Metrics for Image Surface Approximation Based on Triangular Meshes

Surface approximation plays an important role in several application fields, such as computer-aided design, computer graphics, remote sensing, computer vision, robotics, architecture, and manufacturing. A common problem present in these areas is to develop efficient methods for generating, processing, analyzing, and visualizing large amount of 3D data. Triangular meshes constitute a flexible representation of sampled points that are not regularly distributed in space, such that the model can be adaptively adjusted to the data density. The choice of metrics for building the triangular meshes is crucial to produce high quality models. This paper proposes and evaluates different measures to incrementally refine a Delaunay triangular mesh for image surface approximation until either a certain accuracy is obtained or a maximum number of iterations is achieved. Experiments on several data sets are performed to compare the quality of the resulting meshes.