Super-Resolution of Face Images in .NET

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Super-Resolution of Face Images
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The methods for face super-resolution are mainly classi ed into two approaches: statistical inference-based approaches and subspace-based approaches. To reconstruct a high-resolution image from its low-resolution counterpart, we should estimate some parameters or features in a high-resolution image space. To solve these inference problems, statistical inference-based approaches have been applied. Statistical inference-based approaches aim to nd a high-resolution image which has a maximum probability for a given low-resolution image by Bayesian or other statistical formulations. The maximum a posteriori (MAP) estimator has been one of the most widely used solution for face super-resolution [1, 8, 9]. Baker and Kanade [1, 6] developed a face hallucination method using a Bayesian formulation and image pyramids such as Gaussian, Laplacian, and feature pyramids. This approach infers the high-frequency components from a parent structure based on training samples. Finally, the high-resolution image in the Gaussian pyramid is inferred pixel by pixel so as to maximize the posterior probability given the low-resolution image. Next, subspace-based approaches are based on the assumption that a highresolution image and its low-resolution counterpart have similar coef cients, features, or distributions in the high- and low-resolution image spaces. So, the subspaces such as eigenfaces obtained by principal component analysis [10] in the two spaces are learned and a high-resolution image is represented by the similarity between the two subspaces. Wang and Tang [11, 12] developed an ef cient face hallucination algorithm using an eigentransformation algorithm. However, all these methods have not utilized the neighborhood relationship in the distribution of face images. Facial images change appearance due to multiple factors such as pose variations, lighting acquisition conditions, and facial expressions. Most of the previous work has not considered this distribution and dealt with all the diverse images equally. In the previous work of face image analysis using manifold learning methods, it has been shown that face images lie on a manifold [13 16]. Also, it has been demonstrated that the variation of a certain facial factor such as pose or expression makes a submanifold in the manifold structure [7, 17]. Thus, it is expected that manifold learning methods can improve the tasks requiring face image analysis, such as face recognition, super-resolution, or face synthesis. Based on this idea, Chang et al. [18] developed the neighbor embedding algorithm for super-resolution of general images. They assume that the local distribution structure in sample space is preserved in smoothing and down-sampling, and they apply one of the manifold learning methods, locally linear embedding (LLE) [13]. Statistical inference-based approaches and subspace-based approaches have often been merged to solve face super-resolution problems. Liu et al. [9, 19] proposed a two-step approach integrating both the global parametric modeling and the local nonparametric modeling of face images. Their method is based on the inference using the MAP estimator and Markov network, but PCA is also applied to calculating the subspace of the high-resolution image space. Also, Park and Savvides [20, 21] applied the subspaces and features of locality preserving projections (LPP) [15] for their novel face super-resolution method, which is also employed the traditional MAP estimator.
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12.2 Statistical Inference-Based Approaches
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In this chapter, several state-of-the-art methods for face super-resolution are introduced. In particular, we introduce remarkable methods focusing on enhancing the resolution of face images, not all kinds of images. We demonstrate how each method trains and models the characteristics of face images. The rest of this chapter is organized as follows. In Section 12.2 we brie y introduce statistical inference-based approaches for face super-resolution. First of all, we present the MAP estimator, which allows us to make inferences simply and effectively since various super-resolution methods have applied it. As illustrations, we brie y show two methods proposed by Baker and Kanade [1, 6] and Liu et al. [9, 19]. In Section 12.3 the subspace-based approaches for face super-resolution are presented with the methods using PCA [11, 12], LLE [18], and LPP [20, 21]. In Section 12.4 the state-of-the-art methods for face super-resolution are compared to a baseline method. Finally, Section 12.5 concludes this chapter.
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