Robust Positive semidefinite L-Isomap Ensemble
Pattern Recognition Letters
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Affine registration has a long and venerable history in computervision literature, and extensive work have been done for affineregistrations in ℝ2 and ℝ3. Inthis paper, we study affine registrations in ℝm for m 3, and to justify breakingthis dimension barrier, we show two interesting types of matchingproblems that can be formulated and solved as affine registrationproblems in dimensions higher than three: stereo correspondenceunder motion and image set matching. More specifically, for anobject undergoing non-rigid motion that can be linearly modelledusing a small number of shape basis vectors, the stereocorrespondence problem can be solved by affine registering pointsin ℝ3n . And given two collections ofimages related by an unknown linear transformation of the imagespace, the correspondences between images in the two collectionscan be recovered by solving an affine registration problem inℝm, where m is the dimension ofa PCA subspace. The algorithm proposed in this paper estimates theaffine transformation between two point sets inℝm. It does not require continuousoptimization, and our analysis shows that, in the absence of datanoise, the algorithm will recover the exact affine transformationfor almost all point sets with the worst-case time complexity ofO(mk 2), k the size of thepoint set. We validate the proposed algorithm on a variety ofsynthetic point sets in different dimensions with varying degreesof deformation and noise, and we also show experimentally that thetwo types of matching problems can indeed be solved satisfactorilyusing the proposed affine registration algorithm.