The estimation of 3D human pose from 2D joint locations is central to many vision problems involving the analysis of people in images and video. To address the fact that the problem is inherently ill posed, many methods impose a prior over human poses. Unfortunately these priors admit invalid poses because they do not model how joint-limits vary with pose. Here we make two key contributions. First, we collected a motion capture dataset that explores a wide range of human poses. From this we learn a pose-dependent model of joint limits that forms our prior. The dataset and the prior will be made publicly available. Second, we define a general parameterization of body pose and a new, multistage, method to estimate 3D pose from 2D joint locations that uses an over-complete dictionary of human poses. Our method shows good generalization while avoiding impossible poses. We quantitatively compare our method with recent work and show state-of-the-art results on 2D to 3D pose estimation using the CMU mocap dataset. We also show superior results on manual annotations on real images and automatic part-based detections on the Leeds sports pose dataset.

Factorization methods for computation of nonrigid structure have limited practicality, and work well only when there is large enough camera motion between frames, with long sequences and limited or no occlusions. We show that typical nonrigid structure can often be approximated well as locally rigid sub-structures in time and space. Specifically, we assume that: 1) the structure can be approximated as rigid in a short local time window and 2) some point pairs stay relatively rigid in space, maintaining a fixed distance between them during the sequence. We first use the triangulation constraints in rigid SFM over a sliding time window to get an initial estimate of the nonrigid 3D structure. We then automatically identify relatively rigid point pairs in this structure, and use their length-constancy simultaneously with triangulation constraints to refine the structure estimate. Unlike factorization methods, the structure is estimated independent of the camera motion computation, adding to the simplicity and stability of the approach. Further, local factorization inherently handles significant natural occlusions gracefully, performing much better than the state-of-the art. We show more stable and accurate results as compared to the state-of-the art on even short sequences starting from 15 frames only, containing camera rotations as small as 2 degree and up to 50% missing data.

Techniques are disclosed for generating a bilinear spatiotemporal basis model. A method includes the steps of predefining a trajectory basis for the bilinear spatiotemporal basis model, receiving three-dimensional spatiotemporal data for a training sequence, estimating a shape basis for the bilinear spatiotemporal basis model using the three-dimensional spatiotemporal data, and computing coefficients for the bilinear spatiotemporal basis model using the trajectory basis and the shape basis.

A variety of dynamic objects, such as faces, bodies, and cloth, are represented in computer graphics as a collection of moving spatial landmarks. Spatiotemporal data is inherent in a number of graphics applications including animation, simulation, and object and camera tracking. The principal modes of variation in the spatial geometry of objects are typically modeled using dimensionality reduction techniques, while concurrently, trajectory representations like splines and autoregressive models are widely used to exploit the temporal regularity of deformation. In this article, we present the bilinear spatiotemporal basis as a model that simultaneously exploits spatial and temporal regularity while maintaining the ability to generalize well to new sequences. This factorization allows the use of analytical, predefined functions to represent temporal variation (e.g., B-Splines or the Discrete Cosine Transform) resulting in efficient model representation and estimation. The model can be interpreted as representing the data as a linear combination of spatiotemporal sequences consisting of shape modes oscillating over time at key frequencies. We apply the bilinear model to natural spatiotemporal phenomena, including face, body, and cloth motion data, and compare it in terms of compaction, generalization ability, predictive precision, and efficiency to existing models. We demonstrate the application of the model to a number of graphics tasks including labeling, gap-filling, denoising, and motion touch-up.

Existing approaches to nonrigid structure from motion assume that the instantaneous 3D shape of a deforming object is a linear combination of basis shapes. These basis are object dependent and therefore have to be estimated anew for each video sequence. In contrast, we propose a dual approach to describe the evolving 3D structure in trajectory space by a linear combination of basis trajectories. We describe the dual relationship between the two approaches, showing that they both have equal power for representing 3D structure. We further show that the temporal smoothness in 3D trajectories alone can be used for recovering nonrigid structure from a moving camera. The principal advantage of expressing deforming 3D structure in trajectory space is that we can define an object independent basis. This results in a significant reduction in unknowns, and corresponding stability in estimation. We propose the use of the Discrete Cosine Transform (DCT) as the object independent basis and empirically demonstrate that it approaches Principal Component Analysis (PCA) for natural motions. We report the performance of the proposed method, quantitatively using motion capture data, and qualitatively on several video sequences exhibiting nonrigid motions including piecewise rigid motion, partially nonrigid motion (such as a facial expressions), and highly nonrigid motion (such as a person walking or dancing).

Most nonrigid objects exhibit temporal regularities in their deformations. Recently it was proposed that these regularities can be parameterized by assuming that the non- rigid structure lies in a small dimensional trajectory space. In this paper, we propose a factorization approach for 3D reconstruction from multiple static cameras under the com- pact trajectory subspace representation. Proposed factor- ization is analogous to rank-3 factorization of rigid struc- ture from motion problem, in transformed space. The benefit of our approach is that the 3D trajectory basis can be directly learned from the image observations. This also allows us to impute missing observations and denoise tracking errors without explicit estimation of the 3D structure. In contrast to standard triangulation based methods which require points to be visible in at least two cameras, our ap- proach can reconstruct points, which remain occluded even in all the cameras for quite a long time. This makes our solution especially suitable for occlusion handling in motion capture systems. We demonstrate robustness of our method on challenging real and synthetic scenarios.

In factorization approaches to nonrigid structure from motion, the 3D shape of a deforming object is usually modeled as a linear combination of a small number of basis shapes. The original approach to simultaneously estimate the shape basis and nonrigid structure exploited orthonormality constraints for metric rectification. Recently, it has been asserted that structure recovery through orthonormality constraints alone is inherently ambiguous and cannot result in a unique solution. This assertion has been accepted as conventional wisdom and is the justification of many remedial heuristics in literature. Our key contribution is to prove that orthonormality constraints are in fact sufficient to recover the 3D structure from image observations alone. We characterize the true nature of the ambiguity in using orthonormality constraints for the shape basis and show that it has no impact on structure reconstruction. We conclude from our experimentation that the primary challenge in using shape basis for nonrigid structure from motion is the difficulty in the optimization problem rather than the ambiguity in orthonormality constraints.

Existing approaches to nonrigid structure from motion assume that the instantaneous 3D shape of a deforming object is a linear combination of basis shapes, which have to be estimated anew for each video sequence. In contrast, we propose that the evolving 3D structure be described by a linear combination of basis trajectories. The principal advantage of this approach is that we do not need to estimate any basis vectors during computation. We show that generic bases over trajectories, such as the Discrete Cosine Transform (DCT) basis, can be used to compactly describe most real motions. This results in a significant reduction in unknowns, and corresponding stability in estimation. We report empirical performance, quantitatively using motion capture data, and qualitatively on several video sequences exhibiting nonrigid motions including piece-wise rigid motion, partially nonrigid motion (such as a facial expression), and highly nonrigid motion (such as a person dancing).