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

Beyond developable: computational design and fabrication with auxetic materials

We present a computational method for interactive 3D design and rationalization of surfaces via auxetic materials, i.e., flat flexible material that can stretch uniformly up to a certain extent. A key motivation for studying such material is that one can approximate doubly-curved surfaces (such as the sphere) using only flat pieces, making it attractive for fabrication. We physically realize surfaces by introducing cuts into approximately inextensible material such as sheet metal, plastic, or leather. The cutting pattern is modeled as a regular triangular linkage that yields hexagonal openings of spatially-varying radius when stretched. In the same way that isometry is fundamental to modeling developable surfaces, we leverage conformal geometry to understand auxetic design. In particular, we compute a global conformal map with bounded scale factor to initialize an otherwise intractable non-linear optimization. We demonstrate that this global approach can handle non-trivial topology and non-local dependencies inherent in auxetic material. Design studies and physical prototypes are used to illustrate a wide range of possible applications

An approach for real world data modelling with the 3D terrestrial laser scanner for built environment

Capturing and modelling 3D information of the built environment is a big challenge. A number of techniques and technologies are now in use. These include EDM, GPS, and photogrammetric application, remote sensing and traditional building surveying applications. However, use of these technologies cannot be practical and efficient in regard to time, cost and accuracy. Furthermore, a multi disciplinary knowledge base, created from the studies and research about the regeneration aspects is fundamental: historical, architectural, archeologically, environmental, social, economic, etc. In order to have an adequate diagnosis of regeneration, it is necessary to describe buildings and surroundings by means of documentation and plans. However, at this point in time the foregoing is considerably far removed from the real situation, since more often than not it is extremely difficult to obtain full documentation and cartography, of an acceptable quality, since the material, constructive pathologies and systems are often insufficient or deficient (flat that simply reflects levels, isolated photographs,..). Sometimes the information in reality exists, but this fact is not known, or it is not easily accessible, leading to the unnecessary duplication of efforts and resources. In this paper, we discussed 3D laser scanning technology, which can acquire high density point data in an accurate, fast way. Besides, the scanner can digitize all the 3D information concerned with a real world object such as buildings, trees and terrain down to millimetre detail Therefore, it can provide benefits for refurbishment process in regeneration in the Built Environment and it can be the potential solution to overcome the challenges above. The paper introduce an approach for scanning buildings, processing the point cloud raw data, and a modelling approach for CAD extraction and building objects classification by a pattern matching approach in IFC (Industry Foundation Classes) format. The approach presented in this paper from an undertaken research can lead to parametric design and Building Information Modelling (BIM) for existing structures. Two case studies are introduced to demonstrate the use of laser scanner technology in the Built Environment. These case studies are the Jactin House Building in East Manchester and the Peel building in the campus of University Salford. Through these case studies, while use of laser scanners are explained, the integration of it with various technologies and systems are also explored for professionals in Built Environmen

Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner