Reshaping polygonal meshes with smoothed normals extracted from Ultrasound volume data: an optimization

Several methods exploit the relative motion between the probe and the object being scanned to gure out an estimate of the normals of the existing structures in a volume. These methods are revealed as a good estimator for normals, at least better than simple gradient schemes. On the other hand, polygonal meshes can be obtained directly from raw data by means of tiling algorithms. Although these meshes are good representations of isosurfaces in CT or MRI data, as far as ultrasound is concerned, results are quite noisy, so more e ort is needed in developing algorithms that will be able to enhance the structures in the images. In this paper we propose a method that reshapes the geometry of meshes using the information given by normals. Rendering the meshes with the estimated normals a meaningful smoothness is observed. Therefore it is reasonable to obtain a new geometry for the meshes by imposing the normals as an external condition. In order to achieve coherence between the two entities (polygonal meshes and normals), a local optimization approach is proposed. For each vertex, the position that minimizes the norm of the error between the geometric normal and the external normal is worked out. A second term in the objective function favors solutions that are closer to the current state of the mesh. This minimization process is applied to all vertices that constitute the mesh and it is iterated so as to nd a global minimum in the objective function. Our results show a better match of external normals and meshes, which draws more natural surface-rendered images.