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.