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How complex is a random picture? / Aurzada, Frank; Lifshits, Mikhail.

In: Journal of Complexity, Vol. 53, 08.2019, p. 133-161.

Research output: Contribution to journal › Article › peer-review

Harvard

Aurzada, F & Lifshits, M 2019, 'How complex is a random picture?', Journal of Complexity, vol. 53, pp. 133-161. https://doi.org/10.1016/j.jco.2018.11.003, https://doi.org/10.1016/j.jco.2018.11.003

APA

Aurzada, F., & Lifshits, M. (2019). How complex is a random picture? Journal of Complexity, 53, 133-161. https://doi.org/10.1016/j.jco.2018.11.003, https://doi.org/10.1016/j.jco.2018.11.003

Vancouver

Aurzada F, Lifshits M. How complex is a random picture? Journal of Complexity. 2019 Aug;53:133-161. https://doi.org/10.1016/j.jco.2018.11.003, https://doi.org/10.1016/j.jco.2018.11.003

Author

Aurzada, Frank ; Lifshits, Mikhail. / How complex is a random picture?. In: Journal of Complexity. 2019 ; Vol. 53. pp. 133-161.

BibTeX

@article{9d783dc53d6a47ab898886af5c539508,
title = "How complex is a random picture?",
abstract = "We study the amount of information that is contained in “random pictures” by which we mean the sample sets of a Boolean model. To quantify the notion “amount of information” two closely connected questions are investigated: on the one hand, we study the probability that a large number of balls is needed for a full reconstruction of a Boolean model sample set. On the other hand, we study the quantization error of the Boolean model w.r.t. the Hausdorff distance as a distortion measure.",
keywords = "Boolean model, Functional quantization, High resolution quantization, Information based complexity, Metric entropy, DIFFUSION-PROCESSES, CODING COMPLEXITY, QUADRATURE, FUNCTIONAL QUANTIZATION, CONSTRUCTIVE QUANTIZATION",
author = "Frank Aurzada and Mikhail Lifshits",
year = "2019",
month = aug,
doi = "10.1016/j.jco.2018.11.003",
language = "English",
volume = "53",
pages = "133--161",
journal = "Journal of Complexity",
issn = "0885-064X",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - How complex is a random picture?

AU - Aurzada, Frank

AU - Lifshits, Mikhail

PY - 2019/8

Y1 - 2019/8

N2 - We study the amount of information that is contained in “random pictures” by which we mean the sample sets of a Boolean model. To quantify the notion “amount of information” two closely connected questions are investigated: on the one hand, we study the probability that a large number of balls is needed for a full reconstruction of a Boolean model sample set. On the other hand, we study the quantization error of the Boolean model w.r.t. the Hausdorff distance as a distortion measure.

AB - We study the amount of information that is contained in “random pictures” by which we mean the sample sets of a Boolean model. To quantify the notion “amount of information” two closely connected questions are investigated: on the one hand, we study the probability that a large number of balls is needed for a full reconstruction of a Boolean model sample set. On the other hand, we study the quantization error of the Boolean model w.r.t. the Hausdorff distance as a distortion measure.

KW - Boolean model

KW - Functional quantization

KW - High resolution quantization

KW - Information based complexity

KW - Metric entropy

KW - DIFFUSION-PROCESSES

KW - CODING COMPLEXITY

KW - QUADRATURE

KW - FUNCTIONAL QUANTIZATION

KW - CONSTRUCTIVE QUANTIZATION

UR - http://www.scopus.com/inward/record.url?scp=85057790702&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/complex-random-picture

U2 - 10.1016/j.jco.2018.11.003

DO - 10.1016/j.jco.2018.11.003

M3 - Article

AN - SCOPUS:85057790702

VL - 53

SP - 133

EP - 161

JO - Journal of Complexity

JF - Journal of Complexity

SN - 0885-064X

ER -

ID: 35797721