Uncertainty propagation using copulas in a 3D stereo matching pipeline

Roman Malinowski, Sébastien Destercke, Emmanuel Dubois, Loı̈c Dumas, Emmanuelle Sarrazin
Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, PMLR 215:288-298, 2023.

Abstract

This contribution presents a concrete example of uncertainty propagation in a stereo matching pipeline. It considers the problem of matching pixels between pairs of images whose radiometry is uncertain and modeled by possibility distributions. Copulas serve as dependency models between variables and are used to propagate the imprecise models. The propagation steps are detailed in the simple case of the Sum of Absolute Difference cost function for didactic purposes. The method results in an imprecise matching cost curve. To reduce computation time, a sufficient condition for conserving possibility distributions after the propagation is also presented. Finally, results are compared with Monte Carlo simulations, indicating that the method produces envelopes capable of correctly estimating the matching cost.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-malinowski23a, title = {Uncertainty propagation using copulas in a 3{D} stereo matching pipeline}, author = {Malinowski, Roman and Destercke, S\'ebastien and Dubois, Emmanuel and Dumas, Lo{\"\i}c and Sarrazin, Emmanuelle}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {288--298}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/malinowski23a/malinowski23a.pdf}, url = {https://proceedings.mlr.press/v215/malinowski23a.html}, abstract = {This contribution presents a concrete example of uncertainty propagation in a stereo matching pipeline. It considers the problem of matching pixels between pairs of images whose radiometry is uncertain and modeled by possibility distributions. Copulas serve as dependency models between variables and are used to propagate the imprecise models. The propagation steps are detailed in the simple case of the Sum of Absolute Difference cost function for didactic purposes. The method results in an imprecise matching cost curve. To reduce computation time, a sufficient condition for conserving possibility distributions after the propagation is also presented. Finally, results are compared with Monte Carlo simulations, indicating that the method produces envelopes capable of correctly estimating the matching cost.} }
Endnote
%0 Conference Paper %T Uncertainty propagation using copulas in a 3D stereo matching pipeline %A Roman Malinowski %A Sébastien Destercke %A Emmanuel Dubois %A Loı̈c Dumas %A Emmanuelle Sarrazin %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-malinowski23a %I PMLR %P 288--298 %U https://proceedings.mlr.press/v215/malinowski23a.html %V 215 %X This contribution presents a concrete example of uncertainty propagation in a stereo matching pipeline. It considers the problem of matching pixels between pairs of images whose radiometry is uncertain and modeled by possibility distributions. Copulas serve as dependency models between variables and are used to propagate the imprecise models. The propagation steps are detailed in the simple case of the Sum of Absolute Difference cost function for didactic purposes. The method results in an imprecise matching cost curve. To reduce computation time, a sufficient condition for conserving possibility distributions after the propagation is also presented. Finally, results are compared with Monte Carlo simulations, indicating that the method produces envelopes capable of correctly estimating the matching cost.
APA
Malinowski, R., Destercke, S., Dubois, E., Dumas, L. & Sarrazin, E.. (2023). Uncertainty propagation using copulas in a 3D stereo matching pipeline. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:288-298 Available from https://proceedings.mlr.press/v215/malinowski23a.html.

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