{'fraction_non_alphanumeric': 0.022321428571428572, 'fraction_numerical': 0.0, 'mean_word_length': 5.5, '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}}
Spatial-Frequency Representations Of Images With Scale Invariant Properties

Scale-invariant transforms are those that leave the form of the image representation unchanged over changes in image size. These transforms have the important advantages of simplifying pattern recognition tasks when the distance to the objects is variable, while simultaneously reducing the amount of data that must be processed. The properties of scale-invariant systems are investigated here in the spatial-frequency domain, using an image representation called a "scaled transform". A discrete version of the transform is developed and its properties contrasted with those of the Fourier series. It is shown that unlike the Fourier series representation where the magnitude of the frequency vectors, k, occur at fixed frequency intervals ▵k, the scaled-transform frequencies occur at fixed fractional intervals ▵k/k.