Super-Resolution of Face ImagesCS536 Machine LearningiCML 2003Rui HuangIntroduction• Main Idea: Learning-Based Super-Resolution– W.T. Freeman, E.C. Pasztor, & O.T. Carmichael (2000). Learning Low-Level Vision. International Journal of Computer Vision, Vol. 40, No. 1.Introduction cont’d• What we do in this paper:– Apply this learning-based super-resolution method to human face images.– Compare it with several interpolation-based super-resolution methods.• Visual comparison.• RMS (Root Mean Square) intensity error.– Performance (RMS error) vs. amount of training data.– A new face recognition method.Modeling high-resolution and low-resolution image patches as nodes in a Markov Random Fields (MRF) modellow-resolutionpatchesΦ(xi, yi)Ψ(xi, xj)high-resolutionpatchesTwo phases to solve this super-resolution problem:• Learning– Learning the parameters (Φ(xi,yi), Ψ(xi, xj)) of the MRF model from the training data.• Inference– Inferring the high-resolution image corresponding to the given low-resolution image using the Belief Propagation (BP) algorithm.yixiy(xi)Learning compatibility function Φ(xi,yi):Assume Gaussian noise takes you from observed image patch to synthetic sampleLearning phase:dxixjLearning compatibility function Ψ(xi, xj):Assume overlapped regions, d, of high-resolution patches differ by Gaussian observation noise:Learning phase:BP is an inference method proposed by Pearl (1988)to efficiently estimate Bayesian beliefs in the network by the way of iteratively passing messages between neighbors.Inference phase: Belief Propagation (BP)()\() (, )(, ) ()jjkii ij jj jjxkNjiMxxxxyMx∈=Ψ Φ∑∏()() (,) ()kjj jj jjkNjbx xyMx∈=Φ∏ˆargmax ( )jjjjxxbx=(a) High-resolution images(b) Learning-based method(c) Nearest Neighbor Interpolation(d) Bilinear Interpolation(e) Bicubic InterpolationSuper-Resolution-based Face Recognition14 8 8 14 9 3 8 8 86 8 8 8 8 8 8 8 88 8 8 8 8 8 8 12 88 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 88 8 8 8 8 8 8 8 88 8 8 8 8 8 11 8 810 8 8 8 8 8 7 8 82 2 8 8 8 8 8 8 1110 13 8 8 8 8 8 8 113 8 3 8 8 8 8 5 2From the result of the BP algorithm, we can easily know the identity of each high-frequency patch
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