Abstract

this paper, we present a novel histogram based method for estimating and maximising mutual information (MI) between two multimodal and possibly multibanded signals. Histogram based estimation methods are a common means for estimating the MI between two signals and the derivative of MI with respect to these signals. However, these approaches do not scale well towards higher dimensions of the signals involved. This is due to the exponential explosion of the number of bins needed to accurately estimate the marginal and joint densities. We introduce a new estimation method which relies on the combination of non-uniform quantisation of the signal spaces and kernel density estimation to deal with this problem. Furthermore, we show how existing 1D-1D methods can be improved by using a combination of weighted histogram updates and kernel convolutions. These convolutions can be computed e#ciently in the frequency domain which reduces the computational overhead significantly. The weighting scheme, on the other hand, enables us to compute analytical derivatives of MI with respect to either of both signals, which is important for further optimisation purposes. We illustrate our approach with several applications in parametric and non-parametric multimodal image registration. Our case study is the registration of multiband aerial images. More particularly, we demonstrate how optimisation of MI can succesfully allign intensity, infra-red, natural color and pseudo-color images in the cse of parametric (a#ne) and non-parametric (optical flow) transformations

Citations