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.