Research Review On Marching Cubes Algorithm

Isosurface Technology is widely used in visualization and many scalar field visualization problems can be solved by isosurfacing and rendering. Marching Cubes algorithm is the most widely used isosurface method till now. From 1987 when Lorensen brought forward this method, many researchers had been interested in it for its simplicity and efficiency. It is widely used in many areas, such as medical image reconstruction, finite element analysis, implicit surface rendering etc. There have been numerous researches on Marching Cubes till now to improve the efficiency and make it work better. In this paper, the improvement algorithms are reviewed and classified according to the aspects they have improved on the algorithm. This work will have a deep impact on the further research and application in the specific areas.This paper first introduces the background and importance of the study. Some existing work and methods about the algorithm are introduced. Then gives out the definition, the disadvantages and advantages of the algorithms and explains how are these problems are brought about. In the process of isosurfacing, the algorithm lacks consideration of the interior structure of the voxel and take the triangles in the state module as isosurfaces. For there may be some critical points and loops where the isosurfaces may change its shape, the isosurfaces produced in this way may have many problems in topology, precision and efficiency and can not satisfy many applications.There are face ambiguity and body ambiguity problems about the algorithm. In this paper, the methods to solve the face ambiguity are put forwarded first, and then discusses the solutions of body ambiguity problems from four aspects. Through analyzing the properties of the trilinear interpolation function and the experimental results , the differences among the classifications are put forwarded.In this paper, the problems of low accuracy isosurfaces in sparse data field are discussed. The Marching Cubes algorithm firstly computes the intersection points between the isosurfaces and voxels, then uses the points to form triangles which are taken as the final approximate isosurfaces. In this way, the algorithm cannot guarantee the accuracy of the isosurface. A direct method to solve this problem is to increase sampling points, but with the increment of the points, there may be too much space and time needed to process in an interactive way. Another method to improve the accuracy is the adaptive grid method which abstracts the triangle gradually till the accuracy is satisfied. And this method can improve the accuracy without increasing too much computation.This paper also analyzes the circumstance that the algorithm may often produce too many triangles in dense data field and then put forward the main methods to improve the efficiency . There are three types of methods to solve the problem. One way is to avoid sweeping the voxels which don not have any isosurfaces to save time; Another method aims to save the spaces, and the main way is to combine several triangles into one; The multi-resolution method is the widely used one to improve the efficiency. This method considers the factors in both space and time and can satisfy the practical application such as interactive display.At last, this paper summarizes the methods and gives the future research trends of Marching Cubes improvement methods. And this might have important impact on the further research work and practical application.