Image Pre-compensation for Ocular Aberrations

Image Pre- payment for Ocular Aberrations inceptionMotivationOn- interpenetrate plan pre- wages has good prospect with the increasing usage of motley parade screen devices in our daily life. Comparing to spectacles, contact glasses and optical surgery, on-screen see to it pre- honorarium bottom be easily carried out by estimator slowness without each irreversible change in the bosoms, as foresighted as the ocular aberration is cognise. Further, since neither contact lenses nor glasses be advised to be worn all of the time, on screen pre-compensation could even supplement glasses and contact lens determination. It is cognize that compensation for higher aberrations besidesshie raceway to super-sight, which is the neural limit of humans eye. On-screen compensation withal has the prospect of achieving this with customized screens in the foreseeable future.Image Processing Theories clement Visual SystemThe human optic system is the combination of the optic system o f the eye, and the neural processing of the idle in recoilation received Roorda (2011), in which the latter is out of the concern of this rese curlh. The optical system of the eye is an composite construction including the scholarly person, cornea, retina and lens (see Fig.1). The light come through the pupil is refracted by the lens and make an inverse cipher on the retina. During this process, each dearth would ca habit aberrations. For instance, myopia whitethorn issuance from the lens that the refraction is as well high or that the distance from the lens and retina is too long.Fig.1 Cross-section of eye structureThere is a limit resolution dominated by the neural receptor on the retina, which is below the diffraction limit. Although even for normal emmetropic eyes the sight is below neural limit and diffraction limit callable to the minor deficit of eye structure. Austin (2011) For eyes with refractive issues, cause by cornea or lens from an ideal spherical shape, the a berrations would signifi cig arettly dominate over this limit. Thus, in the following interrogation, we shall omit the neural limitation. To increase the efficiency in the following, we great deal simply model the eye structure as much(prenominal) a lens (regarding the cornea and the lens as a whole) with an adjustable size (pupil size) and an visualize plane (retina).Point Spread Function and picture show qualityAs is verbalise in the previous section the aberrations would come from any deficit of eye structure. In order to define the distortion in numeric fashion, we introduce the Point Spread Function (PSF). Fundamentally, the PSF is defined as a mould describes the response of an imaging system to a point extraction or point object. Note that the loss of light would not be considered in the PSF. Then, if we consider the PSF does not change across the field of view, which applies to the substitution 1-2 of visual angle Reference, the build dope be expressed by the whirlpool of the PSF and the object in this area. (1)Where denotes the convolution algorithm. Note that the deconvolution mode is base on the inverse operation of Eq.1, which lead be introduce in Section 1.2.4.Fig.2 A telephone circuit of PSF and MTF of an ideal emmetropic eyes (up) and a typical myopic eyes of -1.00 dioptre (down)Now we introduce cardinal involvements that brush off show the quality of the discover Optical Transfer Function (OTF) and the flexion Transfer Function (MTF). Either OTF or MTF specifies the response to a midweekly sine-wave pattern passing through the lens system, as a aim of its spatial frequency or period, and its orientation WIKI. The OTF is the Fourier shift of the PSF, and the MTF is the real order of magnitude of the OTF. In a 2d system, these two functions are defined as (2)Where denotes the Fourier transform, and denote the phase space and Euclidian space, respectively. (3)Where kernel taking the secure abide by.Zernike Polyn omialsThe Zernike polynomials are a sequence of polynomials that are orthogonal over street arab pupils. Some of the polynomials are related to classical aberrations. In optometry and ophthalmology, Zernike polynomials are the timeworn way to describe aberrations of the cornea or lens from an ideal spherical shape, which result in refraction errors WIKI.The definition of orthogonal Zernike Polynomials recommended in an ANSI beat is delineate as(4)Where m and n denote the radial degree and the azimuthal frequency, respectively. The radial polynomials are defined asAnd the triangular functions(6)Note that nm and nm must be even.The relationship between double tycoon (m, n) and single index (i)Table.1 Eye aberrations presented by Zernike PolynomialsAberrations are expressed as the distortion of the wave trend as it passes through the eye. As is stated, Zernike polynomials are the standard way Campbell (2003) of quantifying this distortion. The aperture function (or pupil function) shtup link Zernike polynomials with the PSFWhere denotes complex aperture function (or pupil function). denotes the phase of the wavefront, and the i is the imaginary unit and denotes the amplitude function, which is usually one inside the circular pupil and zero on the outside. The PSF sens be expressed as the square of Fourier transform of the complex aperture functionWe now know that the PSF can be calculated with a known wavefront and the distortion of the wavefront caused by refractive error can be actually delineated by several orders of Zernike Polynomials with diverse amplitudes, which can be circumstantially measured with a Shack-Hartmann wavefront analyser device.Deconvolution systemWe introduce a way to pre-process the image to neutralize the aberration caused by eyes, which is also called image pre-compensation. Simplistically, to compensate them in advance to proactively weigheract degradations resulting from the ocular aberrations of different users.Point Sp read Function (PSF) is defined as a function describes the response of an imaging system to a point writer or point object. The sinusoidal function is an eigenstate of the PSF (i.e. if the input image is a sinusoidal function, no matter what the PSF is, the output image would also be a sinusoidal function)The Image on the retina (or) can be conjugated with PSF by convolution as shown in Eq.1. Then we do Fourier transform on both side of the equationNote the convolution has changed to coevals in the phase space. If we define a fresh OBJ asThe new image isThis means If we can process the OBJ as defined, we willing sacrifice the intended image in the reviewers eyes. To form the OBJ we introduce Minimum baseborn Square hallucination filtering (or Wiener Filter)Where K is a constant.Computing Theories quick Fourier TransformAs is shown in previous sections, we use two algorithms that wait an amount of calculation, which is Fourier transform (inverse Fourier transform) and convol ution. Since computing machine images can be seen as 2-demension lattices, we will use 2d Discrete Fourier TransformIt is known that this process requires a significant amount of calculation. The conventional way of doing this would take a long time for regular PC. However, for investigate need, we will need to do this calculation in real-time. Thus, we introduce the Fast Fourier Transform (FFT). A definition of FFT could be An FFT is an algorithm computes the discrete Fourier transform (DFT) of a sequence or its inverse. Fourier compend converts a argue from its original domain (often time or space) to federal agency in the frequency domain and vice versa. An FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors. Van Loan (1992)Also, all convolution within our program will be calculated by means of the FFT through the following equation(16)Fig.3 A line of credit of the speed of two means of calculation with resp ect of data length.The purpose of doing so is to renovate the speed of calculation, since the conventional way of calculating convolution is much long-playing than the FFT. This difference of speed is shown in Fig.3.Nyquist LimitAs is stated, we need the image and the PSF to before doing the pre-compensation. The PSF is calculated by aperture function Eq.9. To simulate the pupil, we can use a circular aperture. However, this circular pupil has some restrictions in computer simulation, which is the Nyquist limit.In signal processing if weIf we want to reconstruct all Fourier components of a periodic waveform, there is a restriction that the sampling rate necessarily to be at least twice the highest waveform frequency. The Nyquist limit, also known as Nyquist frequency, is the highest frequency that can be coded at a given over sampling rate in order to be able to amply reconstruct the signal, which is half of the sampling rate of a discrete signal processing system. Cramr Gren ander (1959)For our simulation the sampling rate n is represented asAliasing will occur when .Psychometric TheoriesIn order to quantify the enhancement of the Deconvolution method acting to the subjects, we need to measure the change of the wands of the eyes before and afterward the compensation. Specifically, in our research we need to find out the threshold of minimum contrast and size of an image that the subjects can correctly recognize. This requires the use of some psychometric theories.Adaptive Staircase MethodThe stairway manner is a widely used method in psychophysics test. The point of staircase method is to adjust the intensity of stimuli according to the response of the participant. To illustrate this method we shall use an example introduced by Cronsweet (1962)Suppose the problem is to determine Ss absolute, intensifier threshold for the sound of a click. The first stimulus that E delivers is a click of some arbitrary intensity. S responds either that he did or di d not hear it. If S says yes (he did hear it), the next stimulus is do less intense, and if S says no, the second stimulus is made more intense. If S responds yes to the second stimulus, the trine is made less intense, and if he says no, it is made more intense. This procedure is simply continued until some pre pertinacious criterion or number of trials is reached. The results of a series of 30 trials are shown in Fig.4. The results may be recorded directly on graph-paper doing so helps E nurture the procedure straight.Fig. 4 An example trail by Cornsweet (1962)There are foursome important characteristic of adaptive staircase method (1) jump value (2) Step-size (3) Stopping condition and (4) Modification of step-sizes. Cornsweet 1962The starting value should be near the threshold value. As is shown in Fig.4, the starting point determines how numerous step until it reach a take that near the threshold. The test will be most efficient if the starting value is near to that thre shold.The step-size is 1 db for the example test. Step-size should meet the requirement that it is neither too mammoth that not able to measure the threshold accurately nor too low-pitched to slow down the test process. It is advised that the step-size would be the most sound when it is the size of the differential threshold.The result with the staircase method would be same Fig.4 in general when it hover around a certain level of intensity of stimuli. When reached this asymptotic level, the trails should be taken into account. An efficient way is to preen a number of trails that need to be record and start to count after it reach the asymptotic level.Under some conditions, the step-size need to be changed during the test. For careful essayal design, the first stimulus in each of the staircases are at same intensity-level. Cornsweet 1962 However, then the staring level would be too far from the final level. This can be avoided by exploitation ample steps at the start, and sma ller steps when it approach the final level. For instance, this can be done by decrease the step from 3db to 1db at the third reversal.It should be stated that the adaptive staircase method is a truly efficient way of measurement. For a given reliability of a computed threshold-value, the staircase-method requires the entry of many fewer stimuli than any early(a) psychophysical method.Related Work customary image compensation has long been used since the invention of lens. The invention of the computer and portable scupper devices make it easier to perform on-screen image pre-compensation. On-screen compensation has the value of convenience in that it can easily be carried out with any display-screen device that can compute. In addition, acuity limits in the human mint on the fovea are ground to be between 0.6 and 0.25 arc minutes Schwiegerling 2000, which is better than the typical acuity of emmetropic eyes Pamplona 2012. This means that effective compensation may increase t he performance of emmetropic eyes.Deconvolution MethodOn screen image pre-compensation is base on the idea that the aberrations can be neutralized by pre-compensating the object. Specifically, it requires dividing the Fourier transform of uncorrected image by the Fourier transform of the PSF (i.e. the OTF). A detailed derivation can be found at section1.2.4. Early research by Alonso and Barreto (2003) tested subjects with defocus aberration using this method. Their results showed an improvement in observers visual acuity compared to non-corrected images.However, in practical use, for example, defocus, the defocus magnitude (in dioptres) as well as the pupil size, wavelength and viewing distance (visual angle) is required to calculate and scale the PSF, which means measurement and substitution of these parameters are also required to deliver the intended compensation.Enhancement of Deconvolution MethodRecent research has further improved the deconvolution method. Huang et al (2012) carried out work with dynamic image compensation. They fixed the viewing distance from the screen and measured the real-time pupil size with the help of a Tobii T60 eye tracker device. Then they compensated the image with this real-time pupil size data. The reliability and acuity were improved by this dynamic compensation. Unlike perfect eyes, for which bigger pupil size would lead to smaller diffraction limited PSF, for most eyes, a bigger pupil size would lead to an increase in aberrations. That is also why dynamic compensation is important.As is mentioned in previous section, the principle of pre-compensation is to divide the Fourier transform of the image by the Fourier transform of the OTF. In order to avoid near-zero values in the OTF, most of the research used Minimum Mean Square Error filtering (Wiener filter). However, the outcome usually suffers from an apparent loss of contrast.Recent research has revealed other ways to optimize the compensation to scram higher contrast and sharpie boundaries. The multi-domain approach was introduced by Alonso Jr et al. (2006). They claimed that there are unnecessary parts in pre-compensated image. Simplistically, there is compensation that is irrelevant with respect to the important information in the image. This work showed an improvement of acuity using this method with respect to recognising text. more than recently, Montalto et al. (2015) applied the total variation method to process the pre-compensated image. The result is meagerly better but still suffers from a trade-off between contrast and acuity. Fundamentally, the impaired human eye can be seen as a low-pass filter, and either an increase of image aliasing or a decrease of contrast is inevitable.Other ApproachesThe research described above can be seen as an enhancement and a supplement of the original method carried out by Alonso (2003). However, as is stated, there is a limit of image pre-compensation by the PSF deconvolution method. Others has ca nvas other on-screen methods to achieve a better outcome. Huang et al. (2012) introduced a multilayer approach found on the drawback of normal on screen pre-compensation that was shown by Yellot and Yellot (2007). This method is base on the deconvolution method, but uses a double-layer display rather than normal display. harmonize to Fig.2, if we have two separated displays, then we have two different MTF curve. Then, the near-zero gap in MTF can be filled. This approach has showed a irrefutable improvement of contrast and chichi in their simulation. However, it required a bold front display that does not block the light from the rear display at all, which is not plausible in practical use.Later, Pamplona et al. (2012) investigated a light field theory approach and built a monochrome dual-stack-LCD display (also known as parallax parapets) prototype and a lenticular-based display prototype to form directional light. Huang et al. (2014) restated the potential of using light fie ld theory on image compensation and built another prototype with a parallax barrier mask and higher resolution. The outcome of both methods were similar. They could produce colour images with lonesome(prenominal) a little decrease in contrast and acuity. However, it should be stated that both methods were carried out with a fixed directional light field, which used a fixed camera to photograph the intended corrected image. It is explicit that is not feasible in practical use with moving observer. adjustable directional light has not been implemented due to the limits imposed by diffraction and resolution. In addition, there are minor issues on the loss of brightness as well in these research.Overall, the most applicable way of on-screen image compensation is still deconvolution method. The light field method requires very precise eye tracking to inject the light into pupil, while deconvolution only requires the observer to keep a certain distance and to be in front of the pre-comp ensated image.MethodSubjectsImplementationWe built a program for the test that can proceed the pre-compensation in real-time using deconvolution method. This program can pre-compensate any aberration that can be represented by Zernike polynomialsThe experiment is based on adaptive staircase method. During the experiment, the program shows optotype Landolt-C in four directions (i.e. up, down, go forth and right) which is randomly generated at each trail. The subjects choose the direction of the Landolt-C.Staircase This research intend to find two thresholds contrast and size. Though the We shall describe the staircase method for the contrast threshold. The experiment for size threshold is taken likewise.The four characteristic for our adaptive staircase method areThe start value is relatively large since the subjectThe step-sizeThe experiment ends in N trials after it reached the final levelFor our research, we cannot determine an ideal starting value because the subjects have diffe rent type and intensity of aberration. Thus, we have to change the size-step to make our experiment efficient.The threshold is calculated using the record the last N trails of the experiment, which is determined by the following equationEq.()The program was design as such that Assumptions, Approximations and LimitationsAssumption About SubjectsLimitation Polychromatic issues, No. of Pixels, StaircaseReferencesAlonso, M., Barreto, A. B. (2003, September). Pre-compensation for high-order aberrations of the human eye using on-screen image deconvolution. In Engineering in medicinal drug and Biology Society, 2003. Proceedings of the 25th Annual transnational Conference of the IEEE (Vol. 1, pp. 556-559). IEEE.Alonso Jr, M., Barreto, A., Jacko, J. A., Adjouadi, M. (2006, October). A multi-domain approach for enhancing text display for users with visual aberrations. In Proceedings of the eighth international ACM SIGACCESS conference on Computers and accessibility (pp. 34-39). ACM.Campbe ll, C. E. (2003). 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