Image registration using the Walsh transform

This paper presents a new algorithm which can be used to register images of the same or different modalities, e.g., images with multiple channels, such as X-rays, temperature or elevation, or simply images of different spectral bands. In particular, a correlation-based scheme is used, but instead of gray values, it correlates numbers formulated by different combinations of the extracted local Walsh coefficients of the images. Each image patch is expanded in terms of Walsh basis functions. Each Walsh basis function can be thought of as measuring a different aspect of local structure, e.g., horizontal edge, corner, etc. The coefficients of the expansion, therefore, can be thought of as dense local features, estimating at each point the degree of presence of, for example, a horizontal edge, a corner with contrast of a certain type, etc. These coefficients are normalized and used as digits in a chosen number system which allows one to create a unique number for each type of local structure. The choice of the basis of the number system allows one to give different emphasis to different types of local feature (e.g., corners versus edges), and, thus, the method we present forms a unified framework in terms of which several feature matching methods may be interpreted. The algorithm is compared with wavelet and contour based approaches, using simulated and real images. The two images are assumed to differ from each other by a rotation and a translation only.