Learning affine transformations

    Authors

    G. Bebis; M. Georgiopoulos; N. D. Lobo;M. Shah

    Comments

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    Abbreviated Journal Title

    Pattern Recognit.

    Keywords

    object recognition; artificial neural networks; ALGEBRAIC-FUNCTIONS; RECOGNITION; REPRESENTATION; Computer Science, Artificial Intelligence; Engineering, Electrical &; Electronic

    Abstract

    Under the assumption of weak perspective, two views of the same planar object are related through an affine transformation. In this paper, we consider the problem of training a simple neural network to learn to predict the parameters of the affine transformation. Although the proposed scheme has similarities with other neural network schemes, its practical advantages are more profound. First of all, the views used to train the neural network are not obtained by taking pictures of the object from different viewpoints. Instead, the training views are obtained by sampling the space of affine transformed views of the object. This space is constructed using a single view of the object. Fundamental to this procedure is a methodology, based on singular-value decomposition (SVD) and interval arithmetic (IA), for estimating the ranges of values that the parameters of affine transformation can assume. Second, the accuracy of the proposed scheme is very close to that of a traditional least squares approach with slightly better space and time requirements. A front-end stage to the neural network, based on principal components analysis (PCA), shows to increase its noise tolerance dramatically and also to guides us in deciding how many training views are necessary in order for the network to learn a good, noise tolerant, mapping. The proposed approach has been tested using both artificial and real data. (C) 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

    Journal Title

    Pattern Recognition

    Volume

    32

    Issue/Number

    10

    Publication Date

    1-1-1999

    Document Type

    Article

    Language

    English

    First Page

    1783

    Last Page

    1799

    WOS Identifier

    WOS:000081589800008

    ISSN

    0031-3203

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