The Geometry Algebraic Invariant In Computer Vision

The purpose of computer vision research is to find the corresponding objects in two-dimensional(2D) images captured from the three-dimensional(3D) world. However, this is not always easy. Because the 3D target imaging is a process of projective transformation. The difficulties of research are mainly focused on the following parts:First of all, for the general 3D objects, its imaging may change with the illumination, shooting angles, camera internal parameters etc., thus lead to different images captured. Secondly, the information provided by a single image is often incomplete and inadequate. What`s more, images are only the 2D projection of 3D coordinates and the depth information lose in the process of projection. Finally, the developed methods can only solve the problems caused by the change of rotation, translation and scaling in general. And once other conditions change, these methods are pale. Moreover, the computation of existing invariant consist by geometrical constraints structure are too large and complex.In order to solve the problems above, people shift their attention to study the invariant. It describes the essential feature of 3D objects and highly abstract and generalize the objects geometry information, which can effectively eliminate the adverse effects of various kinds of factors and remains unchanged between 3D objects and 2D images. What`s more, invariant shows the advantages in computer vision and target recognition, because it not only reduces the difficulty of recognition and improves the recognition efficiency, but also solved the problem of the difference in computer vision. So the structure and computation of invariant have important research value and application prospects.For these many reasons, this paper, on the basis of conformal geometric algebra(CGA) theory, proposes two global geometry invariant: the invariant consist of eight points geometry in 3D space and the invariant consist of seven straight lines on three adjacent planes geometry in 3D space. The two invariant has the following advantages:First,due to the proposed invariant`s calculation mainly depends on the extraction features of point and line. And the two features are not only common in any image, but their extraction method is relatively mature, which make the calculation of invariant become relatively accurate and easy.Secondly, the calculation of the invariant just needs a single image. Relative to the use of multiple frames, the proposed method avoid the computation of fundamental matrix between multi-image and camera calibration etc., which make it simpler and convenience.Finally, the proposed algorithm can not only deduce the invariants of other geometric structure, but also conducive to discover more unknown structure invariants. All these show that the invariant algorithm proposed in this paper has good versatility and simplicity. And at the same time, the simulation experiment and real experiment prove that the invariant structure extracted in this paper are not be impacted by the change of various factors such as the camera viewpoint etc. and remain basically the same in different perspective, with better reliability and stability.