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Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulae for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

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Face tracking is an important computer vision technology that has been widely adopted in many areas, from cell phone applications to industry robots. In this paper, we introduce a novel way to parallelize a face contour detecting application based on the color-entropy preprocessed ChanVese model utilizing a total variation G-norm. This particular application is a complicated and unsupervised computational method requiring a large amount of calculations. Several core parts therein are difficult to parallelize due to heavily correlated data processing among iterations and pixels.

Image matching is a fundamental problem in computer vision. One of the well-known techniques is SIFT (scale-invariant feature transform). SIFT searches for and extracts robust features in hierarchical image scale spaces for object identification. However it often lacks efficiency as it identifies many insignificant features such as tree leaves and grass tips in a natural building image. We introduce a content adaptive image matching approach by preprocessing the image with a color-entropy based segmentation and harmonic inpainting. Natural structures such as tree leaves have both high entropy and distinguished color, and so such a combined measure can be both discriminative and robust. The harmonic inpainting smoothly interpolates the image functions over the tree regions and so blurrs and reduces the features and their unnecessary matching there. Numerical experiments on building images show