IEEE Trans Image Process - Learning smooth pattern transformation manifolds.

Tópicos

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Resumo

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image sets that represent observations of geometrically transformed signals. To construct a manifold, we build a representative pattern whose transformations accurately fit various input images. We examine two objectives of the manifold-building problem, namely, approximation and classification. For the approximation problem, we propose a greedy method that constructs a representative pattern by selecting analytic atoms from a continuous dictionary manifold. We present a dc optimization scheme that is applicable to a wide range of transformation and dictionary models, and demonstrate its application to the transformation manifolds generated by the rotation, translation, and anisotropic scaling of a reference pattern. Then, we generalize this approach to a setting with multiple transformation manifolds, where each manifold represents a different class of signals. We present an iterative multiple-manifold-building algorithm such that the classification accuracy is promoted in the learning of the representative patterns. The experimental results suggest that the proposed methods yield high accuracy in the approximation and classification of data compared with some reference methods, while the invariance to geometric transformations is achieved because of the transformation manifold model.

Resumo Limpo

manifold model provid lowdimension represent use process analyz data transformationinvari way paper studi problem learn smooth pattern transform manifold imag set repres observ geometr transform signal construct manifold build repres pattern whose transform accur fit various input imag examin two object manifoldbuild problem name approxim classif approxim problem propos greedi method construct repres pattern select analyt atom continu dictionari manifold present dc optim scheme applic wide rang transform dictionari model demonstr applic transform manifold generat rotat translat anisotrop scale refer pattern general approach set multipl transform manifold manifold repres differ class signal present iter multiplemanifoldbuild algorithm classif accuraci promot learn repres pattern experiment result suggest propos method yield high accuraci approxim classif data compar refer method invari geometr transform achiev transform manifold model

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