Abstract. This paper surveys Delaunay-based meshing techniques for curved objects, and their application in medical imaging and in computer vision to the extraction of geometric models from segmented images. We show that the so-called Delaunay refinement technique allows to mesh surfaces and volumes bounded by surfaces, with theoretical guarantees on the quality of the approximation, from a geometrical and a topological point of view. Moreover, it offers extensive control over the size and shape of mesh elements, for instance through a (possibly non-uniform) sizing field. We show how this general paradigm can be adapted to produce anisotropic meshes, i.e. meshes elongated along prescribed directions. Lastly, we discuss extensions to higher dimensions, and especially to space-time for producing time-varying 3D models. This is also of interest when input images are transformed into data points in some higher dimensional space as is common practice in machine learning. 1

Abstract — World oil demand and advanced oil recovery techniques have made it economically attractive to rehabilitate previously abandoned oil wells. This requires relatively fast mapping of the shape and location of the down-hole well structures. Practical factors prohibit the use of visual and other range sensors in this situation. Here, the feasibility of using a robotic manipulator for tactile mapping is studied. A method is developed that requires only robot joint encoders and avoids the use of any force or tactile sensors, which are complex and unreliable in such a hostile environment. This paper addresses the general problem of intelligent tactile exploration of constrained internal geometries when time is critical. It is assumed that the time required to move a manipulator to acquire a new touch point outweighs computational time. This approach models the down-hole structures with geometric primitives and focuses on exploration efficiency by intelligently searching for new touch points to build the geometric models. The algorithms developed here are shown in simulations and laboratory experiments to substantially reduce the data acquisition effort for exploration with a tactile manipulator. Index Terms — autonomous exploration, manipulator motion-planning, petroleum exploration, robot tactile systems, surface reconstruction. I.

Here the tactile exploration by an autonomous robot when its joints are corrupted by significant backlash is studied. The motivation is the exploration of junctions in oil wells where the harsh conditions dictate the use of tactile exploration. These conditions also results in large, unknown, and variable backlash in the manipulator’s transmissions. Here, a method is developed to simultaneously identify the backlash and map the unknown surface. The method only needs joint encoders, and avoids the use of delicate force or tactile sensors. The mapped surface is described as a combination of geometric primitives. The robot probes the surface in several locations with its tip and computes the contact point through direct kinematics. These contact points are used simultaneously to construct a map of the environment and to identify its joint backlash, improving the precision of the map. The effectiveness of the approach is demonstrated in both simulation case studies and laboratory experiments. 1.

Surface mesh generation through Delaunay refinement is considered as a relevant alternative to the common marching cubes algorithm. One distinctive feature lies into the fact that it interleaves shape probing (through intersection with Voronoi edges) with refinement. The current implementations require seeding the refinement procedure for each connected component so as to guarantee that all components are properly discovered by the mesh refinement procedure. This task is often left to the user. Although this is an easy task for input polyhedral surfaces, it is not when the input surface is defined as an isovalue of an implicit function. In this report we propose an automatic seeding procedure which interleaves refinement, seeding and initialization steps with the qualities of the refinement and the guarantees of careful seeding.