We present a statistical model for @math D human faces in varying expression, which decomposes the surface of the face using a wavelet transform, and learns many localized, decorrelated multilinear models on the resulting coefficients. Using this model we are able to reconstruct faces from noisy and occluded @math D face scans, and facial motion sequences. Accurate reconstruction of face shape is important for applications such as tele-presence and gaming. The localized and multi-scale nature of our model allows for recovery of fine-scale detail while retaining robustness to severe noise and occlusion, and is computationally efficient and scalable. We validate these properties experimentally on challenging data in the form of static scans and motion sequences. We show that in comparison to a global multilinear model, our model better preserves fine detail and is computationally faster, while in comparison to a localized PCA model, our model better handles variation in expression, is faster, and allows us to fix identity parameters for a given subject.
Many statistical models have been used to analyze human faces. The first statistical model for the analysis of @math D faces was proposed by Blanz and Vetter @cite_17 . This model is called the morphable model, and uses Principal Component Analysis (PCA) to analyze shape and texture of registered faces, mainly in neutral expression. It is applied to reconstruct @math D facial shapes from images @cite_17 and @math D face scans @cite_29 @cite_9 . @cite_6 extend the morphable model to consider expressions, by combining it with a PCA model for expression offsets with respect to the neutral expression geometry. An alternative way to incorporate expression changes is to use use a multilinear model, which separates identity and expression variations. This model has been used to modify expressions in videos @cite_21 @cite_23 @cite_1 , or to register and analyze @math D motion sequences @cite_15 . Multilinear models are mathematically equivalent to TensorFaces @cite_24 applied to @math D data rather than images, and provide an effective way to capture both identity and expression variations, and thus in Section we compare to a global multilinear model and show that our model better captures local geometric detail.
@cite_9 @cite_29 @cite_21 @cite_1 @cite_6 @cite_24 @cite_23 @cite_15 @cite_17
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Statistical methods are of paramount importance in discovering the modes of variation in visual data. The Principal Component Analysis (PCA) is probably the most prominent method for extracting a single mode of variation in the data. However, in practice, several factors contribute to the appearance of visual objects including pose, illumination, and deformation, to mention a few. To extract these modes of variations from visual data, several supervised methods, such as the TensorFaces relying on multilinear (tensor) decomposition have been developed. The main drawbacks of such methods is that they require both labels regarding the modes of variations and the same number of samples under all modes of variations (e.g., the same face under different expressions, poses etc.). Therefore, their applicability is limited to well-organised data, usually captured in well-controlled conditions. In this paper, we propose a novel general multilinear matrix decomposition method that discovers the multilinear structure of possibly incomplete sets of visual data in unsupervised setting (i.e., without the presence of labels). We also propose extensions of the method with sparsity and low-rank constraints in order to handle noisy data, captured in unconstrained conditions. Besides that, a graph-regularised variant of the method is also developed in order to exploit available geometric or label information for some modes of variations. We demonstrate the applicability of the proposed method in several computer vision tasks, including Shape from Shading (SfS) (in the wild and with occlusion removal), expression transfer, and estimation of surface normals from images captured in the wild. The "interpretation through synthesis" approach to analyze face images, particularly Active Appearance Models (AAMs) method, has become one of the most successful face modeling approaches over the last two decades. AAM models have ability to represent face images through synthesis using a controllable parameterized Principal Component Analysis (PCA) model. However, the accuracy and robustness of the synthesized faces of AAM are highly depended on the training sets and inherently on the generalizability of PCA subspaces. This paper presents a novel Deep Appearance Models (DAMs) approach, an efficient replacement for AAMs, to accurately capture both shape and texture of face images under large variations. In this approach, three crucial components represented in hierarchical layers are modeled using the Deep Boltzmann Machines (DBM) to robustly capture the variations of facial shapes and appearances. DAMs are therefore superior to AAMs in inferencing a representation for new face images under various challenging conditions. The proposed approach is evaluated in various applications to demonstrate its robustness and capabilities, i.e. facial super-resolution reconstruction, facial off-angle reconstruction or face frontalization, facial occlusion removal and age estimation using challenging face databases, i.e. Labeled Face Parts in the Wild (LFPW), Helen and FG-NET. Comparing to AAMs and other deep learning based approaches, the proposed DAMs achieve competitive results in those applications, thus this showed their advantages in handling occlusions, facial representation, and reconstruction. Research in the areas of 3-D face recognition and 3-D facial expression analysis has intensified in recent years. However, most research has been focused on 3-D static data analysis. In this paper, we investigate the facial analysis problem using dynamic 3-D face model sequences. One of the major obstacles for analyzing such data is the lack of correspondences of features due to the variable number of vertices across individual models or 3-D model sequences. In this paper, we present an effective approach for establishing vertex correspondences using a tracking-model-based approach for vertex registration, coarse-to-fine model adaptation, and vertex motion trajectory (called vertex flow) estimation. We propose to establish correspondences across frame models based on a 2-D intermediary, which is generated using conformal mapping and a generic model adaptation algorithm. Based on our newly created 3-D dynamic face database, we also propose to use a spatiotemporal hidden Markov model (ST-HMM) that incorporates 3-D surface feature characterization to learn the spatial and temporal information of faces. The advantage of using 3-D dynamic data for face recognition has been evaluated by comparing our approach to three conventional approaches: 2-D-video-based temporal HMM model, conventional 2-D-texture-based approach (e.g., Gabor-wavelet-based approach), and static 3-D-model-based approaches. To further evaluate the usefulness of vertex flow and the adapted model, we have also applied a spatial-temporal face model descriptor for facial expression classification based on dynamic 3-D model sequences. The “interpretation through synthesis”, i.e. Active Appearance Models (AAMs) method, has received considerable attention over the past decades. It aims at “explaining” face images by synthesizing them via a parameterized model of appearance. It is quite challenging due to appearance variations of human face images, e.g. facial poses, occlusions, lighting, low resolution, etc. Since these variations are mostly non-linear, it is impossible to represent them in a linear model, such as Principal Component Analysis (PCA). This paper presents a novel Deep Appearance Models (DAMs) approach, an efficient replacement for AAMs, to accurately capture both shape and texture of face images under large variations. In this approach, three crucial components represented in hierarchical layers are modeled using the Deep Boltzmann Machines (DBM) to robustly capture the variations of facial shapes and appearances. DAMs are therefore superior to AAMs in inferring a representation for new face images under various challenging conditions. In addition, DAMs have ability to generate a compact set of parameters in higher level representation that can be used for classification, e.g. face recognition and facial age estimation. The proposed approach is evaluated in facial image reconstruction, facial super-resolution on two databases, i.e. LFPW and Helen. It is also evaluated on FG-NET database for the problem of age estimation.