10,765 research outputs found
Invariant Tensor Feature Coding
We propose a novel feature coding method that exploits invariance. We
consider the setting where the transformations that preserve the image contents
compose a finite group of orthogonal matrices. This is the case in many image
transformations, such as image rotations and image flipping. We prove that the
group-invariant feature vector contains sufficient discriminative information
when learning a linear classifier using convex loss minimization. From this
result, we propose a novel feature modeling for principal component analysis
and k-means clustering, which are used for most feature coding methods, and
global feature functions that explicitly consider the group action. Although
the global feature functions are complex nonlinear functions in general, we can
calculate the group action on this space easily by constructing the functions
as the tensor product representations of basic representations, resulting in
the explicit form of invariant feature functions. We demonstrate the
effectiveness of our methods on several image datasets.Comment: 14 pages, 5 figure
Sparse Coding on Symmetric Positive Definite Manifolds using Bregman Divergences
This paper introduces sparse coding and dictionary learning for Symmetric
Positive Definite (SPD) matrices, which are often used in machine learning,
computer vision and related areas. Unlike traditional sparse coding schemes
that work in vector spaces, in this paper we discuss how SPD matrices can be
described by sparse combination of dictionary atoms, where the atoms are also
SPD matrices. We propose to seek sparse coding by embedding the space of SPD
matrices into Hilbert spaces through two types of Bregman matrix divergences.
This not only leads to an efficient way of performing sparse coding, but also
an online and iterative scheme for dictionary learning. We apply the proposed
methods to several computer vision tasks where images are represented by region
covariance matrices. Our proposed algorithms outperform state-of-the-art
methods on a wide range of classification tasks, including face recognition,
action recognition, material classification and texture categorization
Graph Regularized Tensor Sparse Coding for Image Representation
Sparse coding (SC) is an unsupervised learning scheme that has received an
increasing amount of interests in recent years. However, conventional SC
vectorizes the input images, which destructs the intrinsic spatial structures
of the images. In this paper, we propose a novel graph regularized tensor
sparse coding (GTSC) for image representation. GTSC preserves the local
proximity of elementary structures in the image by adopting the newly proposed
tubal-tensor representation. Simultaneously, it considers the intrinsic
geometric properties by imposing graph regularization that has been
successfully applied to uncover the geometric distribution for the image data.
Moreover, the returned sparse representations by GTSC have better physical
explanations as the key operation (i.e., circular convolution) in the
tubal-tensor model preserves the shifting invariance property. Experimental
results on image clustering demonstrate the effectiveness of the proposed
scheme
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