Digital Color Imaging
TL;DR: A survey of color imaging can be found in this article, where the fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology, along with common mathematical models used for representing these devices.
Abstract: This paper surveys current technology and research in the area of digital color imaging. In order to establish the background and lay down terminology, fundamental concepts of color perception and measurement are first presented us-ing vector-space notation and terminology. Present-day color recording and reproduction systems are reviewed along with the common mathematical models used for representing these devices. Algorithms for processing color images for display and communication are surveyed, and a forecast of research trends is attempted. An extensive bibliography is provided.
Citations
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TL;DR: A locally adaptive perceptual compression scheme based on the design of an adaptive quantizer for compressing color images with the nearly lossless visual quality at a low bit rate is proposed and results show that the compression performance of the proposed scheme using the adaptively coefficient-wise quantization is better than that using the band-wise quantify.
Abstract: The main idea in perceptual image compression is to remove the perceptual redundancy for representing images at the lowest possible bit rate without introducing perceivable distortion. A certain amount of perceptual redundancy is inherent in the color image since human eyes are not perfect sensors for discriminating small differences in color signals. Effectively exploiting the perceptual redundancy will help to improve the coding efficiency of compressing color images. In this paper, a locally adaptive perceptual compression scheme for color images is proposed. The scheme is based on the design of an adaptive quantizer for compressing color images with the nearly lossless visual quality at a low bit rate. An effective way to achieve the nearly lossless visual quality is to shape the quantization error as a part of perceptual redundancy while compressing color images. This method is to control the adaptive quantization stage by the perceptual redundancy of the color image. In this paper, the perceptual redundancy in the form of the noise detection threshold associated with each coefficient in each subband of three color components of the color image is derived based on the finding of perceptually indistinguishable regions of color stimuli in the uniform color space and various masking effects of human visual perception. The quantizer step size for the target coefficient in each color component is adaptively adjusted by the associated noise detection threshold to make sure that the resulting quantization error is not perceivable. Simulation results show that the compression performance of the proposed scheme using the adaptively coefficient-wise quantization is better than that using the band-wise quantization. The nearly lossless visual quality of the reconstructed image can be achieved by the proposed scheme at lower entropy.
6 citations
TL;DR: The methodology presented in this paper is a fast, relatively accurate, non-intrusive and inexpensive method for quantifying NAPL zones in transparent soil models.
6 citations
TL;DR: A new algorithm was used to identify the best concentration for a number of dyes that can be used as tracer to map plumes of contamination and the ideal color space component for reconstruction of each dye was determined.
Abstract: Relating dye concentration and image information is an important consideration in flow studies which employs a tracer to map plumes of contamination This study employs color space information to increase the data available for analysis than gray scale commonly employed The objective of this study is to find a color space in which the relationship between transmitted signal and integrated concentration is quantifiable In particular, the goal was to correlate the spatial concentration of contamination with color pixel information For this purpose, a new algorithm was used to identify the best concentration for a number of dyes that can be used as tracers In addition, the ideal color space component for reconstruction of each dye was determined The effectiveness of this color classification method was assessed using 10,368 color space component images within the framework of peak signal-to-noise ratio for eight different dyes and six color spaces spanning a concentration ranging from 1 to 2,000 ppm, for eight plume lengths
6 citations
TL;DR: It is proved that if the target of the Luther-condition optimization is an orthonormal basis—a special linear combination of the XYZ CMFs which are orthogonal and are in unit length—the discovered Luther-filter is also the filter that maximizes the Vora-Value.
Abstract: By placing a color filter in front of a camera we make new spectral sensitivities. The Luther-condition optimization solves for a color filter so that the camera’s filtered sensitivities are as close to being linearly related to the XYZ color matching functions (CMFs) as possible, that is, a filter is found that makes the camera more colorimetric. Arguably, the more general Vora-Value approach solves for the filter that best matches all possible target spectral sensitivity sets (e.g., any linear combination of the XYZ CMFs). A concern that we investigate here is that the filters found by the Luther and Vora-Value optimizations are different from one another. In this paper, we unify the Luther and Vora-Value approaches to prefilter design. We prove that if the target of the Luther-condition optimization is an orthonormal basis—a special linear combination of the XYZ CMFs which are orthogonal and are in unit length—the discovered Luther-filter is also the filter that maximizes the Vora-Value. A key advantage of using the Luther-condition formulation to maximize the Vora-Value is that it is both simpler to implement and converges to its optimal answer more quickly. Experiments validate our method.
6 citations
TL;DR: Two variants of a colour space transformation algorithm to encode Bayer colour filter array images that are based on integer coefficients, known as optimum reversible colour space transform (ORCT-1 and ORCT-2), improve the lossless bitrate of low complexity prediction model without using high complexity interpolation and inter-colour prediction scheme.
Abstract: We present two variants of a colour space transformation algorithm to encode Bayer colour filter array images that are based on integer coefficients; as a result, the algorithms are fully lossless and reversible in nature. These transformation algorithms are derived using an optimisation model that reduces the spectral redundancy of Bayer colour components, which results in lower prediction error variance and inter-colour correlation. These methods, known as optimum reversible colour space transform (ORCT-1 and ORCT-2), improve the lossless bitrate of low complexity prediction model without using high complexity interpolation and inter-colour prediction scheme. Extensive experimentation is performed using five sets of test images for different lossless compression algorithms: JPEG-LS, JPEG-2000 and JPEG-XR. Experimental results show that, in all cases, the proposed schemes perform competitively with other methods with lower computational complexity, which makes them suitable for low-cost imaging applications.
6 citations
References
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01 Jan 1967
TL;DR: The k-means algorithm as mentioned in this paper partitions an N-dimensional population into k sets on the basis of a sample, which is a generalization of the ordinary sample mean, and it is shown to give partitions which are reasonably efficient in the sense of within-class variance.
Abstract: The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = {S1, S2, * *, Sk} is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends to be low for the partitions S generated by the method. We say 'tends to be low,' primarily because of intuitive considerations, corroborated to some extent by mathematical analysis and practical computational experience. Also, the k-means procedure is easily programmed and is computationally economical, so that it is feasible to process very large samples on a digital computer. Possible applications include methods for similarity grouping, nonlinear prediction, approximating multivariate distributions, and nonparametric tests for independence among several variables. In addition to suggesting practical classification methods, the study of k-means has proved to be theoretically interesting. The k-means concept represents a generalization of the ordinary sample mean, and one is naturally led to study the pertinent asymptotic behavior, the object being to establish some sort of law of large numbers for the k-means. This problem is sufficiently interesting, in fact, for us to devote a good portion of this paper to it. The k-means are defined in section 2.1, and the main results which have been obtained on the asymptotic behavior are given there. The rest of section 2 is devoted to the proofs of these results. Section 3 describes several specific possible applications, and reports some preliminary results from computer experiments conducted to explore the possibilities inherent in the k-means idea. The extension to general metric spaces is indicated briefly in section 4. The original point of departure for the work described here was a series of problems in optimal classification (MacQueen [9]) which represented special
24,320 citations
TL;DR: In this article, the authors derived necessary conditions for any finite number of quanta and associated quantization intervals of an optimum finite quantization scheme to achieve minimum average quantization noise power.
Abstract: It has long been realized that in pulse-code modulation (PCM), with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. It has been shown by Panter and Dite that, in the limit as the number of quanta becomes infinite, the asymptotic fractional density of quanta per unit voltage should vary as the one-third power of the probability density per unit voltage of signal amplitudes. In this paper the corresponding result for any finite number of quanta is derived; that is, necessary conditions are found that the quanta and associated quantization intervals of an optimum finite quantization scheme must satisfy. The optimization criterion used is that the average quantization noise power be a minimum. It is shown that the result obtained here goes over into the Panter and Dite result as the number of quanta become large. The optimum quautization schemes for 2^{b} quanta, b=1,2, \cdots, 7 , are given numerically for Gaussian and for Laplacian distribution of signal amplitudes.
11,872 citations
TL;DR: An efficient and intuitive algorithm is presented for the design of vector quantizers based either on a known probabilistic model or on a long training sequence of data.
Abstract: An efficient and intuitive algorithm is presented for the design of vector quantizers based either on a known probabilistic model or on a long training sequence of data. The basic properties of the algorithm are discussed and demonstrated by examples. Quite general distortion measures and long blocklengths are allowed, as exemplified by the design of parameter vector quantizers of ten-dimensional vectors arising in Linear Predictive Coded (LPC) speech compression with a complicated distortion measure arising in LPC analysis that does not depend only on the error vector.
7,935 citations
Book•
01 Jan 1991TL;DR: The author explains the design and implementation of the Levinson-Durbin Algorithm, which automates the very labor-intensive and therefore time-heavy and expensive process of designing and implementing a Quantizer.
Abstract: 1 Introduction- 11 Signals, Coding, and Compression- 12 Optimality- 13 How to Use this Book- 14 Related Reading- I Basic Tools- 2 Random Processes and Linear Systems- 21 Introduction- 22 Probability- 23 Random Variables and Vectors- 24 Random Processes- 25 Expectation- 26 Linear Systems- 27 Stationary and Ergodic Properties- 28 Useful Processes- 29 Problems- 3 Sampling- 31 Introduction- 32 Periodic Sampling- 33 Noise in Sampling- 34 Practical Sampling Schemes- 35 Sampling Jitter- 36 Multidimensional Sampling- 37 Problems- 4 Linear Prediction- 41 Introduction- 42 Elementary Estimation Theory- 43 Finite-Memory Linear Prediction- 44 Forward and Backward Prediction- 45 The Levinson-Durbin Algorithm- 46 Linear Predictor Design from Empirical Data- 47 Minimum Delay Property- 48 Predictability and Determinism- 49 Infinite Memory Linear Prediction- 410 Simulation of Random Processes- 411 Problems- II Scalar Coding- 5 Scalar Quantization I- 51 Introduction- 52 Structure of a Quantizer- 53 Measuring Quantizer Performance- 54 The Uniform Quantizer- 55 Nonuniform Quantization and Companding- 56 High Resolution: General Case- 57 Problems- 6 Scalar Quantization II- 61 Introduction- 62 Conditions for Optimality- 63 High Resolution Optimal Companding- 64 Quantizer Design Algorithms- 65 Implementation- 66 Problems- 7 Predictive Quantization- 71 Introduction- 72 Difference Quantization- 73 Closed-Loop Predictive Quantization- 74 Delta Modulation- 75 Problems- 8 Bit Allocation and Transform Coding- 81 Introduction- 82 The Problem of Bit Allocation- 83 Optimal Bit Allocation Results- 84 Integer Constrained Allocation Techniques- 85 Transform Coding- 86 Karhunen-Loeve Transform- 87 Performance Gain of Transform Coding- 88 Other Transforms- 89 Sub-band Coding- 810 Problems- 9 Entropy Coding- 91 Introduction- 92 Variable-Length Scalar Noiseless Coding- 93 Prefix Codes- 94 Huffman Coding- 95 Vector Entropy Coding- 96 Arithmetic Coding- 97 Universal and Adaptive Entropy Coding- 98 Ziv-Lempel Coding- 99 Quantization and Entropy Coding- 910 Problems- III Vector Coding- 10 Vector Quantization I- 101 Introduction- 102 Structural Properties and Characterization- 103 Measuring Vector Quantizer Performance- 104 Nearest Neighbor Quantizers- 105 Lattice Vector Quantizers- 106 High Resolution Distortion Approximations- 107 Problems- 11 Vector Quantization II- 111 Introduction- 112 Optimality Conditions for VQ- 113 Vector Quantizer Design- 114 Design Examples- 115 Problems- 12 Constrained Vector Quantization- 121 Introduction- 122 Complexity and Storage Limitations- 123 Structurally Constrained VQ- 124 Tree-Structured VQ- 125 Classified VQ- 126 Transform VQ- 127 Product Code Techniques- 128 Partitioned VQ- 129 Mean-Removed VQ- 1210 Shape-Gain VQ- 1211 Multistage VQ- 1212 Constrained Storage VQ- 1213 Hierarchical and Multiresolution VQ- 1214 Nonlinear Interpolative VQ- 1215 Lattice Codebook VQ- 1216 Fast Nearest Neighbor Encoding- 1217 Problems- 13 Predictive Vector Quantization- 131 Introduction- 132 Predictive Vector Quantization- 133 Vector Linear Prediction- 134 Predictor Design from Empirical Data- 135 Nonlinear Vector Prediction- 136 Design Examples- 137 Problems- 14 Finite-State Vector Quantization- 141 Recursive Vector Quantizers- 142 Finite-State Vector Quantizers- 143 Labeled-States and Labeled-Transitions- 144 Encoder/Decoder Design- 145 Next-State Function Design- 146 Design Examples- 147 Problems- 15 Tree and Trellis Encoding- 151 Delayed Decision Encoder- 152 Tree and Trellis Coding- 153 Decoder Design- 154 Predictive Trellis Encoders- 155 Other Design Techniques- 156 Problems- 16 Adaptive Vector Quantization- 161 Introduction- 162 Mean Adaptation- 163 Gain-Adaptive Vector Quantization- 164 Switched Codebook Adaptation- 165 Adaptive Bit Allocation- 166 Address VQ- 167 Progressive Code Vector Updating- 168 Adaptive Codebook Generation- 169 Vector Excitation Coding- 1610 Problems- 17 Variable Rate Vector Quantization- 171 Variable Rate Coding- 172 Variable Dimension VQ- 173 Alternative Approaches to Variable Rate VQ- 174 Pruned Tree-Structured VQ- 175 The Generalized BFOS Algorithm- 176 Pruned Tree-Structured VQ- 177 Entropy Coded VQ- 178 Greedy Tree Growing- 179 Design Examples- 1710 Bit Allocation Revisited- 1711 Design Algorithms- 1712 Problems
7,015 citations
TL;DR: The mathematics of a lightness scheme that generates lightness numbers, the biologic correlate of reflectance, independent of the flux from objects is described.
Abstract: Sensations of color show a strong correlation with reflectance, even though the amount of visible light reaching the eye depends on the product of reflectance and illumination. The visual system must achieve this remarkable result by a scheme that does not measure flux. Such a scheme is described as the basis of retinex theory. This theory assumes that there are three independent cone systems, each starting with a set of receptors peaking, respectively, in the long-, middle-, and short-wavelength regions of the visible spectrum. Each system forms a separate image of the world in terms of lightness that shows a strong correlation with reflectance within its particular band of wavelengths. These images are not mixed, but rather are compared to generate color sensations. The problem then becomes how the lightness of areas in these separate images can be independent of flux. This article describes the mathematics of a lightness scheme that generates lightness numbers, the biologic correlate of reflectance, independent of the flux from objects
3,480 citations