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The 3-D distribution reconstruction method based on the intersectional approximation of cross-sectional clouds contour parameters

V. E. Antsiperov, O. V. Evseev, Yu. V. Obukhov

Kotel’nikov Institute of Radio-engineering and Electronics of RAS

Received July 8, 2012

Abstract. Continuous distribution reconstruction from discrete point cloud has been receiving extensive attention recently. There are a number of reasons for that occurrence. For example, when using the conventional B-spline approximation technique, the difficulty of parameterization exists since the real point clouds are not always sampled from rectangular regions. Other direct methods (converting, for example, point clouds in stereolithography models) lead to a huge file size and require expert modeling skills. The objective of this work is to establish a new 3-D distribution reconstruction method based on intersectional approximation of cross-sectional clouds contour parameters. We present an interpretation of 3-D distribution reconstruction problem as a problem of constructing 3-D probability density which is in a certain way associated with a discrete set of 2-D conditional probability densities. Based on a good parameterization, the final density distribution is achieved with tight tolerance. One practical example – three-dimensional reconstruction neurons distribution from microscopic images of brain slices have demonstrated the feasibility of the proposed method.

Keywords: reverse engineering, CAD (Computer Aided Design) modeling, three dimensional visualization and analysis, Point cloud density reconstruction, B-splines, methods for 3-D reconstruction of data collected from serial sections.