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What Is the Set of Images of an Object Under All Possible Illumination Conditions?

Authors:

Peter N. Belhumeur,

David J. KriegmanAuthors Info & Claims

International Journal of Computer Vision, Volume 28, Issue 3

Pages 245 - 260

https://doi.org/10.1023/A:1008005721484

Published: 01 July 1998 Publication History

Abstract

The appearance of an object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated. If the appearance of two objects is never identical for any pose or lighting conditions, then-in theory-the objects can always be distinguished or recognized. The question arises: What is the set of images of an object under all lighting conditions and pose In this paper, we consider only the set of images of an object under variable illumination, including multiple, extended light sources and shadows. We prove that the set of n -pixel images of a convex object with a Lambertian reflectance function, illuminated by an arbitrary number of point light sources at infinity, forms a convex polyhedral cone in R^n and that the dimension of this illumination cone equals the number of distinct surface normals. Furthermore, the illumination cone can be constructed from as few as three images. In addition, the set of n -pixel images of an object of any shape and with a more general reflectance function, seen under all possible illumination conditions, still forms a convex cone in R^n . Extensions of these results to color images are presented. These results immediately suggest certain approaches to object recognition. Throughout, we present results demonstrating the illumination cone representation.

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Cited By

Huang QXu CLi GWu ZLiu SHe SCai JKankanhalli MPrabhakaran BBoll SSubramanian RZheng LSingh VCesar PXie LXu D(2024)Portrait Shadow Removal via Self-Exemplar Illumination EqualizationProceedings of the 32nd ACM International Conference on Multimedia10.1145/3664647.3681000(7474-7482)Online publication date: 28-Oct-2024
https://dl.acm.org/doi/10.1145/3664647.3681000
Souza LSogi NGatto BKobayashi TFukui K(2023)Grassmannian learning mutual subspace method for image set recognitionNeurocomputing10.1016/j.neucom.2022.10.040517:C(20-33)Online publication date: 14-Jan-2023
https://dl.acm.org/doi/10.1016/j.neucom.2022.10.040
Sogi NZhu RXue JFukui K(2022)Constrained mutual convex cone method for image set based recognitionPattern Recognition10.1016/j.patcog.2021.108190121:COnline publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1016/j.patcog.2021.108190
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Index Terms

What Is the Set of Images of an Object Under All Possible Illumination Conditions?
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision problems
      2. Computer vision tasks
        Scene understanding
  2. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
2. Theory of computation
  1. Design and analysis of algorithms

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Information & Contributors

Information

Published In

cover image International Journal of Computer Vision

International Journal of Computer Vision Volume 28, Issue 3

July 1, 1998

77 pages

ISSN:0920-5691

Editors:
Takeo Kanade
Carnegie Mellon Univ., Pittsburgh, PA
,
Oliver Faugeras
INRIA, Valbonne, France

Issue’s Table of Contents

Copyright © Copyright © 1998 Kluwer Academic Publishers.

Publisher

Kluwer Academic Publishers

United States

Publication History

Published: 01 July 1998

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Cited By

Huang QXu CLi GWu ZLiu SHe SCai JKankanhalli MPrabhakaran BBoll SSubramanian RZheng LSingh VCesar PXie LXu D(2024)Portrait Shadow Removal via Self-Exemplar Illumination EqualizationProceedings of the 32nd ACM International Conference on Multimedia10.1145/3664647.3681000(7474-7482)Online publication date: 28-Oct-2024
https://dl.acm.org/doi/10.1145/3664647.3681000
Souza LSogi NGatto BKobayashi TFukui K(2023)Grassmannian learning mutual subspace method for image set recognitionNeurocomputing10.1016/j.neucom.2022.10.040517:C(20-33)Online publication date: 14-Jan-2023
https://dl.acm.org/doi/10.1016/j.neucom.2022.10.040
Sogi NZhu RXue JFukui K(2022)Constrained mutual convex cone method for image set based recognitionPattern Recognition10.1016/j.patcog.2021.108190121:COnline publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1016/j.patcog.2021.108190
Hassan MSuhail Shaikh MJatoi M(2022)Image quality measurement-based comparative analysis of illumination compensation methods for face image normalizationMultimedia Systems10.1007/s00530-021-00853-y28:2(511-520)Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s00530-021-00853-y
Wang TBuchanan SGilboa DWright JRanzato MBeygelzimer ADauphin YLiang PVaughan J(2021)Deep networks provably classify data on curvesProceedings of the 35th International Conference on Neural Information Processing Systems10.5555/3540261.3542478(28940-28953)Online publication date: 6-Dec-2021
https://dl.acm.org/doi/10.5555/3540261.3542478
Chen LZheng YShi BSubpa-asa ASato I(2021)A Microfacet-Based Model for Photometric Stereo with General Isotropic ReflectanceIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2019.292790943:1(48-61)Online publication date: 1-Jan-2021
https://dl.acm.org/doi/10.1109/TPAMI.2019.2927909
Shahlaei DBlanz V(2020)Hierarchical Bayesian Inverse Lighting of Portraits with a Virtual Light StageIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2019.289163842:4(865-879)Online publication date: 4-Mar-2020
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Zhang WZhao XMorvan JChen L(2019)Improving Shadow Suppression for Illumination Robust Face RecognitionIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2018.280317941:3(611-624)Online publication date: 1-Mar-2019
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Li KHe FYu HChen X(2019)A parallel and robust object tracking approach synthesizing adaptive Bayesian learning and improved incremental subspace learningFrontiers of Computer Science: Selected Publications from Chinese Universities10.1007/s11704-018-6442-413:5(1116-1135)Online publication date: 1-Oct-2019
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