{'fraction_non_alphanumeric': 0.012515644555694618, 'fraction_numerical': 0.0, 'mean_word_length': 5.4, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Measuring Geodesic Distances on the Space of Bounded Diffeomorphisms

This paper considers the problem of measuring the differences between deformations. It is intended to be applied in the context of applications such as the analysis of sets of non-rigidly registered medical images, where diffeomorphic warps between pairs of images establish a dense pixel-to-pixel correspondence. We introduce a new spline with explicit boundary conditions, and show how this can be used to generate general flows of bounded diffeomorphisms. Techniques are developed to describe an arbitrary continuous diffeomorphism and to invert and interpolate between such diffeomorphisms. We show how these constructions and the geodesic distance can be used in the analysis of training sets of general diffeomorphic warps.