2,385 research outputs found
Nearness to Local Subspace Algorithm for Subspace and Motion Segmentation
There is a growing interest in computer science, engineering, and mathematics
for modeling signals in terms of union of subspaces and manifolds. Subspace
segmentation and clustering of high dimensional data drawn from a union of
subspaces are especially important with many practical applications in computer
vision, image and signal processing, communications, and information theory.
This paper presents a clustering algorithm for high dimensional data that comes
from a union of lower dimensional subspaces of equal and known dimensions. Such
cases occur in many data clustering problems, such as motion segmentation and
face recognition. The algorithm is reliable in the presence of noise, and
applied to the Hopkins 155 Dataset, it generates the best results to date for
motion segmentation. The two motion, three motion, and overall segmentation
rates for the video sequences are 99.43%, 98.69%, and 99.24%, respectively
A Fusion Framework for Camouflaged Moving Foreground Detection in the Wavelet Domain
Detecting camouflaged moving foreground objects has been known to be
difficult due to the similarity between the foreground objects and the
background. Conventional methods cannot distinguish the foreground from
background due to the small differences between them and thus suffer from
under-detection of the camouflaged foreground objects. In this paper, we
present a fusion framework to address this problem in the wavelet domain. We
first show that the small differences in the image domain can be highlighted in
certain wavelet bands. Then the likelihood of each wavelet coefficient being
foreground is estimated by formulating foreground and background models for
each wavelet band. The proposed framework effectively aggregates the
likelihoods from different wavelet bands based on the characteristics of the
wavelet transform. Experimental results demonstrated that the proposed method
significantly outperformed existing methods in detecting camouflaged foreground
objects. Specifically, the average F-measure for the proposed algorithm was
0.87, compared to 0.71 to 0.8 for the other state-of-the-art methods.Comment: 13 pages, accepted by IEEE TI
Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification
This paper considers the classification of linear subspaces with mismatched
classifiers. In particular, we assume a model where one observes signals in the
presence of isotropic Gaussian noise and the distribution of the signals
conditioned on a given class is Gaussian with a zero mean and a low-rank
covariance matrix. We also assume that the classifier knows only a mismatched
version of the parameters of input distribution in lieu of the true parameters.
By constructing an asymptotic low-noise expansion of an upper bound to the
error probability of such a mismatched classifier, we provide sufficient
conditions for reliable classification in the low-noise regime that are able to
sharply predict the absence of a classification error floor. Such conditions
are a function of the geometry of the true signal distribution, the geometry of
the mismatched signal distributions as well as the interplay between such
geometries, namely, the principal angles and the overlap between the true and
the mismatched signal subspaces. Numerical results demonstrate that our
conditions for reliable classification can sharply predict the behavior of a
mismatched classifier both with synthetic data and in a motion segmentation and
a hand-written digit classification applications.Comment: 17 pages, 7 figures, submitted to IEEE Transactions on Signal
Processin
- …