Learning quadrangulated patches for 3D shape parameterization and completion

We propose a novel 3D shape parameterization by surface patches, that are oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail on local patches, we learn a patch dictionary that identifies principal surface features of the shape. Unlike previous methods, we are able to encode surface patches of variable size as determined by the user. We propose novel methods for dictionary learning and patch reconstruction based on the query of a noisy input patch with holes. We evaluate the patch dictionary towards various applications in 3D shape inpainting, denoising and compression. Our method is able to predict missing vertices and inpaint moderately sized holes. We demonstrate a complete pipeline for reconstructing the 3D mesh from the patch encoding. We validate our shape parameterization and reconstruction methods on both synthetic shapes and real world scans. We show that our patch dictionary performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201

Vision Science and Technology at NASA: Results of a Workshop

A broad review is given of vision science and technology within NASA. The subject is defined and its applications in both NASA and the nation at large are noted. A survey of current NASA efforts is given, noting strengths and weaknesses of the NASA program

AirCode: Unobtrusive Physical Tags for Digital Fabrication

We present AirCode, a technique that allows the user to tag physically fabricated objects with given information. An AirCode tag consists of a group of carefully designed air pockets placed beneath the object surface. These air pockets are easily produced during the fabrication process of the object, without any additional material or postprocessing. Meanwhile, the air pockets affect only the scattering light transport under the surface, and thus are hard to notice to our naked eyes. But, by using a computational imaging method, the tags become detectable. We present a tool that automates the design of air pockets for the user to encode information. AirCode system also allows the user to retrieve the information from captured images via a robust decoding algorithm. We demonstrate our tagging technique with applications for metadata embedding, robotic grasping, as well as conveying object affordances.Comment: ACM UIST 2017 Technical Paper

Joint segmentation of color and depth data based on splitting and merging driven by surface fitting

This paper proposes a segmentation scheme based on the joint usage of color and depth data together with a 3D surface estimation scheme. Firstly a set of multi-dimensional vectors is built from color, geometry and surface orientation information. Normalized cuts spectral clustering is then applied in order to recursively segment the scene in two parts thus obtaining an over-segmentation. This procedure is followed by a recursive merging stage where close segments belonging to the same object are joined together. At each step of both procedures a NURBS model is fitted on the computed segments and the accuracy of the fitting is used as a measure of the plausibility that a segment represents a single surface or object. By comparing the accuracy to the one at the previous step, it is possible to determine if each splitting or merging operation leads to a better scene representation and consequently whether to perform it or not. Experimental results show how the proposed method provides an accurate and reliable segmentation

Integrable Combinatorics

We review various combinatorial problems with underlying classical or quantum integrable structures. (Plenary talk given at the International Congress of Mathematical Physics, Aalborg, Denmark, August 10, 2012.)Comment: 21 pages, 16 figures, proceedings of ICMP1