Enforcing consistency constraints in uncalibrated multiple homography estimation using latent variables

dc.contributor.authorChojnacki, W.
dc.contributor.authorSzpak, Z.
dc.contributor.authorBrooks, M.
dc.contributor.authorvan Den Hengel, A.
dc.date.issued2015
dc.description.abstractAn approach is presented for estimating a set of interdependent homography matrices linked together by latent variables. The approach allows enforcement of all underlying consistency constraints while accounting for the arbitrariness of the scale of each individual matrix. The input data is assumed to be in the form of a set of homography matrices individually estimated from image data with no regard to the consistency constraints, appended by a set of error covariances, each characterising the uncertainty of a corresponding homography matrix. A statistically motivated cost function is introduced for upgrading, via optimisation, the input data to a set of homography matrices satisfying the constraints. The function is invariant to a change of any of the individual scales of the input matrices. The proposed approach is applied to the particular problem of estimating a set of homography matrices induced by multiple planes in the 3D scene between two views. An optimisation algorithm for this problem is developed that operates on natural underlying latent variables, with the use of those variables ensuring that all consistency constraints are satisfied. Experimental results indicate that the algorithm outperforms previous schemes proposed for the same task and is fully comparable in accuracy with the ‘gold standard’ bundle adjustment technique, rendering the whole approach both of practical and theoretical interest. With a view to practical application, it is shown that the proposed algorithm can be incorporated into the familiar random sampling and consensus technique, so that the resulting modified scheme is capable of robust fitting of fully consistent homographies to data with outliers.
dc.description.statementofresponsibilityWojciech Chojnacki, Zygmunt L. Szpak, Michael J. Brooks, Anton van den Hengel
dc.identifier.citationMachine Vision and Applications: an international journal, 2015; 26(2-3):401-422
dc.identifier.doi10.1007/s00138-015-0660-7
dc.identifier.issn0932-8092
dc.identifier.issn1432-1769
dc.identifier.orcidChojnacki, W. [0000-0001-7782-1956]
dc.identifier.orcidSzpak, Z. [0000-0002-0694-4622]
dc.identifier.orcidBrooks, M. [0000-0001-9612-5884]
dc.identifier.orcidvan Den Hengel, A. [0000-0003-3027-8364]
dc.identifier.urihttp://hdl.handle.net/2440/90183
dc.language.isoen
dc.publisherSpringer Berlin Heidelberg
dc.relation.grantARC
dc.rights© Springer-Verlag Berlin Heidelberg 2015
dc.source.urihttps://doi.org/10.1007/s00138-015-0660-7
dc.subjectMultiple homographies
dc.subjectConsistency constraints
dc.subjectLatent variables
dc.subjectMulti-projective parameter estimation
dc.subjectScale invariance
dc.subjectMaximum likelihood
dc.subjectCovariance
dc.titleEnforcing consistency constraints in uncalibrated multiple homography estimation using latent variables
dc.typeJournal article
pubs.publication-statusPublished

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