IJCSNS International Journal of Computer Science and Network Security, VOL.9 No.9, September 2009 322 Manuscript received September 5, 2009 Manuscript revised September 20, 2009 Combined watershed and deformable simplex mesh for volumetric reconstruction EL Fazazy Khalid, Satori Khalid. LIIAN Laboratory - Faculty of Sciences30000 Fez – MOROCCO Summary Several geometric deformable models have been proposed to deform and manipulate 3D meshes to fit medical object. However, they reveal poor convergence to concave boundaries and necessitate manual interaction to initialize the model. Generally when dealing with volumetric reconstruction, one has to solve two synchronized problems: a segmentation problem consisting in the delineation (fit image boundaries) and an interpolation problem consisting in recovering the missing data. In this paper, we propose a deformable reconstruction system for 3D medical object and we address factors that influence evolution of deformable models. The input to our system is a set of lines extracted with watershed algorithm and deformable simplex meshes that take into account this prior knowledge. Keys words: Volumetric reconstruction, Deformable models, Watershed algorithm, Simplex meshes. 1. Introduction Over the last decade, there has been increasing research activity to address the tremendous variability of object shapes and surmount reconstruction artifacts. However, the requirement to extract valid object boundary elements and reconstruct them into a coherent and consistent anatomical structure makes the development of accurate algorithms challenging. Many methods were employed for segmentation. On one hand, deformable models [1, 2, 3, 4] have being proposed as powerful approach to reconstruct objects by exploiting constraints derived from the image data. They are defined as curves or surfaces that can move within an image domain under the influence of forces: an internal force to ensure the geometric continuity of the model, and an external force to control the closeness of models to the data. However, due to high computational complexity, they reveal poor convergence to concave boundaries and require manual interaction to initialize the model. Other common issues that need to be addressed are: the decision when to stop moving the deformable model. On other hand, the watershed transformation has proven to be a very useful and powerful tool for morphological image segmentation. The intuitive idea underlying this method is quite simple. A grayscale image considered as a topographic relief: when a landscape is immersed from pierced holes (local minima). Different basins will fill up with water. Where water coming from different basins would meet, dams are built (watershed). One of the difficulties with this concept is that it does not allow incorporation of a priori information as energy- based methods. Consequently, there is no control of the smoothness of the segmentation result. In this paper we show how to combine watershed method with a deformable simplex meshes to reconstruct 3D medical object. This leads to an efficient segmentation method integrating the strengths of watershed segmentation and deformable simplex mesh. The remainder of this paper is organized as follows: In the section 2, we review the concepts of deformable simplex mesh. The section 3, focus on problem statement. In section 4, we present our approach to reconstruct the valid object boundaries. The emphasis will be on properties and the rules used to build our combinatorial approach. Then, section (5 and 6) provide results, summarize the proposed method and points out our future research. 2. Simplex meshes Simplex meshes propose an original surface representation to recover 3D object boundaries. They are closely related and dual to triangulation meshes. The main geometric of three-dimensional simplex mesh consists of a simple representation by giving the position of a vertex relatively to its three neighbors. The mesh closeness to modeled object depends on the number of its vertices, the distance of vertices to the data and the relative location of vertices on the surface object Fig.1: (Right) Duality between triangulations and simplex meshes; (Left) the geometry and definition of regularizing force.