7,912 research outputs found
Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds
Sparsity-based representations have recently led to notable results in
various visual recognition tasks. In a separate line of research, Riemannian
manifolds have been shown useful for dealing with features and models that do
not lie in Euclidean spaces. With the aim of building a bridge between the two
realms, we address the problem of sparse coding and dictionary learning over
the space of linear subspaces, which form Riemannian structures known as
Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into
the space of symmetric matrices by an isometric mapping. This in turn enables
us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we
propose closed-form solutions for learning a Grassmann dictionary, atom by
atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann
sparse coding and dictionary learning algorithms through embedding into Hilbert
spaces.
Experiments on several classification tasks (gender recognition, gesture
classification, scene analysis, face recognition, action recognition and
dynamic texture classification) show that the proposed approaches achieve
considerable improvements in discrimination accuracy, in comparison to
state-of-the-art methods such as kernelized Affine Hull Method and
graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio
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
Reliable camera motion estimation from compressed MPEG videos using machine learning approach
As an important feature in characterizing video content, camera motion has been widely applied in various multimedia and computer vision applications. A novel method for fast and reliable estimation of camera motion from MPEG videos is proposed, using support vector machine for estimation in a regression model trained on a synthesized sequence. Experiments conducted on real sequences show that the proposed method yields much improved results in estimating camera motions while the difficulty in selecting valid macroblocks and motion vectors is skipped
Convolutional Deblurring for Natural Imaging
In this paper, we propose a novel design of image deblurring in the form of
one-shot convolution filtering that can directly convolve with naturally
blurred images for restoration. The problem of optical blurring is a common
disadvantage to many imaging applications that suffer from optical
imperfections. Despite numerous deconvolution methods that blindly estimate
blurring in either inclusive or exclusive forms, they are practically
challenging due to high computational cost and low image reconstruction
quality. Both conditions of high accuracy and high speed are prerequisites for
high-throughput imaging platforms in digital archiving. In such platforms,
deblurring is required after image acquisition before being stored, previewed,
or processed for high-level interpretation. Therefore, on-the-fly correction of
such images is important to avoid possible time delays, mitigate computational
expenses, and increase image perception quality. We bridge this gap by
synthesizing a deconvolution kernel as a linear combination of Finite Impulse
Response (FIR) even-derivative filters that can be directly convolved with
blurry input images to boost the frequency fall-off of the Point Spread
Function (PSF) associated with the optical blur. We employ a Gaussian low-pass
filter to decouple the image denoising problem for image edge deblurring.
Furthermore, we propose a blind approach to estimate the PSF statistics for two
Gaussian and Laplacian models that are common in many imaging pipelines.
Thorough experiments are designed to test and validate the efficiency of the
proposed method using 2054 naturally blurred images across six imaging
applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin
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