{'fraction_non_alphanumeric': 0.028037383177570093, 'fraction_numerical': 0.0011682242990654205, 'mean_word_length': 5.16546762589928, '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}}
Estimation of Multiple Orientations and Multiple Motions in Multi-Dimensional Signals

The estimation of multiple orientations in multidimensional signals is a strongly non-linear problem to which a two-step solution is here presented. First, the problem is linearized by introducing the so-called mixed-orientation parameters as a unique, albeit implicit, descriptor of the orientations. Second, the non-linearities are decomposed such as to find the individual orientations. For two-dimensional signals, e.g., images, this decomposition step is solved by simply determining the roots of a polynomial. For multi-dimensional signals, the nD decomposition problem is solved by reducing it to a cascade of 2D decomposition problems. In this way, a full solution for the estimation of any number of orientations in any dimension is achieved for the first time