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miss the point, because the unitary/binary distinction does not concern colour phenomenology, nor colour ontology. The unitary/binary distinction is an epistemological tool built to identify and describe the variety of colours. As a tool, the only thing that matters is its effectiveness. As long as its efficiency is guaranteed, variations among subjects can be tolerated. If some people take green to be a unitary colour, whereas others consider green to be a binary colour, it’s probably because it does not affect their capacity to identify colours. Using a thermometer whether in Celsius or Fahrenheit can both help us to select the right temperature of our bath, provided we have some familiarity with the scale we use.
REFERENCES
[1]Abramov, I. 1997. Physiological mechanisms of color vision, in Color Categories in Thought and Language, ed. Hardin and Maffi, UK: Cambridge University Press.
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[10]Gross, Dinah. “The evolution of the notion of primary colour in colour vision science", in M. Nida-Rümelin et al. (eds.), Experiencing Colors : Philosophy, Phenomenology and Science, in preparation.
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[17]Hume, David 1739/1983, Treatise of Human Nature.
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[22]2005c. Culture and Cognition: What is Universal about the Representation of Color Experience?, The Journal of Cognition & Culture, 5: 293-347.
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Editors: D. Skusevich, P. Matikas, pp. 203-224 |
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Chapter 7
COLOR IMAGE RESTORATION AND THE
APPLICATION TO COLOR PHOTO DENOISING
Lei He
Department of Information Technology, Armstrong Atlantic State University,
Savannah, Georgia, USA
1. INTRODUCTION
Image restoration has been a classical and significant topic of image processing, which refers to the techniques to reconstruct or recover an image from distortion (e.g. motion blur and noise) in different applications, such as satellite imaging, medical imaging, astronomical imaging, and family portraits. For motion blur, image deblurring techniques are used to estimate the actual blurring function and “undo” the blur to restore the original image. In cases where the image is corrupted by noise, image denoising methods are employed to compensate for the degradation the noise caused. In the past two decades, image denoising has been a fundamental and active research topic and widely used as a key step in a variety of image processing and computer vision applications, such as image segmentation, compression, object recognition, and tracking. This chapter focuses on image denoising, specifically for color image denoising and the application to color photo denoising.
Color image denoising has been an active area with the fast progress of optical camera techniques in past decades. There are several major color spaces to represent color images and the most common one is the Red, Green and Blue (RGB) model. Other color systems include YIQ (luminance, hue and saturation) system (NTSC), YCbCr (luminance, blue minus luminance and red minus luminance) system, CMY and CMYK (cyan, magenta, yellow and black) systems, HSV (hue, saturation and value) and HSI (hue, saturation and intensity) systems [29]. The selection of a system is generally application-specific, e.g. RGB for education and presentation, NTSC for television, YCbCr for digital video, HSV for color
Lei.He@armstrong.edu
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palette. Among these color spaces, HSI space has been well accepted for its favorable color description capability that is practical for human interpretation.
As a specific application of color image denoising, color photo noise removal is an important subject due to extensive use of digital cameras in recent years. Color photo noise is introduced in the process of image acquisition, filtering, compression and reconstruction. In digital photography, a high ISO setting of a digital camera is usually used to increase light sensitivity in dark environments, but the resultant image contains more sensor noise than a low ISO image taken with the same exposure . The objective of our work is to denoise high ISO photos to achieve a low ISO photo quality without the use of expensive cameras or accessories. The motivation comes from the practical needs of digital camera users and manufacturers [30]. So far, most existing approaches are used to solve a general denoising problem (e.g. gray, color or multi-spectral images) based on an assumption of additive or multiplicative noise independent of signal and to the best of our knowledge, none of presented literatures focus on the unknown digital camera sensor noise in color photos.
Since the pioneering work in regularization methods [1,2,3], scale-based analysis has played an increasingly important role in signal (image) processing. The idea is to represent an image in multi-scale, so that only important features are preserved and unwanted features (e.g. noise) are removed in low scales. This is based on the conclusion that convolving a signal with a Gaussian kernel is equivalent to evolving it with a heat differential operator where time is the scale [2]. Such methods have direct applications for feature extraction and image denoising. For example, given an image I: Ω 2→m, the corresponding heat diffusion equation is:
∂I |
= It = div( I ) = Iηη + Iξξ , |
(1) |
∂t |
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where η and ξ refer to the normal and tangential directions respectively. For the denoising applications, this linear filtering approach corresponds to isotropic diffusion, which presents a major limitation: important details in an image also get smoothed away along with the noise. Therefore, a nonlinear filter or an anisotropic diffusion is needed to preserve those details from the smoothing process. Since the seminal model proposed by Perona and Malik [4] in the early 1990s, numerous literatures have been presented to recover the “true” image from noisy data through a nonlinear analysis, such as partial differential equation (PDE)-based anisotropic diffusions [5-10,33-40], variational approaches [11-23,32,43-48], robust statistics [24,25], as well as some transformation based approaches (e.g. wavelet [18,20], ridgelet and curvelet-based image denoising [26]), just to name a few. A complete review of current image denoising approaches can also be seen in several recent literatures [25,27,28].
This chapter presents a novel framework specifically for denoising color photos particularly those photos taken at a high ISO setting that resulted in noticeable sensor noise. Compared with existing literatures, there are two major contributions in the presented approach. The first is that the color photo denoising is conducted in the HSI space instead of the traditional RGB space, which is motivated by the fact that the HSI model has a better color description for human interpretation. Our algorithm is based on separating a color photo
This is achieved by reducing the shutter speed or increasing the aperture.
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into hue, saturation, and intensity components, and then processing each component with PDEs or diffusion flows. The intensity denoising is our main focus, which is implemented with a PDE that is a combination of a gradient vector flow (GVF)-based filter [31] and a fourth-order PDE filter [32]. This combined technique provides a robust and accurate denoising process, i.e., it preserves edges well and at the same time overcomes the staircase effect in smooth regions. The hue and saturation denoising are implemented by a weighted orientation diffusion and a modified curvature diffusion respectively. The second contribution is the algorithm performance assessment. In most existing literatures, synthetic noise (e.g. Gaussian, salt & pepper noise) has been used for algorithm performance evaluation. Furthermore, the denoising effect has been assessed mostly by human visual perception, few by the mean squared error (MSE) and the peak signal to noise ratio (PSNR). In contrast, the color photo noise produced by digital cameras is real sensor noise. In this chapter, the proposed algorithm is evaluated by comparing the denoised images with the ground truth. The ground truth and noisy images are produced by the same camera on the same scene with low and high ISO settings by maintaining the same exposure. Because ground truth images are available for those photos taken under a controlled environment, we could assess the performance of our proposed algorithm, several recognized methods, and commercial software using objective error measurements of MSE and PSNR, in addition to the commonly used subjective visual assessment. Both qualitative and quantitative validation shows that the proposed algorithm is more appropriate for color photo denoising than existing approaches.
2.BACKGROUND
2.1.Direct Partial Differential Equation-Based Anisotropic Diffusion
One major category of image denoising approach is implemented via anisotropic diffusion flows, either implemented directly in the form of partial differential equations (PDE) [4-10,33-40], or derived from certain optimization problems using variational approaches [11-23,43-48]. For direct PDE-based approaches, a continuous sequence of smoother images It are generated by It = R(I), with R(I) representing a space-based image regularization term. For anisotropic diffusion, this term restricts the smoothing in two principles: 1) the magnitude of smoothing, e.g. less smoothing at image features; 2) the direction of smoothing, e.g. less smoothing in the directions across image features. A diffusion equation using a general form of R(I) can be formulated as
It = R(I) = r(| I|)Iηη + s(| I|)Iξξ , |
(2) |
where r( ) and s( ) are gradient-based weighting functions (called “diffusivity” or “edge stopping” functions) to control the smoothing amount along the η-ξ directions.
The well-known Perona-Malik (PM) equation is formulated as
It = div(g(| I | I)) =(g(| I|)+| I | g′(| I|))Iηη + g(| I|)Iξξ , |
(3) |