Contrast Enhancement Based on Layered Difference Representation of 2D Histograms
TL;DR: A novel contrast enhancement algorithm based on the layered difference representation of 2D histograms is proposed, which enhances images efficiently in terms of both objective quality and subjective quality.
Abstract: A novel contrast enhancement algorithm based on the layered difference representation of 2D histograms is proposed in this paper. We attempt to enhance image contrast by amplifying the gray-level differences between adjacent pixels. To this end, we obtain the 2D histogram h(k, k+l) from an input image, which counts the pairs of adjacent pixels with gray-levels k and k+l, and represent the gray-level differences in a tree-like layered structure. Then, we formulate a constrained optimization problem based on the observation that the gray-level differences, occurring more frequently in the input image, should be more emphasized in the output image. We first solve the optimization problem to derive the transformation function at each layer. We then combine the transformation functions at all layers into the unified transformation function, which is used to map input gray-levels to output gray-levels. Experimental results demonstrate that the proposed algorithm enhances images efficiently in terms of both objective quality and subjective quality.
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TL;DR: Experiments on a number of challenging low-light images are present to reveal the efficacy of the proposed LIME and show its superiority over several state-of-the-arts in terms of enhancement quality and efficiency.
Abstract: When one captures images in low-light conditions, the images often suffer from low visibility. Besides degrading the visual aesthetics of images, this poor quality may also significantly degenerate the performance of many computer vision and multimedia algorithms that are primarily designed for high-quality inputs. In this paper, we propose a simple yet effective low-light image enhancement (LIME) method. More concretely, the illumination of each pixel is first estimated individually by finding the maximum value in R, G, and B channels. Furthermore, we refine the initial illumination map by imposing a structure prior on it, as the final illumination map. Having the well-constructed illumination map, the enhancement can be achieved accordingly. Experiments on a number of challenging low-light images are present to reveal the efficacy of our LIME and show its superiority over several state-of-the-arts in terms of enhancement quality and efficiency.
1,364 citations
Cites background or methods from "Contrast Enhancement Based on Layer..."
...For instance, contextual and variational contrast enhancement (CVC) [6] tries to find a histogram mapping that pays attention on large gray-level differences, while the work [7] achieves improvement by seeking a layered difference representation of 2D histograms (LDR)....
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...Equalization (AHE), Gamma Correction (GC), Contextual and Variational Contrast enhancement (CVC) [6], Layered Difference Representation (LDR) [7], dehazing based method [14] (DeHz), Multi-deviation Fusion method (MF) [12], Naturalness Preserved Enhancement algorithm (NPE) [11] and Simultaneous Reflection and Illumination Estimation (SRIE) [13]....
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TL;DR: A fusion-based method for enhancing various weakly illuminated images that requires only one input to obtain the enhanced image and represents a trade-off among detail enhancement, local contrast improvement and preserving the natural feel of the image.
464 citations
Cites background or methods from "Contrast Enhancement Based on Layer..."
...In this experiment, we use 40 different kinds of weakly illumination images and enhance them using [1,10,16,20,22,23] and our proposed method....
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...As the global brightness darkens, LDR [1] and GUM [23] fail to improve the visibility and the building cannot be seen clearly....
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...Input images and other six methods [1,10,16,20,22,23] correspond to 0....
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...The proposed method requires a slightly longer running time than LDR [1] and GUM [23], while significantly less time than CVC [10], NEPA [20] and GOLW [22]....
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...We compare the proposed method with six other image enhancement methods: two Retinex-based methods, MSR [16] and NPEA [20], two histogram-based methods, CVC [10] and LDR [1], and two filtering-based methods, GUM [23] and GOLW [22]....
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14 Jun 2020
TL;DR: A novel method, Zero-Reference Deep Curve Estimation (Zero-DCE), which formulates light enhancement as a task of image-specific curve estimation with a deep network and shows that it generalizes well to diverse lighting conditions.
Abstract: The paper presents a novel method, Zero-Reference Deep Curve Estimation (Zero-DCE), which formulates light enhancement as a task of image-specific curve estimation with a deep network. Our method trains a lightweight deep network, DCE-Net, to estimate pixel-wise and high-order curves for dynamic range adjustment of a given image. The curve estimation is specially designed, considering pixel value range, monotonicity, and differentiability. Zero-DCE is appealing in its relaxed assumption on reference images, i.e., it does not require any paired or unpaired data during training. This is achieved through a set of carefully formulated non-reference loss functions, which implicitly measure the enhancement quality and drive the learning of the network. Our method is efficient as image enhancement can be achieved by an intuitive and simple nonlinear curve mapping. Despite its simplicity, we show that it generalizes well to diverse lighting conditions. Extensive experiments on various benchmarks demonstrate the advantages of our method over state-of-the-art methods qualitatively and quantitatively. Furthermore, the potential benefits of our Zero-DCE to face detection in the dark are discussed.
447 citations
Cites background from "Contrast Enhancement Based on Layer..."
...Histogram distribution of images is adjusted at both global [6, 9] and local levels [23, 13]....
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15 Oct 2019
TL;DR: This work builds a simple yet effective network for Kindling the Darkness (denoted as KinD), which, inspired by Retinex theory, decomposes images into two components that are robust against severe visual defects, and user-friendly to arbitrarily adjust light levels.
Abstract: Images captured under low-light conditions often suffer from (partially) poor visibility. Besides unsatisfactory lightings, multiple types of degradations, such as noise and color distortion due to the limited quality of cameras, hide in the dark. In other words, solely turning up the brightness of dark regions will inevitably amplify hidden artifacts. This work builds a simple yet effective network for Kindling the Darkness (denoted as KinD), which, inspired by Retinex theory, decomposes images into two components. One component (illumination) is responsible for light adjustment, while the other (reflectance) for degradation removal. In such a way, the original space is decoupled into two smaller subspaces, expecting to be better regularized/learned. It is worth to note that our network is trained with paired images shot under different exposure conditions, instead of using any ground-truth reflectance and illumination information. Extensive experiments are conducted to demonstrate the efficacy of our design and its superiority over state-of-the-art alternatives. Our KinD is robust against severe visual defects, and user-friendly to arbitrarily adjust light levels. In addition, our model spends less than 50ms to process an image in VGA resolution on a 2080Ti GPU. All the above merits make our KinD attractive for practical use.
428 citations
Cites background from "Contrast Enhancement Based on Layer..."
...One technical line, with histogram equalization (HE) [1], [2], [3] and its follow-ups [4], [5] as representatives, tries to map the value range into [0, 1] and balance the histogram of outputs for avoiding the truncation problem....
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Posted Content•
TL;DR: Zhang et al. as discussed by the authors proposed a zero-reference deep curve estimation (Zero-DCE) method, which formulates light enhancement as a task of image-specific curve estimation with a deep network.
Abstract: The paper presents a novel method, Zero-Reference Deep Curve Estimation (Zero-DCE), which formulates light enhancement as a task of image-specific curve estimation with a deep network. Our method trains a lightweight deep network, DCE-Net, to estimate pixel-wise and high-order curves for dynamic range adjustment of a given image. The curve estimation is specially designed, considering pixel value range, monotonicity, and differentiability. Zero-DCE is appealing in its relaxed assumption on reference images, i.e., it does not require any paired or unpaired data during training. This is achieved through a set of carefully formulated non-reference loss functions, which implicitly measure the enhancement quality and drive the learning of the network. Our method is efficient as image enhancement can be achieved by an intuitive and simple nonlinear curve mapping. Despite its simplicity, we show that it generalizes well to diverse lighting conditions. Extensive experiments on various benchmarks demonstrate the advantages of our method over state-of-the-art methods qualitatively and quantitatively. Furthermore, the potential benefits of our Zero-DCE to face detection in the dark are discussed. Code and model will be available at this https URL.
300 citations
References
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TL;DR: This final installment of the paper considers the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now.
Abstract: In this final installment of the paper we consider the case where the signals or the messages or both are continuously variable, in contrast with the discrete nature assumed until now. To a considerable extent the continuous case can be obtained through a limiting process from the discrete case by dividing the continuum of messages and signals into a large but finite number of small regions and calculating the various parameters involved on a discrete basis. As the size of the regions is decreased these parameters in general approach as limits the proper values for the continuous case. There are, however, a few new effects that appear and also a general change of emphasis in the direction of specialization of the general results to particular cases.
65,425 citations
Book•
01 Jan 1991TL;DR: The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.
Abstract: Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index.
45,034 citations
Book•
01 Jun 1974
TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
Abstract: Since the lm function provides a lot of features it is rather complicated. So we are going to instead use the function lsfit as a model. It computes only the coefficient estimates and the residuals. Now would be a good time to read the help file for lsfit. Note that lsfit supports the fitting of multiple least squares models and weighted least squares. Our function will not, hence we can omit the arguments wt, weights and yname. Also, changing tolerances is a little advanced so we will trust the default values and omit the argument tolerance as well.
6,956 citations
"Contrast Enhancement Based on Layer..." refers background in this paper
...(12) This implies that the output transformation function should increase linearly between xk and xk+l....
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TL;DR: F can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program) and numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted.
Abstract: This paper considers a natural error correcting problem with real valued input/output. We wish to recover an input vector f/spl isin/R/sup n/ from corrupted measurements y=Af+e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the /spl lscr//sub 1/-minimization problem (/spl par/x/spl par//sub /spl lscr/1/:=/spl Sigma//sub i/|x/sub i/|) min(g/spl isin/R/sup n/) /spl par/y - Ag/spl par//sub /spl lscr/1/ provided that the support of the vector of errors is not too large, /spl par/e/spl par//sub /spl lscr/0/:=|{i:e/sub i/ /spl ne/ 0}|/spl les//spl rho//spl middot/m for some /spl rho/>0. In short, f can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; f is recovered exactly even in situations where a significant fraction of the output is corrupted. This work is related to the problem of finding sparse solutions to vastly underdetermined systems of linear equations. There are also significant connections with the problem of recovering signals from highly incomplete measurements. In fact, the results introduced in this paper improve on our earlier work. Finally, underlying the success of /spl lscr//sub 1/ is a crucial property we call the uniform uncertainty principle that we shall describe in detail.
6,853 citations
"Contrast Enhancement Based on Layer..." refers background in this paper
...However, finding the sparsest solutions is NP-hard [25], and the solution dl to our problem cannot be sparse due to the constraints in (10) and (11)....
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Posted Content•
TL;DR: In this paper, it was shown that under suitable conditions on the coding matrix, the input vector can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program).
Abstract: This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector $f \in \R^n$ from corrupted measurements $y = A f + e$. Here, $A$ is an $m$ by $n$ (coding) matrix and $e$ is an arbitrary and unknown vector of errors. Is it possible to recover $f$ exactly from the data $y$? We prove that under suitable conditions on the coding matrix $A$, the input $f$ is the unique solution to the $\ell_1$-minimization problem ($\|x\|_{\ell_1} := \sum_i |x_i|$) $$ \min_{g \in \R^n} \| y - Ag \|_{\ell_1} $$ provided that the support of the vector of errors is not too large, $\|e\|_{\ell_0} := |\{i : e_i
eq 0\}| \le \rho \cdot m$ for some $\rho > 0$. In short, $f$ can be recovered exactly by solving a simple convex optimization problem (which one can recast as a linear program). In addition, numerical experiments suggest that this recovery procedure works unreasonably well; $f$ is recovered exactly even in situations where a significant fraction of the output is corrupted.
6,136 citations