Fully Automated Registration of Vibrational Microscopectroscopic Images in Histologically Stained Tissue Sections Additional File 2

Due to its ability to capture nonlinear dependencies between random variables, mutual information as an information theoretic measure of correlation is particularly suitable and well-established for the registration of images across different image modalities [4]. Several variants of mutual information measures have been proposed in the context of image registration, most notably Viola-Wells mutual information [6] and Mattes mutual information [2]. In our setting we employ discrete mutual information in the spirit of Mattes mutual information, where only indices of segments obtained from an unsupervised presegmentation of the images are directly used rather than binning a continuous random variable. Utilizing discrete mutual information between the index images as our similarity measure, we capture the hidden correlation between the FTIR spectral image and H&E stained image to some extent. However, the precise relationship remains unknown, causing the correlation between the two index images to be rather weak in general (Figure 2 in the main manuscript). When using this weak correlation in a template-matching-like registration as our similarity measure, we encounter the problem of background attraction exemplified in Figure S1. It can in fact be observed that background regions generally achieve a relatively high, often globally maximal, mutual information during template matching. This is mainly because the correlation between two images in the true transformation is relatively weak, while a large plain region (which is a common characteristic of background regions) can significantly reduce the joint entropy, making the mutual information bigger than the regions that are totally uncorrelated. This phenomenon is particularly prominent when employing image pyramid schemes [5], where the mutual information at higher pyramid levels is strongly affected by this phenomenon. Background attraction prohibits correct registration results in many cases for mainly two reasons. First, sometimes mutual information achieves its maximum value at the wrong transformation, leading to false registration positions (Figure S4a). Second, whenever not using exhaustive search to determine the transformation that maximizes mutual information, the optimizer may be trapped in a local, but not global optimum. Note that background regions typically yield large segments in clustering based pre-segmentations, and thus are particularly prone to produce local maxima of large width in the scoring landscape. Thus, even if the global maximum is at the correct position , many types of optimizers may easily get trapped in the wide local maxima of background regions. Even if the optimizer can finally escape, it will require a large number of …