Symmetry Sets And Its Applications In 3D Reconstruction

Visual information is the main source of human feeling.Through a lot of provided visual information,human understand the outside world.To make a computer or a robot similar to the human visual function,which is a long-term dream.Three-Dimensional Reconsruction in the field of computer vision is an essential classic problem,but also the final step needed to complete when we make the computer simulate human visual function.That is to say,how to reconstruct the three-dimensional object information.With the development of modern digital technology, mathematical konwledge in the three-dimensional reconstruction has faced with widespread concern.In this paper,based on domestic and international advanced achievements,fully integrated computer vision,pattern recongnition,singularity theory and other related konwledge,we discuss symmetry sets and its applications in three-dimensional reconstruction.The differentiable mapping of singularity theory is a young mathematical discipline.It is at the junction of the topology, algebraic geometry, differential geometry, algebra, analysis and many other areas of mathematics. One of the basic viewpoints of its study is the so-called genericity, which is not concerned about the type of singular points and the nature for a given map. The main research is the type of singular point for a given dimension mapping,that is the type of singular points and the nature of the singularity sets for the different dimensions of space mapping.Based on the prerequisites-establishing the corresponding relationship of two images,we make relative discussion. When the 3D scene of space was projected to 2D images,the images of the same scene will be very different in different viewpoints.It is obviously difficult to match these images,which contain a number of unfavorable factors.So,matching is also the most difficult issue in computer vision.In this paper, we extract the characteristics of the graphics using symmetry set and then match the graphics,which is different from the traditional statistical methods of pattern recognition.This method can complete the matching rapidly and accurately.And it will also be a very good match,when we take the rotation ,translation and scale transformation.