Geometric Invariance and Its Applications to 3D Object Recognition
几何不变性及其在3D物体识别中的应用

3D object recognition, which requires recognition and localization of the 3D object from 2D images, is one of the main research fields of computer vision. It is well known that the appearance of an object varies with the viewpoint and the intrinsic parameters of a camera, which makes the recognition more difficult. By geometric invariance refer to the unchanged property of the shape of an object under special space transformation. Because projective invariance between 3D object and its 2D image could overcome the problem caused by viewpoint, calibration and feature correspondence effectively, it has been attracting more and more attention and research efforts over the last 20 years. For more comprehension to this field, firstly, the main research contents of the invariance-based 3D object recognition is discussed, including geometry frames and their invariance, as well as the way to apply the geometric invariance. Secondly, a commentarial review of this field is given to show the last evolution of it. Although many kinds of useful projective invariance have been derived so far, the sorts of 3D object to which they could be used are still very limited. So there are some needs to develop more powerful invariance for the 3D object recognition. Finally, in the last part of this paper, the future researches in this field are proposed.