3D Segmentation of Soft Organs by Flipping-Free Mesh Deformation ∗ Feng Ding Dept. of Computer Science National University of Singapore dingfeng@comp.nus.edu.sg Wenxian Yang School of Computer Engineering Nanyang Technological University wxyang@ntu.edu.sg Wee Kheng Leow Dept. of Computer Science National University of Singapore leowwk@comp.nus.edu.sg Sudhakar K Venkatesh YLL School of Medicine National University of Singapore dnrskv@nus.edu.sg Abstract Segmentation of 3D soft organs from complex volume im- ages is a very important and challenging task. The objects of interest may have inhomogeneous voxel intensities and some object boundaries may be indistinct. Existing algo- rithms are either sensitive to noise or computationally ex- pensive. This paper presents a novel algorithm that over- comes these shortcomings. The algorithm adopts a novel flipping-free mesh deformation and registration method that can easily incorporate geometric constraints to reduce sen- sitivity to noise. It efficiently deforms the 3D model in large displacements reducing total computational costs. These properties are confirmed by comprehensive test results. 1. Introduction Segmentation of 3D soft organs from CT and MR is a very important and challenging task for medical image anal- ysis. The objects may have inhomogeneous voxel intensi- ties and some object boundaries may be indistinct. Segmen- tation methods such as thresholding, region growing, wa- tershed and classification work well on simple images with homogeneous regions. Unfortunately, they are sensitive to noise and produce severe over-segmentation when applied to medical images with inhomogeneous regions. Interactive segmentation algorithms such as Grab- Cut [18] and random walks [7] achieve fairly good results in 2D color images. However, they are computationally ex- pensive in both time and space especially for 3D medical data, which often contains more than 512 × 512 × 200 vox- els. The memory usage of graph cut, for instance, may ex- ∗ This research is supported by SBIC RP C-008/2006 and A*STAR SERC 052 101 0103 (NUS R-252-000-319-305). ceed 4GB for such data set, which is beyond the limit of 32-bit computers. Moreover, these algorithms may produce foreground regions with undesirable topology. A recent im- plementation [4] reduces the memory requirement slightly. Deformable models have been successfully applied to medical image segmentation. They can be represented ei- ther implicitly or explicitly. Segmentation methods using implicit models such as the level set method [20] and the fast marching methods [21] represent a 3D surface as an implicit function discretized into voxels, resulting in com- putationally expensive algorithms. The level set method can change the evolving surface’s topology to match highly complex object surface. However, it often leaks out of the object boundaries producing undesired segmentation. In contrast, segmentation methods using explicit mod- els [2, 16] represent a 3D surface as a mesh, which sig- nificantly reduce the space complexity of the algorithms. Deformation is accomplished by displacing the mesh ver- tices. The problem of mesh-based methods is that the dis- placements of vertices may cause self-intersections of the mesh, which can be categorized as flipping or non-flipping. Flipping self-intersection occurs locally if the displacement vectors of neighboring mesh vertices cross in space. As a result, the directions of some surface normals flip after de- formation. This problem cannot be solved by simply reduc- ing the deformation step size. As shown in Fig. 3, surface flippings occur during mesh deformation towards a binary volume data even with a very small deformation step size. Non-flipping self-intersection occurs globally without flip- ping the surface normals but causes penetration of different parts of the mesh. In summary, existing 3D deformable model-based algo- rithms exhibit various weaknesses that need to be overcome. To address these problems, we propose an algorithm for segmenting 3D soft organs such as liver and spleen based