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Infinite Photography: New Mathematical Model for High-Resolution Images

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Abstract

A new mathematical image model is introduced using the photographic process as the starting point. Images are represented as infinite sequences of photons allowing analysis at arbitrarily high resolution and leading to novel computational methods for processing, representation, transmission and storage of images. The resulting space of infinite photographs is proved to have a metric structure and to be intimately connected with bounded Borel measures. Theorems are proved indicating that the imaging power of the photographic process exceeds function spaces in the high resolution limit; this implies in particular that natural photographic images need to be modelled by generalized functions. Furthermore, computational results are presented to illustrate the novel algorithms based on photon sequences. The algorithms include stochastic halftoning, representation of cartoon images with outlines, anti-aliasing, blurring and singularity extraction.

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Authors and Affiliations

  1. Department of Mathematics and System Analysis, Helsinki University of Technology, P.O. Box 1100 (Otakaari 1 M), 02015 TKK, Helsinki, Finland

    Tapio Helin

  2. Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68 (Gustaf Hallstromin katu 2b), 00014, Helsinki, Finland

    Matti Lassas & Samuli Siltanen

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  1. Tapio Helin
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  2. Matti Lassas
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  3. Samuli Siltanen
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Correspondence to Tapio Helin.

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Helin, T., Lassas, M. & Siltanen, S. Infinite Photography: New Mathematical Model for High-Resolution Images. J Math Imaging Vis 36, 140–158 (2010). https://doi.org/10.1007/s10851-009-0177-7

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  • DOI: https://doi.org/10.1007/s10851-009-0177-7

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