An Elliptic PDE Approach for Shape Characterization.

H. Haidar, S. Bouix, J. Levitt, R. W. McCarley, M. E. Shenton, J. S. Soul
Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
September, 2004

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Abstract

This paper presents a novel approach to analyze the shape of anatomical structures. Our methodology is rooted in classical physics and in particular Poisson s equation, a fundamental partial differential equation [1]. The solution to this equation and more specifically its equipotential surfaces display properties that are useful for shape analysis. We present a numerical algorithm to calculate the length of streamlines formed by the gradient field of the solution to this equation for 2D and 3D objects. The length of the streamlines along the equipotential surfaces was used to build a new function which can characterize the shape of objects. We illustrate our method on 2D synthetic and natural shapes as well as 3D medical data.

Reference

Haidar H, Bouix S, Levitt J, McCarley RW, Shenton ME, Soul JS. An elliptic pde approach for shape characterization. In Proceedings of the 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society. San Francisco, USA, 2004;.

Grants

NIH/NIMH 2K02 MH01110, NIH RO1 MH50747, NIH/NIMH 2RO1 MH40799, VA Merit Award(MES) 2000-2008, VA Merit Award(RWM) 1998-2009

Research area

shapeanalysis
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