In defense of orthonormality constraints for nonrigid structure from motion

Akhter, Ijaz; Sheikh, Yaser; Khan, Sardaraz

doi:10.1109/cvprw.2009.5206620

Cited by 34 publications

(74 citation statements)

References 2 publications

(4 reference statements)

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“…Akhter et al made an important theoretical progress in [2] which reveals that: although the ambiguity in shape basis is inherent, the 3D shape itself can be recovered uniquely without ambiguity. In a slightly earlier paper, Hartley and Vidal proved a similar result but under perspective camera model [16].…”

Section: Related Workmentioning

confidence: 99%

A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization

2013

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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.

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Section: Related Workmentioning

confidence: 99%

A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization

2013

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“…Two sequences are used for testing, they are: cloth and an articulated human motion sequence IndianDance from CMU motion capture database. 1 Since no separate training data are provided for human motion sequence, every 10th frame is selected to build training dataset (e.g. frame 1,11,21…are 1 The data were obtained from http://mocap.cs.cmu.edu.…”

Section: Results Of Using Reduced Training Setmentioning

confidence: 99%

“…1 Since no separate training data are provided for human motion sequence, every 10th frame is selected to build training dataset (e.g. frame 1,11,21…are 1 The data were obtained from http://mocap.cs.cmu.edu. selected), whereas frames 5,15,25…are selected as a testing set.…”

Section: Results Of Using Reduced Training Setmentioning

confidence: 99%

“…As a time-varying object usually cannot arbitrarily deform, the idea of this model is to represent a deformable shape as a linear combination of basis shapes. Due to its simplicity, shape basis model has been widely used to tackle the problem of Non-Rigid Structure from Motion (NRSfM) [1,4,42]. However, the shape bases are different in each sequence, thus need to be estimated for every sequence.…”

Section: Introductionmentioning

confidence: 99%

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Robust deformable shape reconstruction from monocular video with manifold forests

Tao

Matuszewski²

2016

Machine Vision and Applications

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Existing approaches to recover structure of 3D deformable objects and camera motion parameters from an uncalibrated images assume the object's shape could be modelled well by a linear subspace. These methods have been proven effective and well suited when the deformations are relatively small, but fail to reconstruct the objects with relatively large deformations. This paper describes a novel approach for 3D non-rigid shape reconstruction, based on manifold decision forest technique. The use of this technique can be justified by noting that a specific type of shape variations might be governed by only a small number of parameters, and therefore can be well represented in a lowdimensional manifold. The key contributions of this work are the use of random decision forests for the shape manifold learning and robust metric for calculation of the re-projection error. The learned manifold defines constraints imposed on the reconstructed shapes. Due to a nonlinear structure of the learned manifold, this approach is more suitable to deal with large and complex object deformations when compared to the linear constraints. The robust metric is applied to reduce the effect of measurement outliers on the quality of the reconstruction. In many practical applications outliers cannot be completely removed and therefore the use of robust techniques is of particular practical interest. The proposed method is validated on 2D points sequences projected from the 3D motion capture data for ground truth comparison and also on real 2D video sequences. Experiments show that the newly proposed method provides better performance compared to previously proposed ones, including the robustness with respect to measurement noise, missing measurements and outliers present in the data.

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“…In [12], Xiao and Kanade pointed out that even enforcing both sets of linear metric constraints above could still lead to ambiguity, if there exist degenerate bases, which are not of full rank three. However, by exploiting the rank three constraints inherently, Akhter et al [13] analytically proved that orthonormality constraints alone are sufficient to recover the exact structure. Ambiguity solely lies in the transformation of linear basis vectors, which does not affect the 3D structure reconstruction.…”

Section: Related Workmentioning

confidence: 99%

Rotation update on manifold in probabilistic NRSFM for robust 3D face modeling

Gao

Ekenel

2015

J Image Video Proc.

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This paper focuses on recovering the 3D structure and motion of human faces from a sequence of 2D images. Based on a probabilistic model, we extensively studied the rotation constraints of the problem. Instead of imposing numerical optimizations, the inherent geometric properties of the rotation matrices are taken into account. The conventional Newton's method for optimization problems was generalized on the rotation manifold, which ultimately resolves the constraints into unconstrained optimization on the manifold. Furthermore, we also extended the algorithm to model within-individual and between-individual shape variances separately. Evaluation results give evidence to the improvement over the state-of-the-art algorithms on the Mocap-Face dataset with additive noise, as well as on the Binghamton University A 3D Facial Expression (BU-3DFE) dataset. Robustness in handling noisy data and modeling multiple subjects shows the capability of our system to deal with real-world image tracks.

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In defense of orthonormality constraints for nonrigid structure from motion

Cited by 34 publications

References 2 publications

A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization

A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization

Robust deformable shape reconstruction from monocular video with manifold forests

Rotation update on manifold in probabilistic NRSFM for robust 3D face modeling

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