Discriminant Projective Non-Negative Matrix Factorization

Projective non-negative matrix factorization (PNMF) projects high-dimensional non-negative examples X onto a lower-dimensional subspace spanned by a non-negative basis W and considers W-T X as their coefficients, i.e., X approximate to WWT X. Since PNM

Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective

This paper addresses the task of dense non-rigid structure-from-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 non-linear deformations.Comment: 10 pages, 7 figure, 4 tables. Accepted for publication in Conference on Computer Vision and Pattern Recognition (CVPR), 2018, typos fixed and acknowledgement adde

Deformable 3-D Modelling from Uncalibrated Video Sequences

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

3D Non-Rigid Reconstruction with Prior Shape Constraints

3D non-rigid shape recovery from a single uncalibrated camera is a challenging, under-constrained problem in computer vision. Although tremendous progress has been achieved towards solving the problem, two main limitations still exist in most previous solutions. First, current methods focus on non-incremental solutions, that is, the algorithms require collection of all the measurement data before the reconstruction takes place. This methodology is inherently unsuitable for applications requiring real-time solutions. At the same time, most of the existing approaches assume that 3D shapes can be accurately modelled in a linear subspace. These methods are simple and have been proven effective for reconstructions of objects with relatively small deformations, but have considerable limitations when the deformations are large or complex. The non-linear deformations are often observed in highly flexible objects for which the use of the linear model is impractical. Note that specific types of shape variation might be governed by only a small number of parameters and therefore can be well-represented in a low dimensional manifold. The methods proposed in this thesis aim to estimate the non-rigid shapes and the corresponding camera trajectories, based on both the observations and the prior learned manifold. Firstly, an incremental approach is proposed for estimating the deformable objects. An important advantage of this method is the ability to reconstruct the 3D shape from a newly observed image and update the parameters in 3D shape space. However, this recursive method assumes the deformable shapes only have small variations from a mean shape, thus is still not feasible for objects subject to large scale deformations. To address this problem, a series of approaches are proposed, all based on non-linear manifold learning techniques. Such manifold is used as a shape prior, with the reconstructed shapes constrained to lie within the manifold. Those non-linear manifold based approaches significantly improve the quality of reconstructed results and are well-adapted to different types of shapes undergoing significant and complex deformations. Throughout the thesis, methods are validated quantitatively on 2D points sequences projected from the 3D motion capture data for a ground truth comparison, and are qualitatively demonstrated on real example of 2D video sequences. Comparisons are made for the proposed methods against several state-of-the-art techniques, with results shown for a variety of challenging deformable objects. Extensive experiments also demonstrate the robustness of the proposed algorithms with respect to measurement noise and missing data

A graphical model based solution to the facial feature point tracking problem

In this paper a facial feature point tracker that is motivated by applications such as human-computer interfaces and facial expression analysis systems is proposed. The proposed tracker is based on a graphical model framework. The facial features are tracked through video streams by incorporating statistical relations in time as well as spatial relations between feature points. By exploiting the spatial relationships between feature points, the proposed method provides robustness in real-world conditions such as arbitrary head movements and occlusions. A Gabor feature-based occlusion detector is developed and used to handle occlusions. The performance of the proposed tracker has been evaluated on real video data under various conditions including occluded facial gestures and head movements. It is also compared to two popular methods, one based on Kalman filtering exploiting temporal relations, and the other based on active appearance models (AAM). Improvements provided by the proposed approach are demonstrated through both visual displays and quantitative analysis