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46
Automatic Estimation and Removal of Noise from a Single Image
, 2008
"... Image denoising algorithms often assume an additive white Gaussian noise (AWGN) process that is independent of the actual RGB values. Such approaches cannot effectively remove color noise produced by today’s CCD digital camera. In this paper, we propose a unified framework for two tasks: automatic ..."
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Cited by 61 (3 self)
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Image denoising algorithms often assume an additive white Gaussian noise (AWGN) process that is independent of the actual RGB values. Such approaches cannot effectively remove color noise produced by today’s CCD digital camera. In this paper, we propose a unified framework for two tasks: automatic estimation and removal of color noise from a single image using piecewise smooth image models. We introduce the noise level function (NLF), which is a continuous function describing the noise level as a function of image brightness. We then estimate an upper bound of the real NLF by fitting a lower envelope to the standard deviations of per-segment image variances. For denoising, the chrominance of color noise is significantly removed by projecting pixel values onto a line fit to the RGB values in each segment. Then, a Gaussian conditional random field (GCRF) is constructed to obtain the underlying clean image from the noisy input. Extensive experiments are conducted to test the proposed algorithm, which is shown to outperform state-of-the-art denoising algorithms.
Power Watershed: A Unifying Graph-Based Optimization Framework
, 2011
"... In this work, we extend a common framework for graph-based image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of ..."
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Cited by 42 (8 self)
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In this work, we extend a common framework for graph-based image segmentation that includes the graph cuts, random walker, and shortest path optimization algorithms. Viewing an image as a weighted graph, these algorithms can be expressed by means of a common energy function with differing choices of a parameter q acting as an exponent on the differences between neighboring nodes. Introducing a new parameter p that fixes a power for the edge weights allows us to also include the optimal spanning forest algorithm for watershed in this same framework. We then propose a new family of segmentation algorithms that fixes p to produce an optimal spanning forest but varies the power q beyond the usual watershed algorithm, which we term power watershed. In particular when q = 2, the power watershed leads to a multilabel, scale and contrast invariant, unique global optimum obtained in practice in quasi-linear time. Placing the watershed algorithm in this energy minimization framework also opens new possibilities for using unary terms in traditional watershed segmentation and using watershed to optimize more general models of use in applications beyond image segmentation.
C.: Loss-specific training of non-parametric image restoration models: A new state of the art
, 2012
"... Abstract. After a decade of rapid progress in image denoising, recent methods seem to have reached a performance limit. Nonetheless, we find that state-of-the-art denoising methods are visually clearly distinguishable and possess complementary strengths and failure modes. Motivated by this observati ..."
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Cited by 31 (6 self)
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Abstract. After a decade of rapid progress in image denoising, recent methods seem to have reached a performance limit. Nonetheless, we find that state-of-the-art denoising methods are visually clearly distinguishable and possess complementary strengths and failure modes. Motivated by this observation, we introduce a powerful non-parametric image restoration framework based on Regression Tree Fields (RTF). Our restoration model is a densely-connected tractable conditional random field that leverages existing methods to produce an image-dependent, globally consistent prediction. We estimate the conditional structure and parameters of our model from training data so as to directly optimize for popular performance measures. In terms of peak signal-to-noise-ratio (PSNR), our model improves on the best published denoising method by at least 0.26dB across a range of noise levels. Our most practical variant still yields statistically significant improvements, yet is over 20 × faster than the strongest competitor. Our approach is well-suited for many more image restoration and low-level vision problems, as evidenced by substantial gains in tasks such as removal of JPEG blocking artefacts. 1
Natural Image Denoising with Convolutional Networks
"... We present an approach to low-level vision that combines two main ideas: the use of convolutional networks as an image processing architecture and an unsupervised learning procedure that synthesizes training samples from specific noise models. We demonstrate this approach on the challenging problem ..."
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Cited by 31 (3 self)
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We present an approach to low-level vision that combines two main ideas: the use of convolutional networks as an image processing architecture and an unsupervised learning procedure that synthesizes training samples from specific noise models. We demonstrate this approach on the challenging problem of natural image denoising. Using a test set with a hundred natural images, we find that convolutional networks provide comparable and in some cases superior performance to state of the art wavelet and Markov random field (MRF) methods. Moreover, we find that a convolutional network offers similar performance in the blind denoising setting as compared to other techniques in the non-blind setting. We also show how convolutional networks are mathematically related to MRF approaches by presenting a mean field theory for an MRF specially designed for image denoising. Although these approaches are related, convolutional networks avoid computational difficulties in MRF approaches that arise from probabilistic learning and inference. This makes it possible to learn image processing architectures that have a high degree of representational power (we train models with over 15,000 parameters), but whose computational expense is significantly less than that associated with inference in MRF approaches with even hundreds of parameters. 1
Modeling multiscale subbands of photographic . . .
, 2009
"... The local statistical properties of photographic images, when represented in a multiscale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSM). Specifically, we model multiscal ..."
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Cited by 25 (4 self)
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The local statistical properties of photographic images, when represented in a multiscale basis, have been described using Gaussian scale mixtures. Here, we use this local description as a substrate for constructing a global field of Gaussian scale mixtures (FoGSM). Specifically, we model multiscale subbands as a product of an exponentiated homogeneous Gaussian Markov random field (hGMRF) and a second independent hGMRF. We show that parameter estimation for this model is feasible and that samples drawn from a FoGSM model have marginal and joint statistics similar to those of the subband coefficients of photographic images. We develop an algorithm for removing additive white Gaussian noise based on the FoGSM model and demonstrate denoising performance comparable with state-of-the-art methods.
Recovering Intrinsic Images with a Global Sparsity Prior On Reflectance
"... We address the challenging task of decoupling material properties from lighting properties given a single image. In the last two decades virtually all works have concentrated on exploiting edge information to address this problem. We take a different route by introducing a new prior on reflectance, ..."
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Cited by 22 (3 self)
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We address the challenging task of decoupling material properties from lighting properties given a single image. In the last two decades virtually all works have concentrated on exploiting edge information to address this problem. We take a different route by introducing a new prior on reflectance, that models reflectance values as being drawn from a sparse set of basis colors. This results in a Random Field model with global, latent variables (basis colors) and pixel-accurate output reflectance values. We show that without edge information high-quality results can be achieved, that are on par with methods exploiting this source of information. Finally, we are able to improve on state-of-the-art results by integrating edge information into our model. We believe that our new approach is an excellent starting point for future developments in this field.
Regression tree fields -- an efficient, non-parametric approach to image labeling problems
, 2012
"... We introduce Regression Tree Fields (RTFs), a fully conditional random field model for image labeling problems. RTFs gain their expressive power from the use of nonparametric regression trees that specify a tractable Gaussian random field, thereby ensuring globally consistent predictions. Our approa ..."
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Cited by 21 (8 self)
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We introduce Regression Tree Fields (RTFs), a fully conditional random field model for image labeling problems. RTFs gain their expressive power from the use of nonparametric regression trees that specify a tractable Gaussian random field, thereby ensuring globally consistent predictions. Our approach improves on the recently introduced decision tree field (DTF) model [14] in three key ways: (i) RTFs have tractable test-time inference, making efficient optimal predictions feasible and orders of magnitude faster than for DTFs, (ii) RTFs can be applied to both discrete and continuous vector-valued labeling tasks, and (iii) the entire model, including the structure of the regression trees and energy function parameters, can be efficiently and jointly learned from training data. We demonstrate the expressive power and flexibility of the RTF model on a wide variety of tasks, including inpainting, colorization, denoising, and joint detection and registration. We achieve excellent predictive performance which is on par with, or even surpassing, DTFs on all tasks where a comparison is possible.
A Content-Aware Image Prior
"... In image restoration tasks, a heavy-tailed gradient distribution of natural images has been extensively exploited as an image prior. Most image restoration algorithms impose a sparse gradient prior on the whole image, reconstructing an image with piecewise smooth characteristics. While the sparse gr ..."
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Cited by 21 (2 self)
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In image restoration tasks, a heavy-tailed gradient distribution of natural images has been extensively exploited as an image prior. Most image restoration algorithms impose a sparse gradient prior on the whole image, reconstructing an image with piecewise smooth characteristics. While the sparse gradient prior removes ringing and noise artifacts, it also tends to remove mid-frequency textures, degrading the visual quality. We can attribute such degradations to imposing an incorrect image prior. The gradient profile in fractal-like textures, such as trees, is close to a Gaussian distribution, and small gradients from such regions are severely penalized by the sparse gradient prior. To address this issue, we introduce an image restoration algorithm that adapts the image prior to the underlying texture. We adapt the prior to both low-level local structures as well as mid-level textural characteristics. Improvements in visual quality is demonstrated on deconvolution and denoising tasks. Orthogonal gradients
Learning Tree Conditional Random Fields
"... We examine maximum spanning tree-based methods for learning the structure of tree Conditional Random Fields (CRFs) P (Y|X). We use edge weights which take advantage of local inputs X and thus scale to large problems. For a general class of edge weights, we give a negative learnability result. Howeve ..."
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Cited by 19 (1 self)
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We examine maximum spanning tree-based methods for learning the structure of tree Conditional Random Fields (CRFs) P (Y|X). We use edge weights which take advantage of local inputs X and thus scale to large problems. For a general class of edge weights, we give a negative learnability result. However, we demonstrate that two members of the class–local Conditional Mutual Information and Decomposable Conditional Influence– have reasonable theoretical bases and perform very well in practice. On synthetic data and a large-scale fMRI application, our methods outperform existing techniques. 1.
