We propose a new optimizer in the context of multimodal image registration. The optimized criterion is the mutual in formation between the images to align. This criterion requires that their joint histogram be available. For its computation, we introduce differentiable and separable Parzen windows that satisfy the partition of unity. Along with a continuous model of the images based on splines, this allows us to derive exact and tractable expressions for the gradient and the Hessian of the criterion. Then, we develop an optimizer based on the Marquardt-Levenberg strategy. Our new optimizer is specific to mutual information, in the same sense that Marquardt-Levenberg is specific to least-squares. We show that our optimizer is particularly well-adapted to an iterative coarse-to-fine approach. We validate its accuracy by comparing its performance to that of several results available in the literature.