces for multi body non Rigid Structure from motion
    Pattern Recognition, 2017
    Co-Authors: Suryansh Kumar, Yuchao Dai
    Abstract:

    Abstract Non-Rigid Structure-from-motion (NRSfM) has so far been mostly studied for recovering 3D Structure of a single non-Rigid/deforming object. To handle the real world challenging multiple deforming objects scenarios, existing methods either pre-segment different objects in the scene or treat multiple non-Rigid objects as a whole to obtain the 3D non-Rigid reconstruction. However, these methods fail to exploit the inherent Structure in the problem as the solution of segmentation and the solution of reconstruction could not benefit each other. In this paper, we propose a unified framework to jointly segment and reconstruct multiple non-Rigid objects. To compactly represent complex multi-body non-Rigid scenes, we propose to exploit the Structure of the scenes along both temporal direction and spatial direction, thus achieving a spatio-temporal representation. Specifically, we represent the 3D non-Rigid deformations as lying in a union of subspaces along the temporal direction and represent the 3D trajectories as lying in the union of subspaces along the spatial direction. This spatio-temporal representation not only provides competitive 3D reconstruction but also outputs robust segmentation of multiple non-Rigid objects. The resultant optimization problem is solved efficiently using the Alternating Direction Method of Multipliers (ADMM). Extensive experimental results on both synthetic and real multi-body NRSfM datasets demonstrate the superior performance of our proposed framework compared with the state-of-the-art methods.

  • DICTA - Simultaneous Correspondences Estimation and Non-Rigid Structure Reconstruction
    2016 International Conference on Digital Image Computing: Techniques and Applications (DICTA), 2016
    Co-Authors: Yuchao Dai
    Abstract:

    Given multi-view correspondences, it has been shown that 3D non-Rigid Structure can be recovered through factorization based techniques. However, establishing reliable correspondences across multi-view images of non-Rigid Structure is not an easy task. Existing methods solve multi-view correspondences and 3D non-Rigid Structure in sequel, which cannot exploit the crossover constraints in each sub-problem (\ie, constraints in non-Rigid Structure has not been enforced in establishing multi-view correspondences and verse vise). In this paper, we present a unified framework to simultaneously solve for multi-view correspondences and non-Rigid Structure. We formulate the problem by using the Partial Permutation Matrices (PPMs) and aim at establishing multi-view correspondences while simultaneously enforcing the low-rank constraint in non-Rigid Structure deformation. Additionally, our method can handle outliers and missing data elegantly under the same framework. We solve the simultaneous non-Rigid Structure and correspondences recovery problem via the Alternating Direction Method of Multipliers (ADMM). Experimental results on both synthetic and real images show that the proposed method achieves state-of-the-art performance on both sparse and dense non-Rigid reconstruction problems.

  • CVPR - A simple prior-free method for non-Rigid Structure-from-motion factorization
    2012 IEEE Conference on Computer Vision and Pattern Recognition, 2012
    Co-Authors: Yuchao Dai
    Abstract:

    This paper proposes a simple “prior-free” method for solving non-Rigid Structure-from-motion factorization problems. Other than using the basic low-rank condition, our method does not assume any extra prior knowledge about the nonRigid scene or about the camera motions. Yet, it runs reliably, produces optimal result, and does not suffer from the inherent basis-ambiguity issue which plagued many conventional nonRigid factorization techniques. Our method is easy to implement, which involves solving no more than an SDP (semi-definite programming) of small and fixed size, a linear Least-Squares or trace-norm minimization. Extensive experiments have demonstrated that it outperforms most of the existing linear methods of nonRigid factorization. This paper offers not only new theoretical insight, but also a practical, everyday solution, to non-Rigid Structure-from-motion.

Mingyi He - One of the best experts on this subject based on the ideXlab platform.

  • a simple prior free method for non Rigid Structure from motion factorization
    International Journal of Computer Vision, 2014
    Co-Authors: Hongdong Li, Mingyi He
    Abstract:

    This paper proposes a simple "prior-free" method for solving the non-Rigid Structure-from-motion (NRSfM) factorization problem. Other than using the fundamental low-order linear combination model assumption, our method does not assume any extra prior knowledge either about the non-Rigid Structure or about the camera motions. Yet, it works effectively and reliably, producing optimal results, and not suffering from the inherent basis ambiguity issue which plagued most conventional NRSfM factorization methods. Our method is very simple to implement, which involves solving a very small SDP (semi-definite programming) of fixed size, and a nuclear-norm minimization problem. We also present theoretical analysis on the uniqueness and the relaxation gap of our solutions. Extensive experiments on both synthetic and real motion capture data (assuming following the low-order linear combination model) are conducted, which demonstrate that our method indeed outperforms most of the existing non-Rigid factorization methods. This work offers not only new theoretical insight, but also a practical, everyday solution to NRSfM.

  • a simple prior free method for non Rigid Structure from motion factorization
    Computer Vision and Pattern Recognition, 2012
    Co-Authors: Hongdong Li, Mingyi He
    Abstract:

    This paper proposes a simple “prior-free” method for solving non-Rigid Structure-from-motion factorization problems. Other than using the basic low-rank condition, our method does not assume any extra prior knowledge about the nonRigid scene or about the camera motions. Yet, it runs reliably, produces optimal result, and does not suffer from the inherent basis-ambiguity issue which plagued many conventional nonRigid factorization techniques. Our method is easy to implement, which involves solving no more than an SDP (semi-definite programming) of small and fixed size, a linear Least-Squares or trace-norm minimization. Extensive experiments have demonstrated that it outperforms most of the existing linear methods of nonRigid factorization. This paper offers not only new theoretical insight, but also a practical, everyday solution, to non-Rigid Structure-from-motion.

Timothy F Cootes - One of the best experts on this subject based on the ideXlab platform.

  • analysis of features for Rigid Structure vehicle type recognition
    British Machine Vision Conference, 2004
    Co-Authors: Vladimir Petrovic, Timothy F Cootes
    Abstract:

    We describe an investigation into feature representations for Rigid Structure recognition framework for recognition of objects with a multitude of classes. The intended application is automatic recognition of vehicle type for secure access and traffic monitoring applications, a problem not hitherto considered at such a level of accuracy. We demonstrate that a relatively simple set of features extracted from sections of car front images can be used to obtain high performance verification and recognition of vehicle type (both car model and class). We describe the approach and resulting system in full, and the results of experiments comparing a wide variety of different features. The final system is capable of recognition rates of over 93% and verification equal error rates of fewer than 5.6% when tested on over 1000 images containing 77 different classes. The system is shown to be robust for a wide range of weather and lighting conditions.

  • BMVC - Analysis of Features for Rigid Structure Vehicle Type Recognition
    Procedings of the British Machine Vision Conference 2004, 2004
    Co-Authors: Vladimir Petrovic, Timothy F Cootes
    Abstract:

    We describe an investigation into feature representations for Rigid Structure recognition framework for recognition of objects with a multitude of classes. The intended application is automatic recognition of vehicle type for secure access and traffic monitoring applications, a problem not hitherto considered at such a level of accuracy. We demonstrate that a relatively simple set of features extracted from sections of car front images can be used to obtain high performance verification and recognition of vehicle type (both car model and class). We describe the approach and resulting system in full, and the results of experiments comparing a wide variety of different features. The final system is capable of recognition rates of over 93% and verification equal error rates of fewer than 5.6% when tested on over 1000 images containing 77 different classes. The system is shown to be robust for a wide range of weather and lighting conditions.