Formalization and computational aspects of image analysis

Luis Alvarez; Jean Michel Morel

doi:10.1017/S0962492900002415

Formalization and computational aspects of image analysis

Luis Alvarez
, Jean Michel Morel

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

97 Citations (Scopus)

Abstract

In this article we shall present a unified and axiomatized view of several theories and algorithms of image multiscale analysis (and low level vision) which have been developed in the past twenty years. We shall show that under reasonable invariance and assumptions, all image (and shape) analyses can be reduced to a single partial differential equation. In the same way, movie analysis leads to a single parabolic differential equation. We discuss some applications to image segmentation and movie restoration. The experiments show how accurate and invariant the numerical schemes must be and we compare several (old and new) algorithms by discussing how well they match the axiomatic invariance requirements. © 1994, Cambridge University Press. All rights reserved.

Original language	English
Pages (from-to)	1-59
Journal	Acta Numerica
Volume	3
Issue number	1
DOIs	https://doi.org/10.1017/S0962492900002415
Publication status	Published - Jan 1994
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Access Output

10.1017/S0962492900002415

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{ba35be6ebd04402bb1a8094b22aeb08a,

title = "Formalization and computational aspects of image analysis",

abstract = "In this article we shall present a unified and axiomatized view of several theories and algorithms of image multiscale analysis (and low level vision) which have been developed in the past twenty years. We shall show that under reasonable invariance and assumptions, all image (and shape) analyses can be reduced to a single partial differential equation. In the same way, movie analysis leads to a single parabolic differential equation. We discuss some applications to image segmentation and movie restoration. The experiments show how accurate and invariant the numerical schemes must be and we compare several (old and new) algorithms by discussing how well they match the axiomatic invariance requirements. {\textcopyright} 1994, Cambridge University Press. All rights reserved.",

author = "Luis Alvarez and Morel, \{Jean Michel\}",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected]. ",

year = "1994",

month = jan,

doi = "10.1017/S0962492900002415",

language = "English",

volume = "3",

pages = "1--59",

journal = "Acta Numerica",

issn = "0962-4929",

publisher = "Cambridge University Press",

number = "1",

}

TY - JOUR

T1 - Formalization and computational aspects of image analysis

AU - Alvarez, Luis

AU - Morel, Jean Michel

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 1994/1

Y1 - 1994/1

N2 - In this article we shall present a unified and axiomatized view of several theories and algorithms of image multiscale analysis (and low level vision) which have been developed in the past twenty years. We shall show that under reasonable invariance and assumptions, all image (and shape) analyses can be reduced to a single partial differential equation. In the same way, movie analysis leads to a single parabolic differential equation. We discuss some applications to image segmentation and movie restoration. The experiments show how accurate and invariant the numerical schemes must be and we compare several (old and new) algorithms by discussing how well they match the axiomatic invariance requirements. © 1994, Cambridge University Press. All rights reserved.

AB - In this article we shall present a unified and axiomatized view of several theories and algorithms of image multiscale analysis (and low level vision) which have been developed in the past twenty years. We shall show that under reasonable invariance and assumptions, all image (and shape) analyses can be reduced to a single partial differential equation. In the same way, movie analysis leads to a single parabolic differential equation. We discuss some applications to image segmentation and movie restoration. The experiments show how accurate and invariant the numerical schemes must be and we compare several (old and new) algorithms by discussing how well they match the axiomatic invariance requirements. © 1994, Cambridge University Press. All rights reserved.

UR - https://www.scopus.com/pages/publications/84974253506

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84974253506&origin=recordpage

U2 - 10.1017/S0962492900002415

DO - 10.1017/S0962492900002415

M3 - RGC 21 - Publication in refereed journal

SN - 0962-4929

VL - 3

SP - 1

EP - 59

JO - Acta Numerica

JF - Acta Numerica

IS - 1

ER -

Formalization and computational aspects of image analysis

Abstract

Bibliographical note

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this