Proceedings of the 1997 IEEE International Conference on Robotics and Automation Albuquerque, New Mexico - April 1997 Fast Generation of Adaptive Quadrilateral Meshes from Range Images Miguel Angel Garcia$ Angel Doming0 Sappa? Luis Basaiiezt Department of Software (Computer Graphics Section) Institute of Cybernetics Polytechnic University of Catalonia Diagonal 647, planta 8.08028 Barcelona, SPAIN fax: +34 3 401 60 50, E-mail: garcia@turing.upc.es Abstract This paper proposes a fast technique for generating adaptive quadrilateral meshes from range images with no optimization. The obtained meshes adapt to the features of the input images by concentrating points in areas of high curvature and by dispersing them in low variation regions. This leads to more accurate approximations of the given range images than when uniform sampling with the same number of points is applied. Experimental results with real range images representing both free-form and polyhedral and cylindrical objects are presented. 1 Introduction Range sensors are becoming a popular way of obtaining 3D information in robotics owing to the development of low-cost devices able to provide dense images at high speeds [9]. However, the processing of dense range images containing hundreds of thousands of pixels is still costly and difficult to apply to real-time applications. One way of speeding up the processing of range images consists of reducing the amount of data contained in the images while keeping enough details that allow the appli- cation of further algorithms, such as segmentation or shape recognition. This can be done by removing points in areas of low variation and keeping them in areas of high curvature. In general, the objective becomes the genera- tion of a mesh that approximates the given range image with fewer data points. Further processing algorithms can then be applied to that mesh instead of to the dense range image directly [8]. Meshes generated from range images can be either reg- ular (quadrilateral) or irregular. Irregular meshes do not impose any conditions upon the distribution of the data points they hold. Therefore, they allow the representation of both scattered and regularly distributed points in space. This work has been partially supported by the Government of Spain under the CICYT project TAP96-0868. The second author has been supported by the Spanish Agency for International Cooperation and the National University of La Pampa (Argentina). Among them, irregular triangular meshes are a widely- used representation owing to the availability of efficient triangulation algorithms. Several iterative optimization techniques have been proposed for approximating range images by triangular meshes (e.g., [2][10]). A faster approach which avoids such costly optimizations was pro- posed by Garcia [6]. Quadrilateral meshes are a less flexible data representa- tion compared to irregular meshes, since they require that the data points are distributed in rows and columns. How- ever, quadrilateral meshes are convenient and sometimes necessary for different applications, for example, for esti- mating the surfaces of the original objects contained in the image by applying tensor-product B-splines or NURBS, which are the “de facto” standard for free-form surface modeling in CAD/CAM. Although many techniques have been devised for reconstructing surfaces from irregular meshes (e.g., [7]), they are unable to perform as good as tensor-product methods. Besides, it is always possible to obtain a triangular mesh from a quadrilateral one by split- ting each rectangular cell into two triangles. This argument and the existence of algorithms that work with quadrilateral meshes (e.g., [4] [5]) justify the utility of generating quadrilateral meshes from range images. The simplest way of generating a quadrilateral mesh from a range image is by sampling that image at specific intervals both horizontally and vertically. However, this process produces aliasing effects, since details in the image between two sampled points will be ignored. Thus, the objective is the generation of non-uniform quadrilat- eral grids, that vary their point density depending on the amount of information (details) present in the image. The underlying goal is to be able to capture more information with the same amount of data points. Similarly to the irregular case, previous methods for generating adaptive quadrilateral meshes from range images are based on iterative optimization techniques. Variational formulations and elastic models are some examples (e.g., [1][ 111). A recent algorithm segments the given image into patches and fits quadrilateral meshes to each patch [3]. However, those previous techniques are 0-7803-361 2-7-4/97 $5.00 @ 1997 IEEE 281 3