Sharp edges are important shape features and their extraction has been extensively studied both on point clouds and surfaces. We consider the problem of extracting sharp edges from a sparse set of colour-and-depth (RGB-D) images. The noise-ridden depth measurements are challenging for existing feature extraction methods that work solely in the geometric domain (e.g. points or meshes). By utilizing both colour and depth information, we propose a novel feature extraction method that produces much cleaner and more coherent feature lines. We make two technical contributions. First, we show that intensity edges can augment the depth map to improve normal estimation and feature localization from a single RGB-D image. Second, we designed a novel algorithm for consolidating feature points obtained from multiple RGB-D images. By utilizing normals and ridge/valley types associated with the feature points, our algorithm is effective in suppressing noise without smearing nearby features.

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

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.

A time domain blind source separation algorithm of convolutive sound mixtures is studied based on a compact partial inversion formula in closed form. An L1-constrained minimization problem is formulated to find demixing filter coefficients for source separation while capturing scaling invariance and sparseness of solutions. The minimization aims to reduce (lagged) cross correlations of the mixture signals, which are modeled stochastically. The problem is non-convex, however it is put in a nonlinear least squares form where the robust and convergent Levenberg-Marquardt iterative method is applicable to compute local minimizers. Efficiency is achieved in recovering lower dimensional demixing filter solutions than the physical ones. Computations on recorded and synthetic mixtures show satisfactory performance, and are compared with other iterative methods.

This paper presents a skeleton-based method for deforming meshes (the skeleton need not be the medial axis). The significant difference from previous skeleton-based methods is that the latter use the skeleton to control movement of vertices, whereas we use it to control the simplices defining the model. By doing so, errors that occur near joints in other methods can be spread over the whole mesh, via an optimization process, resulting in smooth transitions near joints of the skeleton. By controlling simplices, our method has the additional advantage that no vertex weights need be defined on the bones, which is a tedious requirement in previous skeleton-based methods. Furthermore, by incorporating the translation vector in our optimization, unlike other methods, we do not need to fix an arbitrary vertex, and the deformed mesh moves with the deformed skeleton. Our method can also easily be used to control deformation by moving a few chosen line segments, rather than a skeleton.