Automatic construction of robust spherical harmonic subspaces

In this paper we propose a method to automatically recover a class specific low dimensional spherical harmonic basis from a set of in-the-wild facial images. We combine existing techniques for uncalibrated photometric stereo and low rank matrix decompositions in order to robustly recover a combined model of shape and identity. We build this basis without aid from a 3D model and show how it can be combined with recent efficient sparse facial feature localisation techniques to recover dense 3D facial shape. Unlike previous works in the area, our method is very efficient and is an order of magnitude faster to train, taking only a few minutes to build a model with over 2000 images. Furthermore, it can be used for real-time recovery of facial shape

Automatic construction of robust spherical harmonic subspaces

In this paper we propose a method to automatically recover a class specific low dimensional spherical harmonic basis from a set of in-the-wild facial images. We combine existing techniques for uncalibrated photometric stereo and low rank matrix decompositions in order to robustly recover a combined model of shape and identity. We build this basis without aid from a 3D model and show how it can be combined with recent efficient sparse facial feature localisation techniques to recover dense 3D facial shape. Unlike previous works in the area, our method is very efficient and is an order of magnitude faster to train, taking only a few minutes to build a model with over 2000 images. Furthermore, it can be used for real-time recovery of facial shape

Single View Reconstruction for Human Face and Motion with Priors

Single view reconstruction is fundamentally an under-constrained problem. We aim to develop new approaches to model human face and motion with model priors that restrict the space of possible solutions. First, we develop a novel approach to recover the 3D shape from a single view image under challenging conditions, such as large variations in illumination and pose. The problem is addressed by employing the techniques of non-linear manifold embedding and alignment. Specifically, the local image models for each patch of facial images and the local surface models for each patch of 3D shape are learned using a non-linear dimensionality reduction technique, and the correspondences between these local models are then learned by a manifold alignment method. Local models successfully remove the dependency of large training databases for human face modeling. By combining the local shapes, the global shape of a face can be reconstructed directly from a single linear system of equations via least square. Unfortunately, this learning-based approach cannot be successfully applied to the problem of human motion modeling due to the internal and external variations in single view video-based marker-less motion capture. Therefore, we introduce a new model-based approach for capturing human motion using a stream of depth images from a single depth sensor. While a depth sensor provides metric 3D information, using a single sensor, instead of a camera array, results in a view-dependent and incomplete measurement of object motion. We develop a novel two-stage template fitting algorithm that is invariant to subject size and view-point variations, and robust to occlusions. Starting from a known pose, our algorithm first estimates a body configuration through temporal registration, which is used to search the template motion database for a best match. The best match body configuration as well as its corresponding surface mesh model are deformed to fit the input depth map, filling in the part that is occluded from the input and compensating for differences in pose and body-size between the input image and the template. Our approach does not require any makers, user-interaction, or appearance-based tracking. Experiments show that our approaches can achieve good modeling results for human face and motion, and are capable of dealing with variety of challenges in single view reconstruction, e.g., occlusion

Phenomenological modeling of image irradiance for non-Lambertian surfaces under natural illumination.

Various vision tasks are usually confronted by appearance variations due to changes of illumination. For instance, in a recognition system, it has been shown that the variability in human face appearance is owed to changes to lighting conditions rather than person\u27s identity. Theoretically, due to the arbitrariness of the lighting function, the space of all possible images of a fixed-pose object under all possible illumination conditions is infinite dimensional. Nonetheless, it has been proven that the set of images of a convex Lambertian surface under distant illumination lies near a low dimensional linear subspace. This result was also extended to include non-Lambertian objects with non-convex geometry. As such, vision applications, concerned with the recovery of illumination, reflectance or surface geometry from images, would benefit from a low-dimensional generative model which captures appearance variations w.r.t. illumination conditions and surface reflectance properties. This enables the formulation of such inverse problems as parameter estimation. Typically, subspace construction boils to performing a dimensionality reduction scheme, e.g. Principal Component Analysis (PCA), on a large set of (real/synthesized) images of object(s) of interest with fixed pose but different illumination conditions. However, this approach has two major problems. First, the acquired/rendered image ensemble should be statistically significant vis-a-vis capturing the full behavior of the sources of variations that is of interest, in particular illumination and reflectance. Second, the curse of dimensionality hinders numerical methods such as Singular Value Decomposition (SVD) which becomes intractable especially with large number of large-sized realizations in the image ensemble. One way to bypass the need of large image ensemble is to construct appearance subspaces using phenomenological models which capture appearance variations through mathematical abstraction of the reflection process. In particular, the harmonic expansion of the image irradiance equation can be used to derive an analytic subspace to represent images under fixed pose but different illumination conditions where the image irradiance equation has been formulated in a convolution framework. Due to their low-frequency nature, irradiance signals can be represented using low-order basis functions, where Spherical Harmonics (SH) has been extensively adopted. Typically, an ideal solution to the image irradiance (appearance) modeling problem should be able to incorporate complex illumination, cast shadows as well as realistic surface reflectance properties, while moving away from the simplifying assumptions of Lambertian reflectance and single-source distant illumination. By handling arbitrary complex illumination and non-Lambertian reflectance, the appearance model proposed in this dissertation moves the state of the art closer to the ideal solution. This work primarily addresses the geometrical compliance of the hemispherical basis for representing surface reflectance while presenting a compact, yet accurate representation for arbitrary materials. To maintain the plausibility of the resulting appearance, the proposed basis is constructed in a manner that satisfies the Helmholtz reciprocity property while avoiding high computational complexity. It is believed that having the illumination and surface reflectance represented in the spherical and hemispherical domains respectively, while complying with the physical properties of the surface reflectance would provide better approximation accuracy of image irradiance when compared to the representation in the spherical domain. Discounting subsurface scattering and surface emittance, this work proposes a surface reflectance basis, based on hemispherical harmonics (HSH), defined on the Cartesian product of the incoming and outgoing local hemispheres (i.e. w.r.t. surface points). This basis obeys physical properties of surface reflectance involving reciprocity and energy conservation. The basis functions are validated using analytical reflectance models as well as scattered reflectance measurements which might violate the Helmholtz reciprocity property (this can be filtered out through the process of projecting them on the subspace spanned by the proposed basis, where the reciprocity property is preserved in the least-squares sense). The image formation process of isotropic surfaces under arbitrary distant illumination is also formulated in the frequency space where the orthogonality relation between illumination and reflectance bases is encoded in what is termed as irradiance harmonics. Such harmonics decouple the effect of illumination and reflectance from the underlying pose and geometry. Further, a bilinear approach to analytically construct irradiance subspace is proposed in order to tackle the inherent problem of small-sample-size and curse of dimensionality. The process of finding the analytic subspace is posed as establishing a relation between its principal components and that of the irradiance harmonics basis functions. It is also shown how to incorporate prior information about natural illumination and real-world surface reflectance characteristics in order to capture the full behavior of complex illumination and non-Lambertian reflectance. The use of the presented theoretical framework to develop practical algorithms for shape recovery is further presented where the hitherto assumed Lambertian assumption is relaxed. With a single image of unknown general illumination, the underlying geometrical structure can be recovered while accounting explicitly for object reflectance characteristics (e.g. human skin types for facial images and teeth reflectance for human jaw reconstruction) as well as complex illumination conditions. Experiments on synthetic and real images illustrate the robustness of the proposed appearance model vis-a-vis illumination variation. Keywords: computer vision, computer graphics, shading, illumination modeling, reflectance representation, image irradiance, frequency space representations, {hemi)spherical harmonics, analytic bilinear PCA, model-based bilinear PCA, 3D shape reconstruction, statistical shape from shading

Subspace Representations for Robust Face and Facial Expression Recognition

Analyzing human faces and modeling their variations have always been of interest to the computer vision community. Face analysis based on 2D intensity images is a challenging problem, complicated by variations in pose, lighting, blur, and non-rigid facial deformations due to facial expressions. Among the different sources of variation, facial expressions are of interest as important channels of non-verbal communication. Facial expression analysis is also affected by changes in view-point and inter-subject variations in performing different expressions. This dissertation makes an attempt to address some of the challenges involved in developing robust algorithms for face and facial expression recognition by exploiting the idea of proper subspace representations for data. Variations in the visual appearance of an object mostly arise due to changes in illumination and pose. So we first present a video-based sequential algorithm for estimating the face albedo as an illumination-insensitive signature for face recognition. We show that by knowing/estimating the pose of the face at each frame of a sequence, the albedo can be efficiently estimated using a Kalman filter. Then we extend this to the case of unknown pose by simultaneously tracking the pose as well as updating the albedo through an efficient Bayesian inference method performed using a Rao-Blackwellized particle filter. Since understanding the effects of blur, especially motion blur, is an important problem in unconstrained visual analysis, we then propose a blur-robust recognition algorithm for faces with spatially varying blur. We model a blurred face as a weighted average of geometrically transformed instances of its clean face. We then build a matrix, for each gallery face, whose column space spans the space of all the motion blurred images obtained from the clean face. This matrix representation is then used to define a proper objective function and perform blur-robust face recognition. To develop robust and generalizable models for expression analysis one needs to break the dependence of the models on the choice of the coordinate frame of the camera. To this end, we build models for expressions on the affine shape-space (Grassmann manifold), as an approximation to the projective shape-space, by using a Riemannian interpretation of deformations that facial expressions cause on different parts of the face. This representation enables us to perform various expression analysis and recognition algorithms without the need for pose normalization as a preprocessing step. There is a large degree of inter-subject variations in performing various expressions. This poses an important challenge on developing robust facial expression recognition algorithms. To address this challenge, we propose a dictionary-based approach for facial expression analysis by decomposing expressions in terms of action units (AUs). First, we construct an AU-dictionary using domain experts' knowledge of AUs. To incorporate the high-level knowledge regarding expression decomposition and AUs, we then perform structure-preserving sparse coding by imposing two layers of grouping over AU-dictionary atoms as well as over the test image matrix columns. We use the computed sparse code matrix for each expressive face to perform expression decomposition and recognition. Most of the existing methods for the recognition of faces and expressions consider either the expression-invariant face recognition problem or the identity-independent facial expression recognition problem. We propose joint face and facial expression recognition using a dictionary-based component separation algorithm (DCS). In this approach, the given expressive face is viewed as a superposition of a neutral face component with a facial expression component, which is sparse with respect to the whole image. This assumption leads to a dictionary-based component separation algorithm, which benefits from the idea of sparsity and morphological diversity. The DCS algorithm uses the data-driven dictionaries to decompose an expressive test face into its constituent components. The sparse codes we obtain as a result of this decomposition are then used for joint face and expression recognition

{3D} Morphable Face Models -- Past, Present and Future

In this paper, we provide a detailed survey of 3D Morphable Face Models over the 20 years since they were first proposed. The challenges in building and applying these models, namely capture, modeling, image formation, and image analysis, are still active research topics, and we review the state-of-the-art in each of these areas. We also look ahead, identifying unsolved challenges, proposing directions for future research and highlighting the broad range of current and future applications

State of the Art in Dense Monocular Non-Rigid 3D Reconstruction

3D reconstruction of deformable (or non-rigid) scenes from a set of monocular 2D image observations is a long-standing and actively researched area of computer vision and graphics. It is an ill-posed inverse problem, since--without additional prior assumptions--it permits infinitely many solutions leading to accurate projection to the input 2D images. Non-rigid reconstruction is a foundational building block for downstream applications like robotics, AR/VR, or visual content creation. The key advantage of using monocular cameras is their omnipresence and availability to the end users as well as their ease of use compared to more sophisticated camera set-ups such as stereo or multi-view systems. This survey focuses on state-of-the-art methods for dense non-rigid 3D reconstruction of various deformable objects and composite scenes from monocular videos or sets of monocular views. It reviews the fundamentals of 3D reconstruction and deformation modeling from 2D image observations. We then start from general methods--that handle arbitrary scenes and make only a few prior assumptions--and proceed towards techniques making stronger assumptions about the observed objects and types of deformations (e.g. human faces, bodies, hands, and animals). A significant part of this STAR is also devoted to classification and a high-level comparison of the methods, as well as an overview of the datasets for training and evaluation of the discussed techniques. We conclude by discussing open challenges in the field and the social aspects associated with the usage of the reviewed methods.Comment: 25 page