Energy-Based Segmentation of Very Sparse Range Surfaces

Abstract

This paper describes a new segmentation technique for very sparse surfaces which is based on minimizing the energy of the surfaces in the scene. While it could be used in almost any system as part of surface reconstruction/model recovery, the algorithm is designed to be usable when the depth information is scattered and very sparse, as is generally the case with depth generated by stereo algorithms. We show results from a sequential algorithm that processes laser range-finder data or synthetic data. We then discuss a parallel implementation running on the parallel Connection Machine. The idea of segmentation by energy minimization is not new. However, prior techniques have relied on discrete regularization or Markov random fields to model the surfaces to build smooth surfaces and detect depth edges. Both of the aforementioned techniques are ineffective at energy minimization for very sparse data. In addition, this method does not require edge detection and is thus also applicable when edge information is unreliable or unavailable. Our model is extremely general; it does not depend on a model of the surface shape but only on the energy for bending a surface. Thus the surfaces can grow in a more data-directed manner. The technique presented herein models the surfaces with reproducing kernel-based splines, which can be shown to solve a regularized surface reconstruction problem. From the functional form of these splines we derive computable bounds on the energy of a surface over a given finite region. The computation of the spline, and the corresponding surface representation are quite efficient for very sparse data. An interesting property of the algorithm is that it makes no attempt to determine segmentation boundaries; the algorithm can be viewed as a classification scheme which segments the data into collections of points which are "from" the same surface. Among the significant advantages of the method is the capacity to process overlapping transparent surfaces, as well as surfaces with large occluded areas