IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning active appearance models from image sequences
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We propose modeling images and related visual objects as bags ofpixels or sets of vectors. For instance, gray scale images aremodeled as a collection or bag of (X, Y, I) pixel vectors. Thisrepresentation implies a permutational invariance over the bag ofpixels which is naturally handled by endowing each image with apermutation matrix. Each matrix permits the image to span amanifold of multiple configurations, capturing the vector set'sinvariance to orderings or permutation transformations. Permutationconfigurations are optimized while jointly modeling many images viamaximum likelihood. The solution is a uniquely solvable convexprogram which computes correspondence simultaneously for all images(as opposed to traditional pairwise correspondence solutions).Maximum likelihood performs a nonlinear dimensionality reduction,choosing permutations that compact the permuted image vectors intoa volumetrically minimal subspace. This is highly suitable forprincipal components analysis which, when applied to thepermutationally invariant bag of pixels representation, outperformsPCA on appearance-based vectorization by orders ofmagnitude.Furthermore, the bag of pixels subspace benefits fromautomatic correspondence estimation, giving rise to meaningfullinear variations such as morphings, translations, and jointlyspatio-textural image transformations. Results are shown forseveral datasets.