A procedure for the parameterization of surface meshes of objects with spherical topology is presented. The generation of such a parameterisation has been formulated and solved as a large constrained optimization problem by C. Brechbuhler (1995), but the convergence of this algorithm becomes unstable for object meshes consisting of several thousand vertices. We propose a new more stable algorithm to overcome this problem using multi-resolution meshes. A triangular mesh is mapped to a sphere by harmonic mapping. Next, a mesh hierarchy is constructed. The coarsest level is then optimized using a modification of the original procedure to map object surfaces to the unit sphere. The result is used as a starting point for the mapping of the next finer mesh, a process which is repeated until the final result is obtained. The new approach is compared to the original one and some parameterized object surfaces are presented.

This paper presents a new approach to the correction of intensity inhomogeneities in magnetic resonance imaging (MRI) that significantly improves intensity-based tissue segmentation. The distortion of the image brightness values by a low-frequency bias field impedes visual inspection and segmentation. The new correction method called parametric bias field correction (PABIC) is based on a simplified model of the imaging process, a parametric model of tissue class statistics, and a polynomial model of the inhomogeneity field. We assume that the image is composed of pixels assigned to a small number of categories with a priori known statistics. Further we assume that the image is corrupted by noise and a low-frequency inhomogeneity field. The estimation of the parametric bias field is formulated as a nonlinear energy minimization problem using an evolution strategy (ES). The resulting bias field is independent of the image region configurations and thus overcomes limitations of methods based on homomorphic filtering. Furthermore, PABIC can correct bias distortions much larger than the image contrast. Input parameters are the intensity statistics of the classes and the degree of the polynomial function. The polynomial approach combines bias correction with histogram adjustment, making it well suited for normalizing the intensity histogram of datasets from serial studies. We present simulations and a quantitative validation with phantom and test images. A large number of MR image data acquired with breast, surface, and head coils, both in two dimensions and three dimensions, have been processed and demonstrate the versatility and robustness of this new bias correction scheme.