Diving Deeper into Underwater Image Enhancement: A Survey <s> Automatic evaluation metrics <s> We propose a new universal objective image quality index, which is easy to calculate and applicable to various image processing applications. Instead of using traditional error summation methods, the proposed index is designed by modeling any image distortion as a combination of three factors: loss of correlation, luminance distortion, and contrast distortion. Although the new index is mathematically defined and no human visual system model is explicitly employed, our experiments on various image distortion types indicate that it performs significantly better than the widely used distortion metric mean squared error. Demonstrative images and an efficient MATLAB implementation of the algorithm are available online at http://anchovy.ece.utexas.edu//spl sim/zwang/research/quality_index/demo.html. <s> BIB001 </s> Diving Deeper into Underwater Image Enhancement: A Survey <s> Automatic evaluation metrics <s> Objective methods for assessing perceptual image quality traditionally attempted to quantify the visibility of errors (differences) between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative complementary framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a structural similarity index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000. A MATLAB implementation of the proposed algorithm is available online at http://www.cns.nyu.edu//spl sim/lcv/ssim/. <s> BIB002 </s> Diving Deeper into Underwater Image Enhancement: A Survey <s> Automatic evaluation metrics <s> Contrast is a fundamental attribute of images that plays an important role in human visual perception of image quality. With numerous approaches proposed to enhance image contrast, much less work has been dedicated to automatic quality assessment of contrast changed images. Existing approaches rely on global statistics to estimate contrast quality. Here we propose a novel local patch-based objective quality assessment method using an adaptive representation of local patch structure, which allows us to decompose any image patch into its mean intensity, signal strength and signal structure components and then evaluate their perceptual distortions in different ways. A unique feature that differentiates the proposed method from previous contrast quality models is the capability to produce a local contrast quality map, which predicts local quality variations over space and may be employed to guide contrast enhancement algorithms. Validations based on four publicly available databases show that the proposed patch-based contrast quality index (PCQI) method provides accurate predictions on the human perception of contrast variations. <s> BIB003 </s> Diving Deeper into Underwater Image Enhancement: A Survey <s> Automatic evaluation metrics <s> Quality evaluation of underwater images is a key goal of underwater video image retrieval and intelligent processing. To date, no metric has been proposed for underwater color image quality evaluation (UCIQE). The special absorption and scattering characteristics of the water medium do not allow direct application of natural color image quality metrics especially to different underwater environments. In this paper, subjective testing for underwater image quality has been organized. The statistical distribution of the underwater image pixels in the CIELab color space related to subjective evaluation indicates the sharpness and colorful factors correlate well with subjective image quality perception. Based on these, a new UCIQE metric, which is a linear combination of chroma, saturation, and contrast, is proposed to quantify the non-uniform color cast, blurring, and low-contrast that characterize underwater engineering and monitoring images. Experiments are conducted to illustrate the performance of the proposed UCIQE metric and its capability to measure the underwater image enhancement results. They show that the proposed metric has comparable performance to the leading natural color image quality metrics and the underwater grayscale image quality metrics available in the literature, and can predict with higher accuracy the relative amount of degradation with similar image content in underwater environments. Importantly, UCIQE is a simple and fast solution for real-time underwater video processing. The effectiveness of the presented measure is also demonstrated by subjective evaluation. The results show better correlation between the UCIQE and the subjective mean opinion score. <s> BIB004 </s> Diving Deeper into Underwater Image Enhancement: A Survey <s> Automatic evaluation metrics <s> Underwater images suffer from blurring effects, low contrast, and grayed out colors due to the absorption and scattering effects under the water. Many image enhancement algorithms for improving the visual quality of underwater images have been developed. Unfortunately, no well-accepted objective measure exists that can evaluate the quality of underwater images similar to human perception. Predominant underwater image processing algorithms use either a subjective evaluation, which is time consuming and biased, or a generic image quality measure, which fails to consider the properties of underwater images. To address this problem, a new nonreference underwater image quality measure (UIQM) is presented in this paper. The UIQM comprises three underwater image attribute measures: the underwater image colorfulness measure (UICM), the underwater image sharpness measure (UISM), and the underwater image contrast measure (UIConM). Each attribute is selected for evaluating one aspect of the underwater image degradation, and each presented attribute measure is inspired by the properties of human visual systems (HVSs). The experimental results demonstrate that the measures effectively evaluate the underwater image quality in accordance with the human perceptions. These measures are also used on the AirAsia 8501 wreckage images to show their importance in practical applications. <s> BIB005
• MSE and PSNR: We begin our discussion with Mean Square Error (MSE) as the signal measure. The MSE aims to provide a quantitative score that represents the similarity or distortion between the two signals. Usually, one of the signals is the original * , Chongyi Li * signal, and the other one is recovered from some distortion or contamination. Mathematically, the MSE between the two signals can be expressed as: where x and y are two signals, in this case, images and x i and y i are the pixels at i th location. Similarly, N are the number of pixels. Furthermore, in the image processing literature, peak signal to noise ratio (PSNR) measure is computed from MSE as: where L is the dynamic range of image pixel intensities (i.e., 255 for image). The usage of MSE and PSNR has many attractive features e.g. 1) it is simple, 2) all norms are valid distance metrics, 3) it has a clear physical meaning, and 4) these are excellent metrics in the context of optimization. The mentioned measures assume that the signal fidelity is independent of the relationship between 1) the original signal, 2) the distorted and original signal, and 3) the signs of the error signal. Unfortunately, none of them even roughly holds in the context of measuring the visual perception of image fidelity  . In the next section, we discuss alternatives to these measures. • SSIM: Another commonly used measure is the Structural SIMilarity (SSIM) index. The main ideas of SSIM were presented by Wang & Bovik BIB001 and formulated in  BIB002 . Let us consider that x and y are the patches taken from the two different images but locations to be compared against each other. Then SSIM takes three measures into account, which are the similarity of the patch 1) luminance l(x, y), 2) contrasts c(x, y), and 3) the local structures s(x, y). As pointed out in BIB002 , these similarities are expressed and computed using simple statistics and are combined to produce local SSIM as: where µ x and µ y are means while σ x and σ y are standard deviations of the patches x and y, respectively. Similarly, σ xy cross-correlation of the patches after removing their means. The constants C 1 , C 2 and C 3 stabilize the terms to avoid near-zero divisions. • PCQI: Patch-based contrast quality index (PCQI) BIB003 relies on patch-based approach as contrary to relying on global statistics. The PCQI depends on three independent quantities of an image patch i.e. mean, signal strength and structure. Mathematically, a patch-based contrast image quality index (PCQI) is given by: where q i (x, y) is to compare mean intensity, q c (x, y) is to determine the structural distortion and q s (x, y) is the contrast change. PCQI is mathematically expensive as compared to other metrics. Next, we discuss quantitative measures, which are more specific to underwater image enhancement. • UCIQE: Underwater color image quality evaluation abbreviated as UCIQE BIB004 , is based chroma, contrast, and saturation of CIELab and is defined as: where σ c , con l and µ s are the standard deviation of chroma, the contrast of luminance, and the mean of saturation. It is to be noted here that for underwater images, human perception has a good correlation with the variance of chroma. • UIQM: UIQM BIB005 stands for underwater image quality measure and is different from earlier defined evaluation metrics. The UIQ employs the HVS model only, and does not require a reference image; hence, a better candidate for evaluation of underwater images. UIQM is dependent on three attribute measures the underwater images, which are 1) image colorfulness measure (UICM), 2) sharpness measure (UISM), and 3) contrast measure (UIConM). Following is the formulation of UIQM: where c 1 , c 2 and c 3 are the parameters which are application dependent, e.g., more weight should be given to c 1 for underwater color correct while c 2 for increasing visibility in the underwater scene.