__Keywords:__superresolution face video sequence multiscale motion estimation fast superresolution method

A.V. Nasonov, A.S. Krylov, O.S. Ushmaev

An application of general approach of video sequence superresolution to image enhancement is considered in this work. It is proposed to use several frames to obtain single image with a better quality instead of performing face recognition for every frame. High quality superresolution problem and fast superresolution problem are posed.
General superresolution problem is mathematically modeled by a set of equations, one equation per each low resolution frame . Every equation represents a condition that an application of downsampling with taking into account the motion to reconstructed high-resolution image results in low resolution frames :
where is the downsampling operator. This operator performs low-pass filtering modeled as a convolution with Gauss filter followed by decimation operator . This problem does not have an explicit solution. Another formulations are used, subject to the considered problem.
The problem of high quality superresolution is posed as the error minimization problem , where . Using the norm results in sharp images. This problem is ill-posed. Regularization method based on Tikhonov regularization method is used to solve this problem. By this method an ill-posed problem is replaced with a similar well-posed problem by adding constraints. Subgradient method is used to get a numerical solution.
The result of fast superresolution is a rough approximation of the solution of the minimization problem . Fast non-iterative algorithm in used in this case. Regularization algorithm of operator inversion is replaced by direct upsampling operator . In this work, upsampling operator based on Gauss filter is used.
The work also proposes new multiscale method of motion estimation for consecutive frames. In this method, the motion is first estimated with downscales frames, then it is approximated more precisely for original frames using the motion estimated with downscales frames. Motion estimation is performed by Kanade-Lucas method. This method uses a representation of image using image as , where and are motion vector components.
The analysis of proposed high quality superresolution method, fast superresolution method and new multiscale motion estimation method shows practical applicability of the developed methods to video surveillance problems.

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