Active Appearance Models (AAMs) are generative models commonly used to model faces. Another closely related type of face models are 3D Morphable Models (3DMMs). Although AAMs are 2D, they can still be used to model 3D phenomena such as faces moving across pose. We first study the representational power of AAMs and show that they can model anything a 3DMM can, but possibly require more shape parameters. We quantify the number of additional parameters required and show that 2D AAMs can generate model instances that are not possible with the equivalent 3DMM. We proceed to describe how a non-rigid structure-from-motion algorithm can be used to construct the corresponding 3D shape modes of a 2D AAM. We then show how the 3D modes can be used to constrain the AAM so that it can only generate model instances that can also be generated with the 3D modes. Finally, we propose a realtime algorithm for fitting the AAM while enforcing the constraints, creating what we call a "Combined 2D+3D AAM." 1

Abstract. We cast the problem of motion segmentation of feature trajectories as linear manifold finding problems and propose a general framework for motion segmentation under affine projections which utilizes two properties of trajectory data: geometric constraint and locality. The geometric constraint states that the trajectories of the same motion lie in a low dimensional linear manifold and different motions result in different linear manifolds; locality, by which we mean in a transformed space a data and its neighbors tend to lie in the same linear manifold, provides a cue for efficient estimation of these manifolds. Our algorithm estimates a number of linear manifolds, whose dimensions are unknown beforehand, and segment the trajectories accordingly. It first transforms and normalizes the trajectories; secondly, for each trajectory it estimates a local linear manifold through local sampling; then it derives the affinity matrix based on principal subspace angles between these estimated linear manifolds; at last, spectral clustering is applied to the matrix and gives the segmentation result. Our algorithm is general without restriction on the number of linear manifolds and without prior knowledge of the dimensions of the linear manifolds. We demonstrate in our experiments that it can segment a wide range of motions including independent, articulated, rigid, non-rigid, degenerate, non-degenerate or any combination of them. In some highly challenging cases where other state-of-the-art motion segmentation algorithms may fail, our algorithm gives expected results. 2 1

This paper describes methods for recovering time-varying shape and motion of non-rigid 3D objects from uncalibrated 2D point tracks. For example, given a video recording of a talking person, we would like to estimate the 3D shape of the face at each instant, and learn a model of facial deformation. Time-varying shape is modeled as a rigid transformation combined with a non-rigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed, and thus additional assumptions about deformations are required. We first suggest restricting shapes to lie within a lowdimensional subspace, and describe estimation algorithms. However, this restriction alone is insufficient to constrain reconstruction. To address these problems, we propose a reconstruction method using a Probabilistic Principal Components Analysis (PPCA) shape model, and an estimation algorithm that simultaneously estimates 3D shape and motion for each instant, learns the PPCA model parameters, and robustly fills-in missing data points. We then extend the model to model temporal dynamics in object shape, allowing the algorithm to robustly handle severe cases of missing data.

We consider the problem of modeling a scene containing multiple dynamic textures undergoing multiple rigid-body motions, e.g., a video sequence of water taken by a rigidly moving camera. We propose to model each moving dynamic texture with a time varying linear dynamical system (LDS) plus a 2-D translational motion model. We first consider a scene with a single moving dynamic texture and show how to simultaneously learn the parameters of the time varying LDS as well as the optical flow of the scene using the socalled dynamic texture constancy constraint (DTCC). We then consider a scene with multiple non-moving dynamic textures and show that learning the parameters of each time invariant LDS as well as their region of support is equivalent to clustering data living in multiple subspaces. We solve this problem with a combination of PCA and GPCA. Finally, we consider a scene with multiple moving dynamic textures, and show how to simultaneously learn the parameters of multiple time varying LDS and multiple 2-D translational models, by clustering data living in multiple dynamically evolving subspaces. We test our approach on sequences of flowers, water, grass, and a beating heart. 1.

Abstract—Three-dimensional detection and shape recovery of a nonrigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data. Here, we introduce an approach to creating such models for deformable 3D surfaces. We exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets. We use this set of angles to create a representative set of potential shapes, which we feed to a simple dimensionality reduction technique to produce low-dimensional 3D deformation models. We show that these models can be used to accurately model a wide range of deforming 3D surfaces from video sequences acquired under realistic conditions. Index Terms—3D shape recovery, deformation model, nonrigid surfaces. 1

The non-rigid motion of a driver's head (i.e. the motion of their mouth, eye-brows, cheeks, etc) can tell us a lot about their mental state; e.g. whether they are drowsy, alert, aggressive, comfortable, tense, distracted, etc. In this paper, we describe our recent research on nonrigid face tracking. In particular, we present both 2D and 3D algorithms for tracking the non-rigid motion of the driver's head using an Active Appearance Model. Both algorithms operate at over 200 frames per second. We also present algorithms for converting a 2D model into a 3D model and for fitting with occlusion and large pose variation.

Monocular gaze estimation is usually performed by locating the pupils, and the inner and outer eye corners in the image of the driver’s head. Of these feature points, the eye corners are just as important, and perhaps harder to detect, than the pupils. The eye corners are usually found using local feature detectors and trackers. In this paper, we describe a monocular driver gaze tracking system which uses a global head model, specifically an Active Appearance Model (AAM), to track the whole head. From the AAM, the eye corners, eye region, and head pose are robustly extracted and then used to estimate the gaze.

Reconstruction of 3D structures from uncalibrated image sequences has a wealthy history. Most work has been focused on rigid objects or static scenes. This paper studies the problem of perspective reconstruction of deformable structures such as dynamic scenes from an uncalibrated image sequence. The task requires decomposing the image measurements into a composition of three factors: 3D deformable structures, rigid rotations and translations, and intrinsic camera parameters. We develop a factorization algorithm that consists of two steps. In the first step we recover the projective depths iteratively using the sub-space constraints embedded in the image measurements of the deformable structures. In the second step, we scale the image measurements by the reconstructed projective depths. We then extend the linear closed-form solution for weakperspective reconstruction [23] to factorize the scaled measurements and simultaneously reconstruct the deformable shapes and underlying shape model, the rigid motions, and the varying camera parameters such as focal lengths. The accuracy and robustness of the proposed method is demonstrated quantitatively on synthetic data and qualitatively on real image sequences. 1.

Abstract. We present a closed form solution to the nonrigid shape and motion (NRSM) problem from point correspondences in multiple perspective uncalibrated views. Under the assumption that the nonrigid object deforms as a linear combination of K rigid shapes, we show that the NRSM problem can be viewed as a reconstruction problem from multiple projections from P 3K to P 2. Therefore, one can linearly solve for the projection matrices by factorizing a multifocal tensor. However, this projective reconstruction in P 3K does not satisfy the constraints of the NRSM problem, because it is computed only up to a projective transformation in P 3K. Our key contribution is to show that, by exploiting algebraic dependencies among the entries of the projection matrices, one can upgrade the projective reconstruction to determine the affine configuration of the points in R 3, and the motion of the camera relative to their centroid. Moreover, if K ≥ 2, then either by using calibrated cameras, or by assuming a camera with fixed internal parameters, it is possible to compute the Euclidean structure by a closed form method. 1

This paper studies the problem of 3D non-rigid shape and motion recovery from a monocular video sequence, under the degenerate deformations. The shape of a deformable object is regarded as a linear combination of certain shape bases. When the bases are non-degenerate, i.e. of full rank 3, a closed-form solution exists by enforcing linear constraints on both the camera rotation and the shape bases [18]. In practice, degenerate deformations occur often, i.e. some bases are of rank 1 or 2. For example, cars moving or pedestrians walking independently on a straight road refer to rank-1 deformations of the scene. This paper quantitatively shows that, when the shape is composed of only rank- 3 and rank-1 bases, i.e. the 3D points either are static or independently move along straight lines, the linear rotation and basis constraints are sufficient to achieve a unique solution. When the shape bases contain rank-2 ones, imposing only the linear constraints results in an ambiguous solution space. In such cases, we propose an alternating linear approach that imposes the positive semi-definite constraint to determine the desired solution in the solution space. The performance of the approach is evaluated quantitatively on synthetic data and qualitatively on real videos.