# Objective Prediction of Human Visual Acuity Using Image Quality Metrics
## 1 Introduction  
The quality of the optical system, the quality of the retinal image, and subjective visual quality are three highly related concepts in the visual optics field. They are approached by objective functions, such as the modulation transfer function (_MTF_) of the system, the Zernike decomposition of the wavefront, or by subjective parameters, such as subjects' decimal uncorrected visual acuity (VA). The relation among these three concepts is clear: if the quality of the human visual system (HVS) is poor, the quality of the resulting image will also be bad and, as a result, VA will be poor. The retinal image is affected by aberrations of the system, scattering and diffraction of light, and retinal sampling. Nevertheless, the vision process is not simple because it results from the proper combination of physical, optical, physiological, neural, and psychological aspects. Thus, it is relatively normal to find people who indicate they \"correctly view\" a certain image because they recognize the structure of the object, but not its details. Therefore, they pose no need for refractive correction. [PERSON] and [PERSON] [1] suggested that the visual quality metrics obtained on the retinal plane are more consistent with subjective measurements than those calculated on the pupil plane. Presently, the mostwidespread objective criterion to predict visual quality is the visual Strehl ratio (_VSOTF_). [PERSON] et al. [2] obtained a correlation between defocus and astigmatism, and 31 different visual quality metrics. They concluded that the _VSOTF_ might be a good objective parameter. They also concluded that the value of the root mean square (_RMS_) wavefront error, or other parameters like the Strehl ratio (SR), are not reliable indicators of the subjective quality of the retinal image. Thus, they chose a metric that combined the point spread function (_PSF_) of the system with a spatial sensitivity function. [PERSON] et al. [3] demonstrated the need for single-value metrics other than RMS to assess the VA effects of low aberration levels. Later, [PERSON] and [PERSON] [4] proposed a model for VA that incorporates the set of ocular aberrations, optical and neural filtering, and neural noise. An alternative approach to assess the image quality of the HVS can be addressed from the perspective of the image and video processing field. On the one hand, human tolerance to image degradation is quantified with mean opinion scores (_MOS_) [5]. On the other hand, a series of image quality assessment (_IQA_) algorithms are used to maintain, control, and improve the quality of processed images. Early works focused on comparing the degraded image to the initial one by using two objective parameters: peak signal-to-noise ratio (_PSNR_) and mean square error (_MSE_) or its square root (_RMSE_). _MSE_ is the standard method applied in image comparisons because it is simple and fast but is not usually a good estimator of subjective perception because it does not consider HVS characteristics. It is also an unbounded metric, which makes it difficult to correlate with VA [6]. The _PSNR_ metric is also based on pixel-by-pixel by comparing the reference image to the distorted image through _MSE_, and it is still one of the most popular ways to assess the quality difference between images [7]. Its disadvantages are that it is not a bounded metric, and it does not consider HVS properties. Thus, it does not correlate well with subjective tests. In the last few years, one of the most commonly used metrics has been the structural similarity index (_SSIM_) [8] because of the good correlation with _MOS_. IQA objective methods can be classified into three types, full-reference, reduced-reference, and non-reference, depending on the use of a reference image, some of the information of that image, or no available reference image to make the comparison, respectively. In this paper, we focus on studying seven metrics that derive from full-reference algorithms to objectively determine subjects' VA.