Regularized pointwise map recovery from functional correspondence

The concept of using functional maps for representing dense correspondences between deformable shapes has proven to be extremely effective in many applications. However, despite the impact of this framework, the problem of recovering the point-to-point correspondence from a given functional map has received surprisingly little interest. In this paper, we analyse the aforementioned problem and propose a novel method for reconstructing pointwise correspondences from a given functional map. The proposed algorithm phrases the matching problem as a regularized alignment problem of the spectral embeddings of the two shapes. Opposed to established methods, our approach does not require the input shapes to be nearly-isometric, and easily extends to recovering the point-to-point correspondence in part-to-whole shape matching problems. Our numerical experiments demonstrate that the proposed approach leads to a significant improvement in accuracy in several challenging cases

Compression for Smooth Shape Analysis

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric operators like normals, curvatures, or Laplace-Beltrami eigenfunctions at large computational and memory costs. We avoid this bottleneck with a compression technique that represents a smooth shape as subdivision surfaces and exploits the subdivision scheme to parametrize smooth functions on that shape with a few control parameters. This compression does not affect the accuracy of the Laplace-Beltrami operator and its eigenfunctions and allow us to compute shape descriptors and shape matchings at an accuracy comparable to triangular meshes but a fraction of the computational cost. Our framework can also compress surfaces represented by point clouds to do shape analysis of 3D scanning data

An in Situ Technique for Elemental Analysis of Lunar Surfaces

An in situ analytical technique that can remotely determine the elemental constituents of solids has been demonstrated. Laser-Induced Breakdown Spectroscopy (LIBS) is a form of atomic emission spectroscopy in which a powerful laser pulse is focused on a solid to generate a laser spark, or microplasma. Material in the plasma is vaporized, and the resulting atoms are excited to emit light. The light is spectrally resolved to identify the emitting species. LIBS is a simple technique that can be automated for inclusion aboard a remotely operated vehicle. Since only optical access to a sample is required, areas inaccessible to a rover can be analyzed remotely. A single laser spark both vaporizes and excites the sample so that near real-time analysis (a few minutes) is possible. This technique provides simultaneous multielement detection and has good sensitivity for many elements. LIBS also eliminates the need for sample retrieval and preparation preventing possible sample contamination. These qualities make the LIBS technique uniquely suited for use in the lunar environment

Laer-induced Breakdown Spectroscopy Instrument for Element Analysis of Planetary Surfaces

One of the most fundamental pieces of information about any planetary body is the elemental and mineralogical composition of its surface materials. We are developing an instrument to obtain such data at ranges of up to several hundreds of meters using the technique of Laser-Induced Breakdown Spectroscopy (LIBS). We envision our instrument being used from a spacecraft in close rendezvous with small bodies such as comets and asteroids, or deployed on surface-rover vehicles on large bodies such as Mars and the Moon. The elemental analysis is based on atomic emission spectroscopy of a laser-induced plasma or spark. A pulsed, diode pumped Nd:YAG laser of several hundred millijoules optical energy is used to vaporize and electronically excite the constituent elements of a rock surface remotely located from the laser. Light emitted from the excited plasma is collected and introduced to the entrance slit of a small grating spectrometer. The spectrally dispersed spark light is detected with either a linear photo diode array or area CCD array. When the latter detector is used, the optical and spectrometer components of the LIBS instrument can also be used in a passive imaging mode to collect and integrate reflected sunlight from the same rock surface. Absorption spectral analysis of this reflected light gives mineralogical information that provides a remote geochemical characterization of the rock surface. We performed laboratory calibrations in air and in vacuum on standard rock powders to quantify the LIBS analysis. We performed preliminary field tests using commercially available components to demonstrate remote LIBS analysis of terrestrial rock surfaces at ranges of over 25 m, and we have demonstrated compatibility with a six-wheeled Russian robotic rover vehicle. Based on these results, we believe that all major and most minor elements expected on planetary surfaces can be measured with absolute accuracy of 10-15 percent and much higher relative accuracy. We have performed preliminary systems analysis of a LIBS instrument to evaluate probable mass and power requirements; results of this analysis are summarized

Non-Rigid Puzzles

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non-rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non-rigid multi-part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non-rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario

Iterative graph cuts for image segmentation with a nonlinear statistical shape prior

Shape-based regularization has proven to be a useful method for delineating objects within noisy images where one has prior knowledge of the shape of the targeted object. When a collection of possible shapes is available, the specification of a shape prior using kernel density estimation is a natural technique. Unfortunately, energy functionals arising from kernel density estimation are of a form that makes them impossible to directly minimize using efficient optimization algorithms such as graph cuts. Our main contribution is to show how one may recast the energy functional into a form that is minimizable iteratively and efficiently using graph cuts.Comment: Revision submitted to JMIV (02/24/13

SHREC'16: partial matching of deformable shapes

Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods