111 research outputs found
Large Scale Variational Bayesian Inference for Structured Scale Mixture Models
Natural image statistics exhibit hierarchical dependencies across multiple
scales. Representing such prior knowledge in non-factorial latent tree models
can boost performance of image denoising, inpainting, deconvolution or
reconstruction substantially, beyond standard factorial "sparse" methodology.
We derive a large scale approximate Bayesian inference algorithm for linear
models with non-factorial (latent tree-structured) scale mixture priors.
Experimental results on a range of denoising and inpainting problems
demonstrate substantially improved performance compared to MAP estimation or to
inference with factorial priors.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
Search Space Reduction in Exemplar Based Image Inpainting
This paper aims at developing accelerated exemplary inpaint method. The feature set is considered to be the pixels along with their 8-neighbors. A Multi Phase Search Space Reduction framework namely Systematic Reduction of Information System (SRIS) is employed. SRIS, basically is a roughest based approach which imputes the missing values in an adaptive manner. In this approach the order of inpainting pixels is determined by a simple but effective priority term. The best exemplar is determined based on a similarity metric which is derived by element wise difference of informative pixels of inpaint window and the corresponding pixels of the source region window
New similarity Measure for Exemplar Based in Painting
In this paper we intend to illustrate a utility and application of Kriging approximations in image processing problem designated by inpainting or filling in. We also review three state of the art infilling algorithms that deal with higher order PDE, Total Variation and exemplar-based approach. The computer model, a simple idea, we propose addresses this problem in deterministic way, and thus a response from a model lacks random error, i.e., repeated runs for the same input parameters gives the same response from the model. In its simple sense, Kriginng problem is related to the more general problem of predicting output from a computer model at untried inputs. Hence it lends it self for solving inpainting problem. Experimental results show that the proposed model yields qualitative results that are comparable to the existing complex approaches. The proposed method is very effective and simple to fill small gaps
Recent Progress in Image Deblurring
This paper comprehensively reviews the recent development of image
deblurring, including non-blind/blind, spatially invariant/variant deblurring
techniques. Indeed, these techniques share the same objective of inferring a
latent sharp image from one or several corresponding blurry images, while the
blind deblurring techniques are also required to derive an accurate blur
kernel. Considering the critical role of image restoration in modern imaging
systems to provide high-quality images under complex environments such as
motion, undesirable lighting conditions, and imperfect system components, image
deblurring has attracted growing attention in recent years. From the viewpoint
of how to handle the ill-posedness which is a crucial issue in deblurring
tasks, existing methods can be grouped into five categories: Bayesian inference
framework, variational methods, sparse representation-based methods,
homography-based modeling, and region-based methods. In spite of achieving a
certain level of development, image deblurring, especially the blind case, is
limited in its success by complex application conditions which make the blur
kernel hard to obtain and be spatially variant. We provide a holistic
understanding and deep insight into image deblurring in this review. An
analysis of the empirical evidence for representative methods, practical
issues, as well as a discussion of promising future directions are also
presented.Comment: 53 pages, 17 figure
Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization
We present a graph-based variational algorithm for classification of
high-dimensional data, generalizing the binary diffuse interface model to the
case of multiple classes. Motivated by total variation techniques, the method
involves minimizing an energy functional made up of three terms. The first two
terms promote a stepwise continuous classification function with sharp
transitions between classes, while preserving symmetry among the class labels.
The third term is a data fidelity term, allowing us to incorporate prior
information into the model in a semi-supervised framework. The performance of
the algorithm on synthetic data, as well as on the COIL and MNIST benchmark
datasets, is competitive with state-of-the-art graph-based multiclass
segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science
volume "Pattern Recognition Applications and Methods 2013", part of series on
Advances in Intelligent and Soft Computin
Efficient variational inference in large-scale Bayesian compressed sensing
We study linear models under heavy-tailed priors from a probabilistic
viewpoint. Instead of computing a single sparse most probable (MAP) solution as
in standard deterministic approaches, the focus in the Bayesian compressed
sensing framework shifts towards capturing the full posterior distribution on
the latent variables, which allows quantifying the estimation uncertainty and
learning model parameters using maximum likelihood. The exact posterior
distribution under the sparse linear model is intractable and we concentrate on
variational Bayesian techniques to approximate it. Repeatedly computing
Gaussian variances turns out to be a key requisite and constitutes the main
computational bottleneck in applying variational techniques in large-scale
problems. We leverage on the recently proposed Perturb-and-MAP algorithm for
drawing exact samples from Gaussian Markov random fields (GMRF). The main
technical contribution of our paper is to show that estimating Gaussian
variances using a relatively small number of such efficiently drawn random
samples is much more effective than alternative general-purpose variance
estimation techniques. By reducing the problem of variance estimation to
standard optimization primitives, the resulting variational algorithms are
fully scalable and parallelizable, allowing Bayesian computations in extremely
large-scale problems with the same memory and time complexity requirements as
conventional point estimation techniques. We illustrate these ideas with
experiments in image deblurring.Comment: 8 pages, 3 figures, appears in Proc. IEEE Workshop on Information
Theory in Computer Vision and Pattern Recognition (in conjunction with
ICCV-11), Barcelona, Spain, Nov. 201
Multiclass Data Segmentation using Diffuse Interface Methods on Graphs
We present two graph-based algorithms for multiclass segmentation of
high-dimensional data. The algorithms use a diffuse interface model based on
the Ginzburg-Landau functional, related to total variation compressed sensing
and image processing. A multiclass extension is introduced using the Gibbs
simplex, with the functional's double-well potential modified to handle the
multiclass case. The first algorithm minimizes the functional using a convex
splitting numerical scheme. The second algorithm is a uses a graph adaptation
of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates
between diffusion and thresholding. We demonstrate the performance of both
algorithms experimentally on synthetic data, grayscale and color images, and
several benchmark data sets such as MNIST, COIL and WebKB. We also make use of
fast numerical solvers for finding the eigenvectors and eigenvalues of the
graph Laplacian, and take advantage of the sparsity of the matrix. Experiments
indicate that the results are competitive with or better than the current
state-of-the-art multiclass segmentation algorithms.Comment: 14 page
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