23,520 research outputs found
Hypernetwork functional image representation
Motivated by the human way of memorizing images we introduce their functional
representation, where an image is represented by a neural network. For this
purpose, we construct a hypernetwork which takes an image and returns weights
to the target network, which maps point from the plane (representing positions
of the pixel) into its corresponding color in the image. Since the obtained
representation is continuous, one can easily inspect the image at various
resolutions and perform on it arbitrary continuous operations. Moreover, by
inspecting interpolations we show that such representation has some properties
characteristic to generative models. To evaluate the proposed mechanism
experimentally, we apply it to image super-resolution problem. Despite using a
single model for various scaling factors, we obtained results comparable to
existing super-resolution methods
Sparse Image Representation with Epitomes
Sparse coding, which is the decomposition of a vector using only a few basis
elements, is widely used in machine learning and image processing. The basis
set, also called dictionary, is learned to adapt to specific data. This
approach has proven to be very effective in many image processing tasks.
Traditionally, the dictionary is an unstructured "flat" set of atoms. In this
paper, we study structured dictionaries which are obtained from an epitome, or
a set of epitomes. The epitome is itself a small image, and the atoms are all
the patches of a chosen size inside this image. This considerably reduces the
number of parameters to learn and provides sparse image decompositions with
shiftinvariance properties. We propose a new formulation and an algorithm for
learning the structured dictionaries associated with epitomes, and illustrate
their use in image denoising tasks.Comment: Computer Vision and Pattern Recognition, Colorado Springs : United
States (2011
Anisotropic Mesh Adaptation for Image Representation
Triangular meshes have gained much interest in image representation and have
been widely used in image processing. This paper introduces a framework of
anisotropic mesh adaptation (AMA) methods to image representation and proposes
a GPRAMA method that is based on AMA and greedy-point removal (GPR) scheme.
Different than many other methods that triangulate sample points to form the
mesh, the AMA methods start directly with a triangular mesh and then adapt the
mesh based on a user-defined metric tensor to represent the image. The AMA
methods have clear mathematical framework and provides flexibility for both
image representation and image reconstruction. A mesh patching technique is
developed for the implementation of the GPRAMA method, which leads to an
improved version of the popular GPRFS-ED method. The GPRAMA method can achieve
better quality than the GPRFS-ED method but with lower computational cost.Comment: 25 pages, 15 figure
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
Twisted Alexander Polynomials and Representation Shifts
For any knot, the following are equivalent. (1) The infinite cyclic cover has
uncountably many finite covers; (2) there exists a finite-image representation
of the knot group for which the twisted Alexander polynomial vanishes; (3) the
knot group admits a finite-image representation such that the image of the
fundamental group of an incompressible Seifert surface is a proper subgroup of
the image of the commutator subgroup of the knot group.Comment: 7 pages, no figure
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