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3D Reconstruction

When the dynamic objects are imaged by a camera i, they exist within frustums that circumscribe their projected regions on the image and whose apexes are focus point of the camera. We call all the projected regions in the same image together a dynamic region and let us denote a subspace consisting of these viewing frustums by .

As the dynamic objects can exist only outside , we only care a subspace named existence shadow subspace (ESS) defined by Equation (1).


The dynamic objects exist somewhere inside .

In the case where the dynamic objects are imaged by n cameras, they exist within the product of all of these frustums. We denote this subspace as where


Suppose there are n cameras in the real space and the cameras capture images simultaneously. We call this set of images a frame. 3D reconstruction process named 3D composer can generate at each frame in the condition that it is given because and the focus positions of the cameras are given in advance. Since is described by a binary image, the amount of transferred data is quite small.

This 3D reconstruction calculation in Equation (2) is easily expanded to parallel distributed computing because several 3D composers can reconstruct different subspaces simultaneously. Thus we achieve spatio-division of the 3D reconstruction process based on the locality of 3D reconstruction calculation.

In the actual implementation, 3D composer generates by voxel representation.

Yoshinari Kameda
Mon Sep 21 11:42:41 JST 1998