Computer Vision and Mathematical Methods in Medical and by James F. Greenleaf, Mostafa Fatemi, Marek Belohlavek

By James F. Greenleaf, Mostafa Fatemi, Marek Belohlavek (auth.), Milan Sonka, Ioannis A. Kakadiaris, Jan Kybic (eds.)

Medical imaging and clinical snapshot analysisare speedily constructing. whereas m- ical imaging has already develop into a regular of recent treatment, scientific picture research remains to be normally played visually and qualitatively. The ev- expanding quantity of obtained facts makes it very unlikely to make use of them in complete. both vital, the visible methods to scientific picture research are recognized to su?er from an absence of reproducibility. A signi?cant researche?ort is dedicated to constructing algorithms for processing the wealth of knowledge on hand and extracting the appropriate info in a automated and quantitative type. scientific imaging and photo research are interdisciplinary components combining electric, machine, and biomedical engineering; computing device technological know-how; mathem- ics; physics; facts; biology; medication; and different ?elds. clinical imaging and machine imaginative and prescient, curiously sufficient, have built and proceed constructing a bit of independently. however, bringing them jointly can provide to b- e?t either one of those ?elds. We have been enthusiastic whilst the organizers of the 2004 eu convention on computing device imaginative and prescient (ECCV) allowed us to prepare a satellite tv for pc workshop dedicated to clinical snapshot analysis.

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Extra info for Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis: ECCV 2004 Workshops CVAMIA and MMBIA, Prague, Czech Republic, May 15, 2004, Revised Selected Papers

Example text

For a decade, engineers and researchers worked to reduce the above mathematical formulism into practical implementation but encountered many difficulties. The most complex and expensive computational step, the differentiation-backprojection operation, acts on curved surface in a fashion that was not completely understood. In 2001, cone-beam inversion formulae derived by Katsevich [9] and Yang [16] considerably simplified cone-beam reconstruction. Katsevich gave the first helical cone-beam inversion formula as an iterated 2-D integral which suggests the minimum use of data.

We have demonstrated the feasibility of our approach through accurate preliminary reconstructions of phantom data and a cadaver knee and have as well performed analysis of the accuracy of our pose finding method and the reconstruction. The results from this work have the potential to provide an inexpensive and readily available 3D imaging capability that can benefit many medical applications. Advances in visualization and localization based on this method will allow minimally invasive procedures to be used more frequently, thus reducing the trauma to the patient.

Denote the projective coordinates of the said lines by (λ, α1 ) and (λ, α2 ) respectively. The unit normal of the given plane, denoted by β, is perpendicular to both α1 and α2 . Therefore, β = α1 × α2 /|α1 × α2 |. The radial distance of the plane, denoted by l, can be evaluated as l = Φ(λ) · β. The coordinate (l, β) determines the position of a plane seen in the global Euclidean coordinate. 40 X. P. 2 Integral Transforms on Projective Spaces Each cone-beam projection consists of rays emitting from a source point.

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