几何不变性及其在3D物体识别中的应用

三维物体识别是计算机视觉研究的重要内容之一，它要求从3D物体的2D图象中识别和定位物体．由于物体成像时会受到观察视角、摄像机参数的影响，因此使得同一物体在不同观察视角、不同摄像机参数等条件下所得到的图象存在差异．但由于几何不变性方法可以有效地消除这种差异带给3D物体识别的不利影响，所以，近20年来这种方法受到了广泛的关注和研究．为使人们了解该领域的研究现状，以对该领域的研究有所启发，首先讨论了基于几何不变性的3D物体识别方法的研究内容，包括研究的几何框架和其不变性以及几何不变性在3D物体识别中的主要应用；其次，总结性地评述了该领域的研究现状；最后，提出了研究的发展方向．

Geometric Invariance and Its Applications to 3D Object Recognition

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.