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Proceedings Paper

A new algorithm for determining 3D biplane imaging geometry: theory and implementation
Author(s): Vikas Singh; Jinhui Xu; Kenneth R. Hoffmann; Guang Xu; Zhenming Chen; Anant Gopal
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Paper Abstract

Biplane imaging is a primary method for visual and quantitative assessment of the vasculature. A key problem (called Imaging Geometry Determination problem or IGD for short) in this method is to determine the rotation-matrix (R) and the translation vector (t) which relate the two coordinate systems. In this paper, we propose a new approach, called IG-Sieving, to calculate R and t using corresponding points in the two images. Our technique first generates an initial estimate of R and t from the gantry angles of the imaging system, and then optimizes them by solving an optimal-cell-search problem in a 6-D parametric space (three variables defining R plus the three variables of t). To efficiently find the optimal imaging geometry (IG) in 6-D, our approach divides the high dimensional search domain into a set of lower-dimensional regions, (holding two variables constant at each optimization step), thereby reducing the optimal-cell-search problem to a set of optimization problems in 3D sub-spaces (one other variable is correlated). For each such sub-space, our approach first applies efficient computational geometry techniques to identify "possibly-feasible" IG’s, and then uses a criterion we call fall-in-number to sieve out good IGs. We show that in a bounded number of optimization steps, a (possibly infinite) set of near optimal IGs (which are equally good) can be determined. Simulation results indicate that our method can reconstruct 3D points with average 3D center-of-mass errors of about 0.8cm for input image-data errors as high as 0.1cm, which is comparable to existing techniques. More importantly, our algorithm provides a novel insight into the geometric structure of the solution space, which could be exploited to significantly improve the accuracy of other biplane algorithms.

Paper Details

Date Published: 29 April 2005
PDF: 12 pages
Proc. SPIE 5747, Medical Imaging 2005: Image Processing, (29 April 2005); doi: 10.1117/12.594378
Show Author Affiliations
Vikas Singh, SUNY/Buffalo (United States)
Jinhui Xu, SUNY/Buffalo (United States)
Kenneth R. Hoffmann, SUNY/Buffalo (United States)
Guang Xu, SUNY/Buffalo (United States)
Zhenming Chen, SUNY/Buffalo (United States)
Anant Gopal, SUNY/Buffalo (United States)

Published in SPIE Proceedings Vol. 5747:
Medical Imaging 2005: Image Processing
J. Michael Fitzpatrick; Joseph M. Reinhardt, Editor(s)

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