Computational geometric methods in volumetric intersection for 3D reconstruction

摘要

Generation and analysis of 3D models is an important task that enables automatic inspection, placement, and manipulation of physical objects by robotic systems. This work presents a new approach to the generation of 3D models of arbitrarily shaped physical objects. The models are generated from intensity images obtained from known view positions. The objects are modelled by contours on successive parallel planes. The model becomes more refined as more images are used. The contour model supports the ability to generate the surface of an object by means of tessellation. We have developed a model that supports efficient intersection, not only to perform reconstruction, but also to support inclusion testing and collision detection. We have implemented this algorithm using images of real objects. The algorithm's time complexity is linear with the number of views used and with the number of objects reconstructed. The resolution of the algorithm in reconstructing the contours is limited only by machine precision constraints. This is because the intersection points of the contours are determined analytically, by solving sets of simultaneous equations, which describe the line segments that compose the contours.