Fast Approximation of Range Images by Triangular Meshes Generated through Adaptive Randomized Sampling Miguel Angel García Division of Robotics and Artificial Intelligence Institute of Cybernetics Polytechnic University of Catalonia / Spanish Council for Scientific Research Diagonal 647, planta 2. 08028 Barcelona, SPAIN fax: +34 3 401 66 05, e-mail: garcia@ic.upc.es Abstract This paper describes and evaluates an efficient technique that allows the fast generation of 3D triangular meshes from range images avoiding optimization procedures. Such a tool is advantageous in order to integrate range imagery into world models based on scattered representations. Fur- thermore, this technique can also be used as a fast preprocessing stage of registration, segmentation or recog- nition algorithms, owing to its abstraction capabilities that tend to eliminate redundant information. The proposed method has two stages. First, the vertices of the mesh are computed through adaptive randomized sampling of the range image based on curvature estima- tions. Then, the mesh is generated by triangulating the sampled vertices through an efficient 2 1 / 2 D Delaunay algo- rithm. The sampling process concentrates points in areas of large curvature and tends to preserve surface and orienta- tion discontinuities. Multiresolution representations are supported in a natural way. Furthermore, this method is an inherently parallel process well suited to be implemented on high performance architectures. The proposed technique is finally evaluated with several real range images that include both free-form and polyhedral surfaces. 1 Introduction The use of triangular meshes is quite common in Robot- ics and other related fields where scattered points in space are managed. These meshes enable the description of com- plex objects with storage efficiency. They have been proposed as the solution for a large variety of problems, such as surface representation [8], pose estimation [1] or multiview integration [12]. On the other hand, constant technological advances are enabling the development of increasingly inexpensive and reliable range sensors that are contributing to the wide- spread use of range images in many computer vision tasks. The author has been supported by the Government of Spain both under an FPI fellowship and under the CICYT project TAP93-0415. A complementary grant has been received from the Polytechnic University of Catalonia The final aim of this research is the definition of a world model that allows the efficient representation of 3D geo- metrical information in Robotics. In order to represent real objects, the utilized mathematical model should be able to describe both free-form and polyhedral surfaces of arbi- trary topology. In a first step towards this objective, the author has recently presented an efficient technique that allows the modelling of smooth arbitrary surfaces defined by 3D irregular triangulations of scattered control points [5]. This method is based on geometric data fusion of neighbourhoods of control points and supports the integra- tion of heterogeneous information [6]. In order that a world model based on such scattered rep- resentations may be successfully used in Robotics, and considering that range images are becoming a usual form of sensory input, a set of mechanisms must be provided that allow the fast approximation of those dense images by scat- tered representations compatible with the model. A major requirement for the obtainment of these approximations is time efficiency, since their use is intended for Robotics, where real-time responses are fundamental. The approach consisting of storing all the points of the range images is unfeasible, since even a modest model, such as the one describing the contents of a room, would require a huge volume of storage to maintain the detailed and highly redundant information provided by dense representations. Several techniques have been proposed in the literature for the generation of triangular meshes from dense point sets [2][7][12]. However, they are based on optimization procedures that involve all the original points, in order to produce meshes that minimize the error between the dense image and its triangular approximation. All these methods are costly, since a simple range image may contain several hundreds of thousands of points. Hence, this drawback may complicate their application to robotic systems that must interact with their environment in real-time. The aim of the proposed algorithm is the rapid genera- tion of triangular approximations of range images avoiding the use of optimization techniques. Obviously, this goal implies a certain trade-off between representation accuracy IEEE International Conference on Robotics and Automation, Nagoya, Japan, 1995, 2043-2048.