article

The Nonlinear Statistics of High-Contrast Patches in Natural Images

Authors:

Kim S. Pedersen,

David MumfordAuthors Info & Claims

International Journal of Computer Vision, Volume 54, Issue 1-3

Pages 83 - 103

https://doi.org/10.1023/A:1023705401078

Published: 01 August 2003 Publication History

Abstract

Recently, there has been a great deal of interest in modeling the non-Gaussian structures of natural images. However, despite the many advances in the direction of sparse coding and multi-resolution analysis, the full probability distribution of pixels values in a neighborhood has not yet been described. In this study, we explore the space of data points representing the values of 3 × 3 high-contrast patches from optical and 3D range images. We find that the distribution of data is extremely “sparse” with the majority of the data points concentrated in clusters and non-linear low-dimensional manifolds. Furthermore, a detailed study of probability densities allows us to systematically distinguish between images of different modalities (optical versus range), which otherwise display similar marginal distributions. Our work indicates the importance of studying the full probability distribution of natural images, not just marginals, and the need to understand the intrinsic dimensionality and nature of the data. We believe that object-like structures in the world and the sensor properties of the probing device generate observations that are concentrated along predictable shapes in state space. Our study of natural image statistics accounts for local geometries (such as edges) in natural scenes, but does not impose such strong assumptions on the data as independent components or sparse coding by linear change of bases.

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Cited By

Pinetz TKobler EPock TEffland A(2022)Blind Single Image Super-Resolution via Iterated Shared Prior LearningPattern Recognition10.1007/978-3-031-16788-1_10(151-165)Online publication date: 27-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-16788-1_10
Li JXia S(2021)On the local behavior of spaces of range image patchesMultimedia Tools and Applications10.1007/s11042-020-09913-380:11(16441-16472)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s11042-020-09913-3
Moor MHorn MRieck BBorgwardt KDaumé HSingh A(2020)Topological autoencodersProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525591(7045-7054)Online publication date: 13-Jul-2020
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Index Terms

The Nonlinear Statistics of High-Contrast Patches in Natural Images
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
2. Mathematics of computing
  1. Probability and statistics

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Copyright © Copyright © 2003 Kluwer Academic Publishers.

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Kluwer Academic Publishers

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Published: 01 August 2003

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Cited By

Pinetz TKobler EPock TEffland A(2022)Blind Single Image Super-Resolution via Iterated Shared Prior LearningPattern Recognition10.1007/978-3-031-16788-1_10(151-165)Online publication date: 27-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-16788-1_10
Li JXia S(2021)On the local behavior of spaces of range image patchesMultimedia Tools and Applications10.1007/s11042-020-09913-380:11(16441-16472)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s11042-020-09913-3
Moor MHorn MRieck BBorgwardt KDaumé HSingh A(2020)Topological autoencodersProceedings of the 37th International Conference on Machine Learning10.5555/3524938.3525591(7045-7054)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.5555/3524938.3525591
Polianskii VPokorny FGupta RLiu YShah MRajan STang JPrakash B(2020)Voronoi Graph Traversal in High Dimensions with Applications to Topological Data Analysis and Piecewise Linear InterpolationProceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining10.1145/3394486.3403266(2154-2164)Online publication date: 23-Aug-2020
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Chen YPaiton DOlshausen B(2018)The sparse manifold transformProceedings of the 32nd International Conference on Neural Information Processing Systems10.5555/3327546.3327712(10534-10545)Online publication date: 3-Dec-2018
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Du HZhang YBao FWang PZhang C(2018)A Texture Preserving Image Interpolation Algorithm Based on Rational FunctionInternational Journal of Multimedia Data Engineering & Management10.4018/IJMDEM.20180401039:2(36-56)Online publication date: 1-Apr-2018
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Shi ZOsher SZhu W(2018)Generalization of the Weighted Nonlocal Laplacian in Low Dimensional Manifold ModelJournal of Scientific Computing10.1007/s10915-017-0549-x75:2(638-656)Online publication date: 1-May-2018
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Ribeiro Tde Oliveira ABarcelos C(2018)Frequency Analysis of Topological Projections onto Klein Bottle for Texture CharacterizationProgress in Pattern Recognition, Image Analysis, Computer Vision, and Applications10.1007/978-3-030-13469-3_40(342-350)Online publication date: 19-Nov-2018
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Liu SMaljovec DWang BBremer PPascucci V(2017)Visualizing High-Dimensional DataIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2016.264096023:3(1249-1268)Online publication date: 1-Mar-2017
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