Dictionary Learning-based Inpainting on Triangular Meshes

The problem of inpainting consists of filling missing or damaged regions in images and videos in such a way that the filling pattern does not produce artifacts that deviate from the original data. In addition to restoring the missing data, the inpainting technique can also be used to remove undesired objects. In this work, we address the problem of inpainting on surfaces through a new method based on dictionary learning and sparse coding. Our method learns the dictionary through the subdivision of the mesh into patches and rebuilds the mesh via a method of reconstruction inspired by the Non-local Means method on the computed sparse codes. One of the advantages of our method is that it is capable of filling the missing regions and simultaneously removes noise and enhances important features of the mesh. Moreover, the inpainting result is globally coherent as the representation based on the dictionaries captures all the geometric information in the transformed domain. We present two variations of the method: a direct one, in which the model is reconstructed and restored directly from the representation in the transformed domain and a second one, adaptive, in which the missing regions are recreated iteratively through the successive propagation of the sparse code computed in the hole boundaries, which guides the local reconstructions. The second method produces better results for large regions because the sparse codes of the patches are adapted according to the sparse codes of the boundary patches. Finally, we present and analyze experimental results that demonstrate the performance of our method compared to the literature

Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

Shape correction of thin mirrors in a reconfigurable modular space telescope

In order to facilitate the construction of future large space telescopes, the development of low cost, low mass mirrors is necessary. However, such mirrors suffer from a lack of structural stability, stiffness, and shape accuracy. Active materials and actuators can be used to alleviate this deficiency. For observations in the visible wavelengths, the mirror surface must be controlled to an accuracy on the order of tens of nanometers. This paper presents an exploration of several mirror design concepts and compares their effectiveness at providing accurate shape control. The comparison test is the adjustment of a generic mirror from its manufactured spherical shape to the shape required by various off-axis mirrors in a segmented primary mirror array. A study of thermal effects is also presented and, from these results, a recommended design is chosen

High order continuous polygonal patches

A polygonal patch method is described which can be used to fill a polygonal hole within a given k'th order continuous rectangular patch complex. The method is relatively easy to implement, since it only re- quires Ck extensions of the rectangular patch complex defined in terms of the rectangular patch parameterizations. The method is illustrated by reference to C2 bicubic B-spline surfaces