Image matching is an essential task in image processing and computer vision. It is also a challenging one since an imaged object can change its appearance and shape due to a large camera motion or lighting change. The focus of the present work is on recovering a general two-dimensional projective transformation between two images of a scene taken at different viewpoints with a wide baseline or at different times with a lighting change.

All the present approach takes is a new way of looking at this classic task. First, an image patch is thought of as a collection of radial fines from a pole, and, accordingly, the log-polar/inverse-polar coordinate system is adapted to two projectively-correlated patches. Second, in these two types of polar space, the transformation between images is analyzed in terms of lines rather than blocks. In addition, all relevant mathematical operations are one-dimensional and directly applied to radial image liner. Third, a two-step recovering strategy is adopted. That is, a full recovery of a projective transformation is decomposed into two partial recovering processes, one for affine parameters and the other for projective ones.

These ideas unite two different methods we propose for recovering the projective transformations between images. One is the one-dimensional mapping based on the concept of direct image-fine matching and the other is the ray projection based on the concept of integral geometry. These two methods are complementary with each other in the sense that the former exploits the appearance of an imaged object, while the latter mainly uses the shape. Both methods have been evaluated experimentally. In particular, the 1-D mapping has been successfully used to recover a variety of projective geometric transformations between real images of textured and structured scenes. Also, its performance has been demonstrated in such applications as image registration and point-correspondence detection. Moreover, the ray projection has been successfully employed to recover different projective geometric and affine photometric transformations between real images of indoor and outdoor scenes. Its robustness is demonstrated to image blur and occlusion. Its versatility is illustrated through such an application as matching different objects in different classes.