Total Degree Formula for the Generic Offset to a Parametric Surface

We provide a resultant-based formula for the total degree w.r.t. the spatial variables of the generic offset to a parametric surface. The parametrization of the surface is not assumed to be proper.Comment: Preprint of an article to be published at the International Journal of Algebra and Computation, World Scientific Publishing, DOI:10.1142/S021819671100680

Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds

We apply compensated convex transforms to define a multiscale Hausdorff stable method to extract intersections between smooth compact manifolds represented by their characteristic functions or as point clouds embedded in Rn. We prove extraction results on intersections of smooth compact manifolds and for points of high curvature. As a result of the Hausdorff–Lipschitz continuity of our transforms, we show that our method is stable against dense sampling of smooth manifolds with noise. Examples of explicitly calculated prototype models for some simple cases are presented, which are also used in the proofs of our main results. Numerical experiments in two- and three-dimensional space, and applications to geometric objects are also shown

Three-Dimensional Object Registration Using Wavelet Features

Recent developments in shape-based modeling and data acquisition have brought three-dimensional models to the forefront of computer graphics and visualization research. New data acquisition methods are producing large numbers of models in a variety of fields. Three-dimensional registration (alignment) is key to the useful application of such models in areas from automated surface inspection to cancer detection and surgery. The algorithms developed in this research accomplish automatic registration of three-dimensional voxelized models. We employ features in a wavelet transform domain to accomplish registration. The features are extracted in a multi-resolutional format, thus delineating features at various scales for robust and rapid matching. Registration is achieved by using a voting scheme to select peaks in sets of rotation quaternions, then separately identifying translation. The method is robust to occlusion, clutter, and noise. The efficacy of the algorithm is demonstrated through examples from solid modeling and medical imaging applications

Indoor robot gardening: design and implementation

This paper describes the architecture and implementation of a distributed autonomous gardening system with applications in urban/indoor precision agriculture. The garden is a mesh network of robots and plants. The gardening robots are mobile manipulators with an eye-in-hand camera. They are capable of locating plants in the garden, watering them, and locating and grasping fruit. The plants are potted cherry tomatoes enhanced with sensors and computation to monitor their well-being (e.g. soil humidity, state of fruits) and with networking to communicate servicing requests to the robots. By embedding sensing, computation, and communication into the pots, task allocation in the system is de-centrally coordinated, which makes the system scalable and robust against the failure of a centralized agent. We describe the architecture of this system and present experimental results for navigation, object recognition, and manipulation as well as challenges that lie ahead toward autonomous precision agriculture with multi-robot teams.Swiss National Science Foundation (contract number PBEL2118737)United States. Army Research Office. Multidisciplinary University Research Initiative (MURI SWARMS project W911NF-05-1-0219)National Science Foundation (U.S.) (NSF IIS-0426838)Intel Corporation (EFRI 0735953 Intel)Massachusetts Institute of Technology (UROP program)Massachusetts Institute of Technology (MSRP program