Image Registration Using Spline Based Warping , Jan Kybic HIGH PASS HIGH PASS HIST

In the following sections we present an image registration method using spline based warping. Given two images, reference and test, we shall nd a warping, i.e. non-linear coordinate transformation, that brings the test image as close as possible to the reference image. We chose to use spline as the warping function which permits us to describe it by a nite number of localised parameters. Furthermore we use splines for image interpolation. We deene a measure of diierence between the reference image and the warped test image. Then we optimise the parameters describing the warping function to minimise this criterion. Pyramid approach is used to make the calculation faster and more robust. The problem is rst solved at a coarse level and this solution is used as a starting point for progressively ner levels. This way the total amount of calculation is greatly reduced. The data ow of the algorithm is presented in gure 1. The general framework will be presented as well as an instantiation for: A warping along the x-axis of a two dimensional image and B two dimensional warping of a two dimensional image. (Part B is not ready yet.) 2. Why Splines? The high interpolation order of splines gives an accurate approximation and also permits to calculate derivatives which enables us to use fast converging methods. The explicit form and small compact support of B-splines yield computationally eecient algorithms. The splines lend themselves also very well to expanding and reducing used to go from coarse to ne representation and vice versa. It is useful to imagine that both the reference and test images were obtained by sampling of their continuous versions f c r , f c t , i.e. f r (i) = f c r (x)j x=i for i 2 S r and similarly for f t. Let us also denote S c r resp. S c t the smallest interval in R M containing S r resp.