Research On Surface Modeling And Its Applications In Image Processing

With the development of Computer Graphics and Computer Aided Design, surface modeling technology has increasingly been adopted by all sectors of society, these fields include aerospace technology, digital city, media design, medical visualization and industrial product design, and so on. In surface modeling technology, one of the key and hot research problems are how to design more complex and realistic 3D models, and how to solve the related research problem based on the continuity and complexity of surface. At firstly, digital surface modeling technology can construct complex 3D models, such as surface, mesh and solid model; secondly, complex surface modeling can supply more varied and acute computing method of 3D data expression for designer. Furthermore, complex surface modeling can mining the related information in discrete and disorder 3D data, in order to process and compute the 3D data for users. In recent years, there are considerable of research achievements for surface modeling technology, however, there are some difficult problems to be resolved, such as how to design surface shape freely by interactive methods, and so on. Currently, how to use surface modeling technology in complex digital image processing is also a hot problem, and there is no efficient method for this to be solved problem.Based on above problems, we will discuss three core problems in this article:1) implicit surface design interactively; 2) Discrete mesh expression method for implicit surface; 3) Digital image zooming based on rational interpolating surface modeling. New theories and algorithms are presented in this article, the detail research works include:1. Implicit surface interactive modelingWe study the design interpolating conditions of implicit surface, present a new shape controlling and adjusting method for variational surface. Firstly we use particle system to have the sampling of variational surface. Adjusted particle position and normal vector are defined as interpolation conditions. New surface is constrained to interpolate the new position and normal vector. For variational surface, analytical expression of smoothing surface is constructed by radial basis function which interpolates given scattered data points. So we can use the adjusted position and normal vector as one of condition in surface expression for optimizing, and get the adjusted surface expression. This new method can achieve adjust variational surface in real time.2. Discrete network expression of implicit surfaceWe study the reasonable point sampling of implicit surface and present a new method for implicit surface triangular mesh construction. Based on Gauss curvature characters of implicit surface we get particle sampling. A shell space can be constructed via extending particles along their positive and negative normal vectors. This shell space is close to given implicit surface and includes the whole surface. We can divide the shell space into tetrahedrons mesh and extract intersection points with implicit surface in space, then connect these points into triangular mesh. The final triangular mesh has small and intensive triangles in high curvature region and big and sparse triangles in low curvature region, so it can express given implicit surface better.3. Digital image zooming based on shape preserving constrainRational function approximation is a typical approximation method that can express some characters of interpolation surface especially such as the variation of adjacent pixels on boundary. So the image boundary can be preserved after zooming. We study the characters of bi-variables rational interpolation function and geometry meaning of its derivative and present a new method for digital image zooming with boundary preserving. In new algorithm, we construct the fitting rational interpolating surface based on function value and derivative value, and then we estimate the derivative value with shape preserving so that rational spline function can have the advised shape of given image and keep the boundary feature. At last, we can re-sample on the interpolation surface and zooming the given image. This new algorithm can be applied in digital image zooming and keep the boundary features.4. Medical image zooming method based on rational interpolating surface with function valueAccording to the formula of the regional sampling in the principles of medical imaging. In medical images, regional sampling is for re-sampling point, and the value is the average of density values of adjacent pixels. For avoiding computation complexity of regional integration of derivative on interpolation surface, we use rational spline model with only functional value to construct interpolation surface. Because the larger scale of density value of medical images, we use density value instead of gray value as functional value for interpolating. To achieve real-time zooming, we present a speed-up method for computing regional integration. From the experimental results we can see the new algorithm can be used in real-time medical image zooming and keep image boundary feature for doctors’ requests for the organization details.For the simplification of interpolation only based on funcational value, general digital images will be blurred if zooming scale is large. According to this problem, we present an image enhancement method via controlling parameters in rational interpolation surface.