Abstract
The neurological disorders are developed in adults due to reduced visual perception. Opto Kinetic Nystagmus (OKN) is a clinical method to detect visual perception. For objective measurements, a computational algorithm based OKN detection is preferable rather than clinical practice. In this paper, a memory-efficient Subsampled Lucas-Kanade Optical Flow (SLKOF) is proposed. The proposal employs the Subsampling of images for various levels. The proposal deals with the computation of OKN gain for different image Subsampling factors using the MATLAB platform. The experimental set up to observe OKN is done using computer-based rotation control of the drum through a stepper motor. The results are compared with the well established Lucas-Kanade (LK) method for Optical flow. It is observed that OKN gain corresponds to 1/4th of a subsampled image of the SLKOF method correlates with the LK method for the majority of the cases. This validation evidently elucidates that the proposal is computationally efficient.
Introduction
Recent clinical studies reveal that the ability to read the Snellen eye chart by an adult learner is not the only factor in gauging visual perception. The Visual function of the Eye is related to the Visual perception of the brain. The visual function of a person can be measured using Visual Acuity (VA) in clinical practice [1]. The grown-up persons with diminished VA need assistance everywhere. Hence, the detection of Visual Acuity plays a significant role. Opto Kinetic Nystagmus (OKN) is one of the detection methods of VA [2]. OKN is an evaluation tool for measuring visual function by starring the moving pattern, i.e., stimulus in front of the person [3, 4]. The different bar sizes are used to stimulate OKN for which Recognition Visual Acuity (RVA) and OKN response relationships are evaluated [5–7].
The techniques involved in the OKN test are sorted as subjective and objective [8]. In the subjective method, the patients are subjected to direct contact with high current or power equipment used for recording eye movements, and it is popularly termed as clinical practice. In the objective method, standard quantitative methods are employed. In some of the quantitative methods, computational algorithms are applied to detect OKN. The detailed survey on the subjective and objective methods used for OKN detection is elaborated in this section. The horizontal movement of the eyes can be measured using an electrophysiological signal generated by using a pair of electrodes placed on both sides of the eyes. This renowned method of recording eye movements is termed as Electrooculography (EOG) [9–12]. The position of the Eye can be obtained using dc recording in EOG. However, the drawback of this method is the drift in electrodes and dc amplifiers. To overcome this problem, ac recording is an alternate solution to measure slow and fast phases of nystagmus and this technique is referred to Electronystagmography (ENG) [13–15]. Nevertheless, the two crucial flaws associated with ENG are ambient electrical noise and muscle electrical activity [16]. So to eliminate electrical interference, Videonystamography (VNG), a method in which cameras are used to visualize two-dimensional movements of the Eye is suggested. Further, the eye movement recording can be used to measure the gain and speed of slow component saccadic velocity in OKN [17, 18]. However, an accurate measure of the slow component of eye movements is not achieved with VNG due to the change in light conditions. Hence, the Infrared (IR) limbus eye tracker is used to record the saccades produced due to OKN stimulated by a patterned full-field curtain and red LED targets [19–21]. Since Infrared detectors are not affected by any other light sources, Infraredoculography (IROG) is used to measure movements of the Eye under ambient light conditions. Even though IROG is used to measure horizontal eye movements with greater accuracy, the eyes become dry and fatigue when subjected to a long period of IR radiation [22]. Scleral search coils are used to reduce this prolonged IR radiation, and these coils control the oculomotor signals which produce the saccadic kinematics of the eye movements [23]. In this method, scleral anaesthesia employed that troubles other parts of the body. Hence, the tracking of corneal reflection without anaesthesia using the SRI Eye tracker produces accurate results on eye movements. Still, the scheduled maintenance of the equipment is the major issue in using this technique [24]. The above-mentioned subjective methods have the following problems. Since the patients are subjected to direct contact with high current or power equipment over a long duration, the frequency of testing the detection of OKN is less.
As a consequence, the testing may lead to erroneous clinician decision. To address the pitfalls in subjective methods, objective methods are used, and the corresponding literature is discussed in detail. The computer is used for measuring the Slow Component Velocity (SCV) of the nystagmus induced by OKN that employs Recursive Least Square Method [RLSM] and thereby, VA can be calculated [25]. Since the rotary chair is used in the sinusoidal rotator of the OKN stimulator system, young children cannot be subjected to this method. Therefore, visual stimuli of Random Dot Kinematograms (RDKs) are presented on CRT monitor to elicit OKN in the case of young children. Then, the horizontal nystagmus is determined with the help of commercial eye-tracking machine-Visage SDK that follows the video of young children, subjected to a visual stimulus [26–28]. The problem incurred in this method is inattention of the pre-verbal young children to the visual stimuli.
To make the eye tracking in an automated manner for monocular and binocular tests, the saccadic movements are traced, and visual acuity is measured using OKN with a software application, namely Vifant OKN [29]. Although, Vifant OKN works well for binocular testing, it fails in some cases of monocular testing. The horizontal movement of the single Eye is presented with the tracking of the pupil using the Kalman filter [30–32]. But the noise in the eye-tracking system using Kalman filter results in reduced amplitude peaks in the OKN signal. Consequently, to minimize the effect of noise, 2D Feature Space can be used. OKN signal can be represented as 2D Feature Space using pre-peak and post-peak amplitudes. Anti-Noise is identified from the OKN signal and removed to maintain the amplitude peaks that are significant [33]. The optical flow-based OKN detection considering the velocity component is attempted, and gain is calculated [34]. Nevertheless, the gain is calculated for the captured frames, large memory is required to store the frames. The memory optimization [35] is used in image and video processing. From the literature, it is inferred that the Visual Acuity is detected through subjective and objective methods. In subjective methods, clinical assessment through high power equipment is employed. As there is limited number of investigations involved, this method results in inaccurate detection of OKN. To mitigate this drawback, objective methods involving computational algorithms to detect OKN have been proposed. Though the algorithms provide better accuracy, the computational complexity of the algorithms imposes limitation on these methods. To address the pitfalls of the existing methods, Subsampled Lucas-Kanade Optical Flow (SLKOF) is proposed. The major contributions of the proposal are highlighted as follows. Subsampling of the image is carried out at different levels OKN gain is computed for all subsampled images Comparison of gains of the original and subsampled images is attempted Optimal subsampling factor whose gain is equal to the gain of the original image is found by attempting more number of trials Reduced computational complexity and memory efficiency that demonstrate the efficacy of the proposal
The paper is formulated as follows: Section 2 describes the proposed method, Section 3 elaborates the implementation of SLKOF for OKN detection and Section 4 outlines the outcomes of the experiments. The paper is eventually concluded in Section 5.
Proposed method
Lucas-Kanade Optical Flow (LKOF) is one of the commonly used methods employed for the selection of a subset of points for a given image. As the LK algorithm [36] suits best for local information, it is applied in the applications having smaller window sizes. Optical flow-based tracking is considered as superior one in terms of accuracy when compared to other tracking methods. Though the algorithm yields accurate results, it yields errors on boundaries with increased computational complexity. Therefore, a novel computationally efficient Subsampled Lucas-Kanade Optical Flow (SLKOF) method is proposed.
The SLKOF employs the least-squares method to solve neighbourhood pixels using the equations for optical flow. In a video, the displacement of the object can be found using perfect tracking of the essential features from one frame to the immediate next one.
Head movement tracking is done using Lucas-Kanade features tracking. SLKOF calculates the horizontal velocity of the Eye from one frame of a video to the next frame, followed by OKN detection. The smaller movements of the Eye can be found with the help of SLKOF algorithm. Since the scale information is not inherently available in most images, scale space is built on our own. As the original image is much time and space consuming, subsampling into a smaller image can be employed. In image subsampling, a portion of the original pixels is considered to create a new smaller image. Further, the original image is subsampled to the levels of 1/2, 1/4, 1/8 and 1/16 to produce a Scale Space. This Scale Space allows the Scale-invariant feature detectors to find the same feature across the images of the same objects at different scales.
Computer Vision algorithms must consider matching the same features where objects appear in different sizes. SLKOF is a computer vision algorithm applied to the consecutive images for OKN gain calculation and is depicted in Fig. 1. The colour video obtained from the experimental work for OKN detection is converted into a number of frames or images. The conversion of colour images to gray level images is done using RGB to Gray conversion model. Then, the horizontal velocity component of the pendular movement of the Eye from the consecutive frames is obtained using Lucas-Kanade Optical Flow (LKOF). The limbal movement of the Eye is only taken into consideration with the rejection of pupil or iris features using corner features selection. The velocity signal is set with a threshold. Only positive and negative peaks higher than the limit are considered in finding a Normalized Average Peak Velocity (NAPV) termed as gain in this work. From the gain value, the detection of OKN is found. If the gain value is higher than one, then the existence of OKN for a person is confirmed or else the absence of OKN.

SLKOF algorithm for OKN detection.
The renowned differential method for flow computation in computer vision is the Lucas-Kanade Optical Flow (LKOF) [36]. The Lucas-Kanade algorithm can be used to find small displacements, and Optical flow estimation is done using corner features. The proposed SLKOF algorithm used to find the small movements of the Eye, as depicted in Fig. 1. The window size of 5 × 5 is used to track the limbal corner features across the frames of the video for eye movements. The least-squares algorithm is used on the equations of the optical flow with the assumption of constant brightness for the pixel p in a local neighbourhood between two consecutive frames of the Eye. The window is centred at q and the optical flow equation having velocity vector (V
x
, V
y
) for the pixels p1, p2, . . , p
n
of the window is,
From the image of an eye, partial derivatives I
x
(p
i
) , I
y
(p
i
) and I
t
(p
i
) are estimated. The matrix form of Equation (1) is represented as,
The Equation (2) can be denoted in vector form for the pixels as,
The least-squares method is used to solve Equation (3),
The Equation (4) can be written as,
The plain least-squares solution above gives the same importance to all n pixels p in the window. In practice, it is usually better to give more weight to the pixels that are closer to the central pixel q. For this reason, the weighted version of the least-squares Equation is used and as follows:
So the weight w
i
is assumed as Gaussian distribution for the distance between p
i
and q as represented in Equation (7). The LKOF algorithm is used to find the horizontal velocity component of the eye movements and the resultant gain (or NAPV)
The NAPV can be calculated by averaging the positive and negative peak amplitudes P for threshold value σ
T
considering the number of amplitudes higher than the threshold as N,
The original eye image should be prefiltered using a weighted average filter to avoid aliasing effect due to Subsampling.
In the spatial domain, this can be done by performing a convolution of eye image f (x, y) with the weighted average filter or kernel T of size i. To obtain Subsampled eye image f
s
(x, y) for an eye image f (x, y) for a factor k, subsampled image of an eye,
The Subsampled images of the Eye at different levels(or factor k) are obtained using Equation (9) is shown in Fig. 2. Then the Subsampled images are subjected to LKOF, and the gain V is calculated. The comparison of gain of original size eye image with the gain of Subsampled eye images at different levels along with the exact match of gain is found using the SLKOF algorithm (Fig. 1).

Subsampling of the eye image (from left to right –Subsampling level 0,1,2,3 and 4).
The proposed approach to detect the presence of OKN and its direction in the experimental video is recorded with low-cost equipment. Hence, it is termed as an inexpensive method in OKN assessment. The distance between the stripes defines the resolving power related to the Eye, which induces the OKN. The schematic representation of the proposed method is depicted in Fig. 3.

Schematic of OKN detection system.
The interface between the stepper motor board and the computer can be made through 26 pin Flat Ribbon Cable (FRC). Further, the experimental set up for OKN detection is presented in Fig. 4. The OKN drum mounted on a stepper motor induces the Opto Kinetic Nystagmus.

Experimental set up for OKN system.
A 57 mm sized permanent magnet stepper motor used in this system is 57SH51. High Torque Hybrid which consists of two stator windings A and B with a motor having two magnetic pole N and S. It will have 1.8° step angle and 50 teeth on its rotor.
There are eight main poles on the stator, each having five teeth in the pole face. The Step angle(A) is given by,
The number of rotations (C) can be calculated using,
The vertically positioned stripes are moved horizontally in two different speeds, namely slow and fast with the speed of 3 stripes/s and 10 stripes/s, respectively.
The subject (person at the age of 21) is instructed to sit and look at the standard black and white striped OKN drum of size 8 inches height by 6 inches diameter (20 cm × 15 cm) at a distance of about 16 inches (40 cm) [37–39]. The striped OKN drum elicits OKN and the recorded videos are subjected to SLKOF. The stepper motor is rotated in clockwise and counterclockwise directions through the coding written for Port A of PPI using the computer interfaced. The proper positioning of the camera captures the subject’s face. The resolution of the camera used is 640 × 480 pixels with a sampling rate of 30 Hz.
The computer used in this OKN detection method has the system configuration of Intel(R) Core (TM)i-5-2450M CPU having 4 GB RAM, 64-bit windows operating system with the operating speed of 2.50 GHz. The videos are first processed, and the conversion of video into frames is done using 64-bit (win64) MATLABR2019b and then cropping of the eye region is done manually. The saccadic movements of the Eye can be detected using the horizontal velocity component of the Optical Flow. The SLKOF algorithm is applied for the consecutive frames and feature points are consistently tracked with the standard features that are good to track algorithm and calculate the velocity difference between the successive frames.
In this work, the OKN values are used to detect visual perception. The OKN stimulating drum is mounted on Stepper Motor and it is rotated at the rate of one revolution for every 2 to 3 s. During this examination, it is observed that the examined eyes involuntarily react slowly with the movement for 0.2 s related to the stripes. The fast movement of the Eye is being observed for 0.1 s related to the stripes. When the OKN has been elicited, this gives evidence of vision. The stimulus is seen by the four experimental participants at the age of 21 with normal vision. The OKN drum controlled by a stepper motor with a step angle of 1.8° at different speeds is used for making the stimulus. The fast and slow rotation of the stepper motor is done through a change in the delay given through coding. For 30 s trials, the stimulus drum is rotated in the left and right directions for 180 degrees. The video captured for the response of the OKN drum is converted into frames. The consecutive frames are chosen for different eye movement directions.
The movement of the eyeball from left towards the right and also in the reverse direction (Frame numbers from 200 to 210) is applied with LKOF and SLKOF algorithms in the OKN analysis. The traces are plotted between Spatial positions of pixels and Displacement of pixels between the frames. In this analysis, the horizontal velocity trace is plotted for the features generated due to the limbus of the Eye without considering eye blinks and eyelashes. Traces showing the results of the pendular movement of an eye as a velocity signal from the LKOF algorithm and SLKOF algorithm for the calculation of Normalized Average Peak Velocity (NAPV) for different subsampling levels is depicted in the Figs. 5 and 6. The results obtained for the Level 0 with Subsampling factor of 1 (V = 0.1144) and Level 3 with Subsampling factor of 1/8(V = -0.1289) illustrates that the pendular movement of the Eye follows the same and opposite to the direction of rotation of the OKN drum respectively. Since to detect the displacement of pixels between frames for small movements, a threshold value (σ T ) of 0.03 is taken into consideration in this work.

Traces showing the results of the pendular movement of an eye as a velocity signal from the LKOF algorithm and SLKOF algorithm for the calculation of Normalized Average Peak Velocity (NAPV) (a) LKOF for original size eye frame (b) SLKOF for Subsampling factor of 1/2 (c) SLKOF for Subsampling factor of 1/4.

Traces showing the results of the pendular movement of an eye as a velocity signal from the SLKOF algorithm for the calculation of Normalized Average Peak Velocity (NAPV) (a) Subsampling factor of 1/8 (b) Subsampling factor of 1/16.
The gain value is minimum since we are concentrating on small movements (less than one pixel between two frames), i.e., on a subpixel basis. For Subsampling level 4 (factor 1/16), the gain value (
The NAPV results for various subsampling factors on the experimental participants for the eye movement from Nasal to Temporal (NT) [40] with different window sizes is depicted in the Tables from 1 to 5. It is inferred that the gain so obtained for the original eye image exhibit closeness with Subsampling Level 2, i.e., 1/4th Subsampling of original eye image for majority of the cases and is depicted in the Tables from 1 to 5. To determine the percentage of match of the NAPV of the original image with that of various subsampling levels, a paired t-test, a statistical analysis is performed.
NAPV results for subsampling factor of 1 on the subjects with various window sizes 10, 20 and 30
NAPV results for subsampling factor of 1/2 on the subjects with various window sizes 10, 20 and 30
NAPV results for subsampling factor of 1/4 on the subjects with various window size 10, 20 and 30
NAPV results for subsampling factor of 1/8 on the subjects with various window sizes 10, 20 and 30
NAPV results for subsampling factor of 1/16 on the subjects with various window sizes 10, 20 and 30
The results of the conducted dependent samples t-test to compare the NAPV of the image at various subsampling levels shows that there is no significant difference in the scores for level 0 (M=–0.10, SD = 0.649) and level 2 (M=–0.112, SD = 0.657) conditions; t (23)=1.019, P = 0.841 whereas other subsampling levels has a significant difference. These results suggest that subsampling level 2 coincides with the subsampling level 0. This clearly demonstrates that the image at the subsampling level 2 can be used for analysis of OKN directly instead of the original size. The NAPV is calculated for different window sizes like 10, 20 and 30 for the eye movement from Nasal to Temporal(NT) for four participants (i.e. subject1, 2, 3 and 4). The Fig. 7(a, b & c) illustrates that the NAPV for Subsampling factor 1/4 with window size 10 produces the maximum gain than the window sizes 20 and 30. This shows that the smaller window size can be applied for subpixel movements of the Eye. From the experimental results, it is evident that the absence of OKN is confirmed for the subjects as the gain values obtained for the subjects is lesser than one. Further, as the 1/4 Subsampled image is sufficient to meet the gain of the original size eye image, it is clear that the computational complexity is reduced approximately by 1/4. The time consumed by the subsampling level 0 is 2.678 s whereas for the subsampling level 2 is 2.413 s. This, in turn, exhibits the computational efficiency of the proposal. The memory required to store the images taken in the experiment at different subsampling levels is illustrated in Table 6. The memory occupied by subsampling level 2 is 4.77KB whereas for subsampling level 0 is 27.8KB Eventhough, the memory used by subsampling level 5 is very minimum of 1.11KB, the NAPV does not matches the original and hence, it is not considered. The execution time and memory consumption for the proposed algorithm is found to be low for a subsampling level 2 than other levels of subsampling. This clearly elucidates the reduced computational complexity of the proposed algorithm.

Comparison of NAPV for four participants (i.e., subjects 1,2,3 and 4) with various window sizes (a) NT 10 (b) NT 20 (c) NT 30.
Memory and computation time for different levels of Subsampling
A Subsampled Lucas-Kanade Optical Flow (SLKOF) algorithm is presented for the detection of Opto Kinetic Nystagmus in adult learners. The proposal incorporates the computation of OKN gain for different image subsampling factors using MATLAB and compared with the original image size. The gain of the images is computed with the subsampling factor of 1/4 which coincides with the gain of the original image for 80% of the cases. Hence, the Subsampling based LKOF tracking of the Eye provides reduced computational complexity and also quick assessment of OKN detection. Also, this is an efficient method for improving the academic performance of adult learners. Eventhough, the quick assessment of OKN is achieved and computational complexity is reduced, the resolution of 1/4 subsampled image is relatively fair when compared with that of the original image’s resolution. So, the resolution improvement along with the increased samples is planned to be implemented in future.
