Partial Differential Equations-Based Segmentation for Radiotherapy Treatment Planning
Frédéric Gibou Doron Levy Carlos Cárdenas Pingyu Liu Arthur Boyer
Mathematical Biosciences & Engineering 2005, 2(2): 209-226 doi: 10.3934/mbe.2005.2.209
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.
keywords: segmentation radiotherapy treatment level-set methods Mumford- Shah.
Fast two dimensional to three dimensional registration of fluoroscopy and CT-scans using Octrees on segmentation maps
Luca Bertelli Frédéric Gibou
Mathematical Biosciences & Engineering 2012, 9(3): 527-537 doi: 10.3934/mbe.2012.9.527
We introduce a computationally efficient approach to the generation of Digital Reconstructed Radiographs (DRRs) needed to perform three dimensional to two dimensional medical image registration and apply this algorithm to virtual surgery. The DRR generation process is the bottleneck of any three dimensional to two dimensional registration system, since its computational complexity scales with the number of voxels in the Computed Tomography Data, which can be of the order of tens to hundreds of millions. Our approach originates from the segmentation of the volumetric data into multiple regions, which allows a compact representation via Octree Data Structures. This, in turn, yields efficient storage and access of the attenuation indexes of the volumetric cells, required in the projection procedure that generates the DRR. A functional based on Mutual Information is then maximized to obtain the alignment of the DRR with the two dimensional X-ray fluoroscopy scans acquired during the operation. Promising experimental results on real data are presented.
keywords: Digital reconstructed radiography Octree mesh generation.

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