Bayesian Tensor Approach for 3-D Face Modeling

Sch. of Comput. Eng., Nanyang Technol. Univ., Singapore
IEEE Transactions on Circuits and Systems for Video Technology (Impact Factor: 2.62). 11/2008; 18(10):1397 - 1410. DOI: 10.1109/TCSVT.2008.2002825
Source: IEEE Xplore


Effectively modeling a collection of three-dimensional (3-D) faces is an important task in various applications, especially facial expression-driven ones, e.g., expression generation, retargeting, and synthesis. These 3-D faces naturally form a set of second-order tensors-one modality for identity and the other for expression. The number of these second-order tensors is three times of that of the vertices for 3-D face modeling. As for algorithms, Bayesian data modeling, which is a natural data analysis tool, has been widely applied with great success; however, it works only for vector data. Therefore, there is a gap between tensor-based representation and vector-based data analysis tools. Aiming at bridging this gap and generalizing conventional statistical tools over tensors, this paper proposes a decoupled probabilistic algorithm, which is named Bayesian tensor analysis (BTA). Theoretically, BTA can automatically and suitably determine dimensionality for different modalities of tensor data. With BTA, a collection of 3-D faces can be well modeled. Empirical studies on expression retargeting also justify the advantages of BTA.

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    • "Consequently, a growing number of face image-based applications have been developed and investigated. These include face detection (Zhang and Zhang 2010), alignment (Liu 2009), tracking (Ong and Bowden 2011), modeling (Tao et al. 2008), and recognition (Chellappa et al. 1995; Zhao et al. 2003) for security control, surveillance monitoring, authentication, biometrics, digital entertainment and rendered services for a legitimate user only, and age synthesis and estimation (Fu et al. 2010) for explosively emerging real-world applications such as forensic art, electronic customer relationship management , and cosmetology. "
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    ABSTRACT: This paper comprehensively surveys the development of face hallucination (FH), including both face super-resolution and face sketch-photo synthesis techniques. Indeed, these two techniques share the same objective of inferring a target face image (e.g. high-resolution face image, face sketch and face photo) from a corresponding source input (e.g. low-resolution face image, face photo and face sketch). Considering the critical role of image interpretation in modern intelligent systems for authentication, surveillance, law enforcement, security control, and entertainment, FH has attracted growing attention in recent years. Existing FH methods can be grouped into four categories: Bayesian inference approaches, subspace learning approaches, a combination of Bayesian inference and subspace learning approaches, and sparse representation-based approaches. In spite of achieving a certain level of development, FH is limited in its success by complex application conditions such as variant illuminations, poses, or views. This paper provides a holistic understanding and deep insight into FH, and presents a comparative analysis of representative methods and promising future directions.
    International Journal of Computer Vision 09/2013; 106(1). DOI:10.1007/s11263-013-0645-9 · 3.81 Impact Factor
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    • "As a result, USP is alleviated [42]. It has been widely applied to remote sensing [56], tracking [50], face recognition [29], video semantic analysis [15], 3-D face modeling [45], probabilistic graphical models [46], [47], and feature selection [43]. However, USP in multivariate regression problem has seldom been dealt with. "
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    ABSTRACT: Conventional regression methods, such as multivariate linear regression (MLR) and its extension principal component regression (PCR), deal well with the situations that the data are of the form of low-dimensional vector. When the dimension grows higher, it leads to the under sample problem (USP): the dimensionality of the feature space is much higher than the number of training samples. However, little attention has been paid to such a problem. This paper first adopts an in-depth investigation to the USP in PCR, which answers three questions: 1) Why is USP produced? 2) What is the condition for USP, and 3) How is the influence of USP on regression. With the help of the above analysis, the principal components selection problem of PCR is presented. Subsequently, to address the problem of PCR, a multivariate multilinear regression (MMR) model is proposed which gives a substitutive solution to MLR, under the condition of multilinear objects. The basic idea of MMR is to transfer the multilinear structure of objects into the regression coefficients as a constraint. As a result, the regression problem is reduced to find two low-dimensional coefficients so that the principal components selection problem is avoided. Moreover, the sample size needed for solving MMR is greatly reduced so that USP is alleviated. As there is no closed-form solution for MMR, an alternative projection procedure is designed to obtain the regression matrices. For the sake of completeness, the analysis of computational cost and the proof of convergence are studied subsequently. Furthermore, MMR is applied to model the fitting procedure in the active appearance model (AAM). Experiments are conducted on both the carefully designed synthesizing data set and AAM fitting databases verified the theoretical analysis.
    IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics: a publication of the IEEE Systems, Man, and Cybernetics Society 06/2012; 42(6). DOI:10.1109/TSMCB.2012.2195171 · 6.22 Impact Factor
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    • "Let us define a tensor T in R M ×N ×S×D×K and then unfold T along mode 1 and mode 2 simultaneously. Thus, T becomes a tensor field [5], [14], [21], [27], [28], [31], [34], [37], [38] with elements in the form of a three-order tensor in R S×D×K , and each element corresponds to a pixel in the image to be segmented. There is an evolving curve C in Ω ∈ R "
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    ABSTRACT: This paper presents a new unified level set model for multiple regional image segmentation. This model builds a unified tensor representation for comprehensively depicting each pixel in the image to be segmented, by which the image aligns itself with a tensor field composed of the elements in form of high order tensor. Then the multi-phase level set functions are evolved in this tensor field by introducing a new weighted distance function. When the evolution converges, the tensor field is partitioned, and meanwhile the image is segmented. The proposed model has following main advantages. Firstly, the unified tensor representation integrates the information from Gaussian smoothed image, which results the model is robust against noise, especially the salt and pepper noise. Secondly, the local geometric features involved into the unified representation increase the weight of boundaries in energy functional, which makes the model more easily to detect the edges in the image and obtain better performance on non-homogenous images. Thirdly, the model offers a general formula for energy functional which can deal with the data type varying from scalar to vector then to tensor, and this formula also unifies single and multi-phase level set methods. We applied the proposed method to synthetic, medical and natural images respectively and obtained promising performance. KeywordsGabor filter bank–geometric active contour–tensor subspace analysis–image segmentation–level set method–partial differentialequation
    04/2011: pages 217-238;
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