Image Clustering with Metric, Local Linear Structure and Affine Symmetry

Jongwoo Lim, Jeffrey Ho, Ming-Hsuan Yang, Kuang-Chih Lee, David Kriegman
ECCV 2004, vol 1, pp 456-468

    This paper addresses the problem of clustering images of objects
    seen from different viewpoints.  That is, given an unlabelled set
    of images of $n$ objects, we seek an unsupervised algorithm that
    can group the images into $n$ disjoint subsets such that each
    subset only contains images of a single object.  We formulate this
    clustering problem under a very broad geometric framework.
    The theme is the interplay between the geometry of appearance
    manifolds and the symmetry of the $2$D affine group.
    Specifically, we identify three important notions for image
    clustering: the $L^2$ distance metric of the image space, the
    local linear structure of the appearance manifolds, and the action
    of the $2$D affine group in the image space.  Based on these
    notions, we propose a new image clustering algorithm.  In a
    broad outline, the algorithm uses the metric to determine a
    neighborhood structure in the image space for each input image.
    Using local linear structure, comparisons (affinities) between
    images are computed only among the neighbors.  These local
    comparisons are agglomerated into an affinity matrix, and a
    spectral clustering algorithm is used to yield the final
    clustering result.  The technical part of the algorithm is to make
    all of these compatible with the action of the $2$D affine group.
    Using human face images and images from the COIL database, we
    demonstrate experimentally that our algorithm is effective in
    clustering images (according to ojbect identity)
    where there is a large range of pose variation.