In this paper, we present a framework for image segmentation based on parametrized active contours. The evolving contour is parametrized according to a reduced set of control points that form a closed polygon and have a clear visual interpretation. The parametrization, called mean value coordinates, stems from the techniques used in computer graphics to animate virtual models. Our framework allows to easily formulate region-based energies to segment an image. In particular, we present three different local region-based energy terms: 1) the mean model; 2) the Gaussian model; 3) and the histogram model. We show the behavior of our method on synthetic and real images and compare the performance with state-of-the-art level set methods.

Summary.We propose algorithms to incrementally modify a mesh of a planar domain by interactively inserting and removing elements (points, segments, polygonal lines, etc.) into or from the planar domain, keeping the quality of the mesh during the process. Our algorithms, that combine mesh improvement techniques, achieve quality by deleting, moving or inserting Steiner points from or into the mesh. The changes applied to the mesh are local and the number of Steiner points added during the process remains low. Moreover, our approach can also be applied to the directly generation of refined Delaunay quality meshes.

No abstract

No abstract

We propose and discuss a new Lepp-surface method able to produce a small triangular approximation of huge sets of terrain grid data by using a two-goal strategy that assures both small approximation error and well-shaped 3D triangles. This is a refinement method which starts with a coarse initial triangulation of the input data, and incrementally selects and adds data points into the mesh as follows: for the edge e having the highest error in the mesh, one or two points close to (one or two) terminal edges associated with e are inserted in the mesh. The edge error is computed by adding the triangle approximation errors of the two triangles that share e, while each L2-norm triangle error is computed by using a curvature tensor (a good approximation of the surface) at a representative point associated with both triangles. The method produces triangular approximations that capture well the relevant features of the terrain surface by naturally producing well-shaped triangles. We compare our method with a pure L2-norm optimization methodThe first, second and fourth authors were partially supported by the Spanish Ministerio de Educacion y Ciencia under grant TIN2010-20590-C02-0