This paper presents a generalization of non-uniform B-spline surfaces called T-splines. T-spline control grids permit T-junctions, so lines of control points need not traverse the entire control grid. T-splines support many valuable operations within a consistent framework, such as local refinement, and the merging of several B-spline surfaces that have different knot vectors into a single gap-free model. The paper focuses on T-splines of degree three, which are C 2 (in the absence of multiple knots). T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T-splines and Catmull-Clark surfaces. Thus, a modeling program for T-NURCCs can handle any NURBS or Catmull-Clark model as special cases. T-NURCCs enable true local refinement of a Catmull-Clark-type control grid: individual control points can be inserted only where they are needed to provide additional control, or to create a smoother tessellation, and such insertions do not alter the limit surface. T-NURCCs use stationary refinement rules and are C 2 except at extraordinary points and features.

This paper presents a generalization of non-uniform B-spline surfaces called T-splines. T-spline control grids permit Tjunctions, so lines of control points need not traverse the entire control grid. T-splines support many valuable operations within a consistent framework, such as local refinement, and the merging of several B-spline surfaces that have different knot vectors into a single gap-free model. The paper focuses on T-splines of degree three, which are C 2 (in the absence of multiple knots). T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T-splines and Catmull-Clark surfaces. Thus, a modeling program for T-NURCCs can handle any NURBS or Catmull-Clark model as special cases. T-NURCCs enable true local refinement of a Catmull-Clark-type control grid: individual control points can be inserted only where they are needed to provide additional control, or to create a smoother tessellation, and such insertions do not alter the limit surface. T-NURCCs use stationary refinement rules and are C 2 except at extraordinary points and features.

One of the central issues in computer-aided geometric design is the representation of free-form surfaces which are needed for many purposes in engineering and science. Several limitations are imposed on most available surface systems: the rectangularity of the network describing a surface and the manipulation of surfaces without regard to the volume enclosed are examples. Polyhedral subdivision methods suggest themselves as a solution to these problems. Their use, however, is not widespread for several reasons such as the lack of boundary control, and interpolation and interrogation capabilities.In this paper the original work on subdivision methods is extended to overcome these problems. Two methods are described, one for controlling the boundary curves of such surfaces, and another for interpolating points on irregular networks. A general surface/surface intersection algorithm is also provided: seven decisions need to be made in order to specify a particular implementation. The algorithm is also suitable for intersecting other classes of surfaces amongst which are the popular Bezier and B-spline surfaces.

Image segmentation is an essential process for image analysis. Several methods were developed to segment multicomponent images, and the success of these methods depends on several factors including 1) the characteristics of the acquired image and 2) the percentage of imperfections in the process of image acquisition. The majority of these methods require a priori knowledge, which is difficult to obtain. Furthermore, they assume the existence of models that can estimate its parameters and fit to the given data. However, such a parametric approach is not robust, and its performance is severely affected by the correctness of the utilized parametric model. In this letter, a new multicomponent image segmentation method is developed using a nonparametric unsupervised artificial neural network called Kohonen's selforganizing map (SOM) and hybrid genetic algorithm (HGA). SOM is used to detect the main features that are present in the image; then, HGA is used to cluster the image into homogeneous regions without any a priori knowledge. Experiments that are performed on different satellite images confirm the efficiency and robustness of the SOM-HGA method compared to the Iterative Self-Organizing DATA analysis technique (ISODATA).Index Terms-Aerial image, genetic algorithm (GA), image segmentation, neural network, satellite image, unsupervised classification.

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