# American Institute of Mathematical Sciences

2005, 2(2): 209-226. doi: 10.3934/mbe.2005.2.209

## Partial Differential Equations-Based Segmentation for Radiotherapy Treatment Planning

 1 Department of Computer Science and Department of Mechanical Engineering, University of California at Santa Barbara, CA 93106-5070, United States 2 Department of Mathematics, Stanford University, Stanford, CA 94305-2125 3 Siemens Medical Solutions, Med SW West, 755 College Road East, Princeton, NJ 08540, United States 4 Department of Radiation Oncology, Stanford University, Stanford, CA 94305, United States, United States

Received  October 2004 Revised  March 2005 Published  March 2005

The purpose of this study is to develop automatic algorithms for the segmentation phase of radiotherapy treatment planning. We develop new image processing techniques that are based on solving a partial differential equation for the evolution of the curve that identifies the segmented organ. The velocity function is based on the piecewise Mumford-Shah functional. Our method incorporates information about the target organ into classical segmentation algorithms. This information, which is given in terms of a three-dimensional wireframe representation of the organ, serves as an initial guess for the segmentation algorithm. We check the performance of the new algorithm on eight data sets of three different organs: rectum, bladder, and kidney. The results of the automatic segmentation were compared with a manual segmentation of each data set by radiation oncology faculty and residents. The quality of the automatic segmentation was measured with the ''$\kappa$-statistics'', and with a count of over- and undersegmented frames, and was shown in most cases to be very close to the manual segmentation of the same data. A typical segmentation of an organ with sixty slices takes less than ten seconds on a Pentium IV laptop.
Citation: Frédéric Gibou, Doron Levy, Carlos Cárdenas, Pingyu Liu, Arthur Boyer. Partial Differential Equations-Based Segmentation for Radiotherapy Treatment Planning. Mathematical Biosciences & Engineering, 2005, 2 (2) : 209-226. doi: 10.3934/mbe.2005.2.209
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