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Color Filter Arrays: A Design Methodology
"... In the companion report [14], we have shown that a full color image sampled with a rectangular color filter array (CFA) is equivalent to the frequency domain multiplexing of multiplex components: a luminance component (luma) at the baseband and several chrominance components (chromas) at high freque ..."
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In the companion report [14], we have shown that a full color image sampled with a rectangular color filter array (CFA) is equivalent to the frequency domain multiplexing of multiplex components: a luminance component (luma) at the baseband and several chrominance components (chromas) at high frequency bands. A matrix, called the frequency structure of a CFA, is defined to represent this modulation, with which we can easily analyze the characteristics of CFAs. The frequency structure can be computed by applying the symbolic discrete Fourier transform (DFT) to the CFA pattern. In this paper, we present a CFA design methodology in the frequency domain. In this methodology, a good frequency structure of the CFA is first selected, mainly according to the following criteria: (i). the number of nonzero chromas should be as small as possible; (ii). the distance between nonzero multiplex components should be as large as possible; and (iii). dependent (e.g., identical, negative, or conjugate)
A new color filter array with optimal properties for noiseless and noisy color image acquisition
 IEEE Trans. ImageProcess.,vol.20
, 2011
"... Abstract — Digital color cameras acquire color images by means of a sensor on which a color filter array (CFA) is overlaid. The Bayer CFA dominates the consumer market, but there has been recently a renewed interest for the design of CFAs [2]–[6]. However, robustness to noise is often neglected in t ..."
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Abstract — Digital color cameras acquire color images by means of a sensor on which a color filter array (CFA) is overlaid. The Bayer CFA dominates the consumer market, but there has been recently a renewed interest for the design of CFAs [2]–[6]. However, robustness to noise is often neglected in the design, though it is crucial in practice. In this work, we present a new 2 × 3periodic CFA which provides, by construction, the optimal tradeoff between robustness to aliasing, chrominance noise and luminance noise. Moreover, a simple and efficient linear demosaicking algorithm is described, which fully exploits the spectral properties of the CFA. Practical experiments confirm the superiority of our design, both in noiseless and noisy scenarios. Index Terms — Color filter array (CFA), color imaging, demosaicking, digital camera pipeline, spatiospectral sampling, luminance/chrominance basis, noise sensitivity. I.
A Geometric Method for Optimal Design of Color Filter Arrays
"... Abstract—A color filter array (CFA) used in a digital camera is a mosaic of spectrally selective filters, which allows only one color component to be sensed at each pixel. The missing two components of each pixel have to be estimated by methods known as demosaicking. The demosaicking algorithm and t ..."
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Abstract—A color filter array (CFA) used in a digital camera is a mosaic of spectrally selective filters, which allows only one color component to be sensed at each pixel. The missing two components of each pixel have to be estimated by methods known as demosaicking. The demosaicking algorithm and the CFA design are crucial for the quality of the output images. In this paper, we present a CFA design methodology in the frequency domain. The frequency structure, which is shown to be just the symbolic DFT of the CFA pattern (one period of the CFA), is introduced to represent images sampled with any rectangular CFAs in the frequency domain. Based on the frequency structure, the CFA design involves the solution of a constrained optimization problem that aims at minimizing the demosaicking error. To decrease the number of parameters and speed up the parameter searching, the optimization problem is reformulated as the selection of geometric points on the boundary of a convex polygon or the surface of a convex polyhedron. Using our methodology, several new CFA patterns are found, which outperform the currently commercialized and published ones. Experiments demonstrate the effectiveness of our CFA design methodology and the superiority of our new CFA patterns. Index Terms—color filter array (CFA), discrete Fourier transform (DFT), sampling, multiplexing, demosaicking I.
NEW COLOR FILTER ARRAYS OF HIGH LIGHT SENSITIVITY AND HIGH DEMOSAICKING PERFORMANCE
"... For high light sensitivity, new CFA designs use panchromatic pixels, aka white pixels, that no visible spectrum energy is filtered. Kodak’s CFA2.0 has 50 % white pixels, but the demosaicking performance is not good. We present in this work a set of new color filter arrays (CFA) of high light sensiti ..."
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For high light sensitivity, new CFA designs use panchromatic pixels, aka white pixels, that no visible spectrum energy is filtered. Kodak’s CFA2.0 has 50 % white pixels, but the demosaicking performance is not good. We present in this work a set of new color filter arrays (CFA) of high light sensitivity and high demosaicking performance which were obtained by using a CFA design methodology in the frequency domain. The new patterns are of size 5x5 and come from the same frequency structure, which has one luma in the base band at (0, 0) and four chromas (two conjugate pairs) placed at (4π/5, 2π/5), (−4π/5, −2π/5), (2π/5, −4π/5) and (−2π/5, 4π/5), respectively. The new patterns are optimized to have only white (panchromatic) and three primary color pixels and the pixels are found to be 40 % white, 20 % red, 20 % green and 20% blue by pixel color constrained optimization. Our demosaicking experiments show that our new CFA patterns outperform Kodak CFA2.0 in both objective and subjective quality.
Joint Demosaicing and Denoising via Learned Nonparametric Random Fields
, 2013
"... We introduce a machine learning approach to demosaicing, the reconstruction of color images from incomplete color filter array samples. There are two challenges to overcome by a demosaicing method: first, it needs to model and respect the statistics of natural images in order to reconstruct natura ..."
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We introduce a machine learning approach to demosaicing, the reconstruction of color images from incomplete color filter array samples. There are two challenges to overcome by a demosaicing method: first, it needs to model and respect the statistics of natural images in order to reconstruct natural looking images; second, it needs to be able to perform well in the presence of noise. To facilitate an objective assessment of current methods we introduce a public ground truth data set of natural images suitable for research in image demosaicing and denoising. We then use this large data set to develop a machine learning approach to demosaicing. Our proposed method addresses both demosaicing challenges by learning a statistical model of images and noise from hundreds of natural images. The resulting model performs simultaneous demosaicing and denoising. We show that the machine learning approach has a number of benefits: 1. the model is trained to directly optimize a userspecified performance measure such as peak signaltonoise ratio (PSNR) or structural similarity (SSIM), 2. we can handle novel color filter array layouts by retraining the model on such layouts, 3. it outperforms the previous stateoftheart, in some setups by 0.7dB PSNR, faithfully reconstructing edges, textures, and smooth areas. Our results demonstrate that in demosaicing and related imaging applications, discriminatively trained machine learning models have the potential for peak performance at comparatively low engineering effort.
Author manuscript, published in "IS&T/SPIE Electronic Imaging: Digital Photography VII, United States (2011)" Evaluation of a Hyperspectral Image Database for
, 2011
"... We present a study on the the applicability of hyperspectral images to evaluate color filter array (CFA) design and the performance of demosaicking algorithms. The aim is to simulate a typical digital still camera processing pipeline and to compare two different scenarios: evaluate the performance ..."
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We present a study on the the applicability of hyperspectral images to evaluate color filter array (CFA) design and the performance of demosaicking algorithms. The aim is to simulate a typical digital still camera processing pipeline and to compare two different scenarios: evaluate the performance of demosaicking algorithms applied to raw camera RGB values before color rendering to sRGB, and evaluate the performance of demosaicking algorithms applied on the final sRGB color rendered image. The second scenario is the most frequently used one in literature because CFA design and algorithms are usually tested on a set of existing images that are already rendered, such as the Kodak Photo CD set containing the wellknown lighthouse image. We simulate the camera processing pipeline with measured spectral sensitivity functions of a real camera. Modeling a Bayer CFA, we select three linear demosaicking techniques in order to perform the tests. The evaluation is done using CMSE, CPSNR, sCIELAB and MSSIM metrics to compare demosaicking results. We find that the performance, and especially the difference between demosaicking algorithms, is indeed significant depending if the mosaicking/demosaicking is applied to camera raw values as opposed to already rendered sRGB images. We argue that evaluating the former gives a better indication how a CFA/demosaicking combination will work in practice, and that it is in the interest of the community to create a hyperspectral image dataset dedicated to that effect.
Evaluation of a Hyperspectral Image Database for Demosaicking
"... We present a study on the the applicability of hyperspectral images to evaluate color filter array (CFA) design and the performance of demosaicking algorithms. The aim is to simulate a typical digital still camera processing pipeline and to compare two different scenarios: evaluate the performance ..."
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We present a study on the the applicability of hyperspectral images to evaluate color filter array (CFA) design and the performance of demosaicking algorithms. The aim is to simulate a typical digital still camera processing pipeline and to compare two different scenarios: evaluate the performance of demosaicking algorithms applied to raw camera RGB values before color rendering to sRGB, and evaluate the performance of demosaicking algorithms applied on the final sRGB color rendered image. The second scenario is the most frequently used one in literature because CFA design and algorithms are usually tested on a set of existing images that are already rendered, such as the Kodak Photo CD set containing the wellknown lighthouse image. We simulate the camera processing pipeline with measured spectral sensitivity functions of a real camera. Modeling a Bayer CFA, we select three linear demosaicking techniques in order to perform the tests. The evaluation is done using CMSE, CPSNR, sCIELAB and MSSIM metrics to compare demosaicking results. We find that the performance, and especially the difference between demosaicking algorithms, is indeed significant depending if the mosaicking/demosaicking is applied to camera raw values as opposed to already rendered sRGB images. We argue that evaluating the former gives a better indication how a CFA/demosaicking combination will work in practice, and that it is in the interest of the community to create a hyperspectral image dataset dedicated to that effect.
The Frequency Structure Matrix: A Representation of Color Filter Arrays
, 2009
"... This letter introduces the frequency structure matrix as a new representation of color filter arrays (CFAs). The matrix records the frequency components of CFA filtered images and their positions in the spectrum. The matrix can be conveniently obtained by applying the symbolic DFT to the CFA pattern ..."
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This letter introduces the frequency structure matrix as a new representation of color filter arrays (CFAs). The matrix records the frequency components of CFA filtered images and their positions in the spectrum. The matrix can be conveniently obtained by applying the symbolic DFT to the CFA pattern. With this new representation, it is easy to analyze the characteristics of CFAs and to formulate the CFA design as an optimization problem. Key Words: color filter array (CFA), discrete Fourier transform (DFT), sampling, multiplexing, demosaicking 1