MISG2001

 

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Inferring eye movements on the basis of head and visual target position

SOLA International

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SOLA

The company

SOLA began in 1956, with nine opticaltechnicians experimenting in a garage in Adelaide,South Australia. Their goal was to cast spectacle lenses from recently discovered plastic materials. After a few early successes, those pioneers founded SOLA (or Scientific Optical Laboratories of Australia), as it was first called) in 1960. SOLA's first overseas subsidiary opened in Japan, in 1968, and in ensuing years, operations were added throughout Asia, Europe and the Americas. In 1979, SOLA was acquired by Pilkington plc, and in 1988 the corporate headquarters moved from Australia to Menlo Park, California. The company's global expansion continued during the 1980's, with new manufacturing operations opening in Venezuela, Taiwan and China. In 1993, SOLA was purchased by AEA Investors Inc., and in March 1995 the company was listed on the New York Stock Exchange. Further double-digit sales growth came from new products, international expansion and through the acqusitions of US lensmakers Neolens and American Optical.

SOLA's regional structure now includes North America, Europe, Asia, Australia, South America and an international Sunlens Division. Across the world over 100 million people go about their daily lives wearing SOLA lenses. The company now operates major research and development centres in Adelaide, South Australia and Petaluma, California; supported by a specialist process engineering team at a plant in Wexford, Ireland. From SOLA's earliest years, lens technology has continued to evolve. The result is thinner, lighter lens forms, innovative new designs and high performance coatings that combine exceptional cosmetics with optical excellence. A measure of SOLA's success in technical development and manufacturing is the fact that over 60% of sales come from new, value-added products.

Introduction

The lens design process increasingly relies on complex ray-tracing that requires the geometry of the visual task to be simulated in order for the optical implications to be calculated and plotted. In order to improve our models the location on the lens surface at which distance, intermediate and near tasks are performed needs to be understood.

Traditional eye trackers are expensive, cumbersome and intrusive, we have developed a non-intrusive, low cost eye-tracking system based on head and stimulus position measures. The ability to estimate eye movements relies on a precise knowledge of the geometry of the reading task, its location, the location of the readers eyes and an ability to correlate the time series data with these positions.

The current system as used in this experiment allows us to measure and estimate, where indicated, the following:

  • Head & book: position - X,Y,Z space (measured)
  • Head & book angle - Turn, elevation and roll degrees (measured)
  • Reading distance (measured)
  • Head turn (measured)
  • Head declination (measured)
  • Eye turn (estimated)
  • Eye declination (estimated)

Methods

Apparatus & procedure

Subjects wear a near or intermediate prescription, depending on the task, fitted to a custom lens clip attached to a demonstrator frame. The clip is fitted with a pair of stock single vision lenses that include the near Sphere and Cyl correction. The lens is circular, 38 mm in diameter. Also attached to the frame is a Polhemus electromagnetic motion sensing cube (see Figure 1). The average distance position of the head receiver cube and the apex of the cornea of the Right eye is 30 mm temporal, 30 mm above and 20 mm in front of the corneal apex.

As wearers perform a standardised near and intermediate reading task the position of both the head and book are recorded (10 Hz sampling rate) in X,Y,Z, Azimuth (head turn), Elevation (head nod angle) and Roll space (side to side tipping) using a Polhemus electromagnetic motion sensor system.

Subject wearing the standardised reading lenses and frame.
Figure 1: Subject wearing the standardised reading lenses and frame. A Progressive Addition Lens (PAL) demonstrator frame was used to mount custom made Single Vision near prescription and intermediate prescription lenses. The model in this photograph is not wearing the clip in lenses. A Polhemus sensor cube (red circle) was mounted to the right frame temple to monitor head movements.
Transmitter and receiver cubes.
Figure 2: Transmitter and receiver cubes. In the configuration shown there is one transmitter cube shown on the stand to the right in the image (large circle) and two receiver cubes, one on the wearer's head attached to the trial-frame and one inside the clip board (small circles).
Transmitter and receiver cubes.
Figure 3: Orientation and position of the transmitter and receiver cubes. The Z axis is NEGATIVE in the direction shown all other axes are positive, the receivers have the same coordinate system.

Near and Intermediate tasks

Subjects read a standardised near and intermediate stimulus as described below. During these tasks head and stimulus position are recorded in real-time with a 10 Hz sampling rate and to an accuracy of approximately 5 mm (X,Y & Z) and 1 degree (Azimuth, Elevation & Roll). The near reading task requires the subject to read text broken into three paragraphs in 10 point Times New Roman font (see Figure 4).

Clipboard and subject reading.
Figure 4:Standardised near reading stimulus and layout. Clip-board (left) and subject reading (right). Three paragraphs of three line 10 point font, Times New Roman letters are printed so that the top and bottom paragraphs are 120 mm above and below the middle paragraph. The paragraphs are 170 mm wide. This is placed on a clip board with a sensor cube imbedded in the board to be coincident with the centre of the middle paragraph. Subjects read silently. The subject here is pictured reading in their lap, the actual set-up allowed for reading at on the desk also.

The intermediate reading target is printed on an A4 page (210 mm x 297 mm) in 'landscape' mode. Three rows of three digit numbers in 10 point 'Times New Roman' font are printed so that the top row is 15 mm from the top of the page, the second row is 90 mm below the first and the final row 90 mm below that. The columns flanking three centre column are 135 mm to the left and right of centre. The target is clipped onto the transmitter stand so that the middle column of numbers is in line with the centre of the transmitter cube. We are mainly interested in eye-turn in the intermediate data. Eye declination is not required.

Clipboard and subject reading.
Figure 5:Intermediate stimulus and layout. Three rows of 10 point font Times New Roman three digit numbers are printed in 'Landscape' mode. For the purpose of clarity in this illustration the 3 digit numbers are super-imposed with black spots. Subjects read the numbers aloud from top left to bottom right in rows. The intermediate stimulus/transmitter stand is arranged so that so that the centre number on the top row is at eye-level and approximately 65 cm from the wearer's eyes.

Data

Near eye declination

Near Eye declination is based on head declination (elevation) in combination with the relative position of the near target. The physical position of the paragraphs is known relative to the book sensor (which is coincident with the middle paragraph). When the subject is calibrated the wearer is assumed to be in the primary gaze position, that is the eyes and head are level with the horizon. The position of the head and book sensor are projected onto a two dimensional plane based on the X and Z coordinates. The angle of the book and position is calculated relative to the angle of the head sensor and its position. Based on a parsing of the data into top middle and bottom paragraphs, the eye declination is calculated using the fact that the top and bottom paragraphs are 120 mm above and below the middle paragraph. This geometry is inclined at the book angle and the relative average eye declination angles to each paragraph are calculated. The software takes the minimum of the three calculated average eye declinations as the basis for the dispensing model. The minimum is selected since the wearer will be reading high in the near zone or low in the intermediate and this will be the most difficult conditions a progressive addition lens will be expected to perform under (progressive lenses have a channel of clear vision with flanking blur, the width of this channel is of considerable design interest). The difference between these two angles reveals the eye declination required to reach the near target, this data is presented in Figure 6.

Average eye declination.
Figure 6:Average Eye Declination for the near reading task.

Near eye turn and corridor width

Eye turn relates directly to the demands a wearer will place on corridor width. Assuming the page is being held centrally, the 1/2 line width is known to be 85mm. The reading distance D is obtained from a trigonometric calculation of a two dimensional projection of the head-sensor and the book sensor in X (back-forward) and Z (vertical) coordinates. In other words, the book is assumed to be held centrally and not off to one side. The inverse tan(85/D) is then used to calculate the eye-rotation angle required for the wearer to reach of the line without a head rotation (EOL). The inferred eye rotation when the wearer reaches the end of the line is then calculated to be EOL - (2 x SDAzimuth), this is done for up to three paragraphs and the mean taken as the final eye-turn value. This value is compared to the standard model to determine the position on the distribution and therefore if the wearer was high, medium or low. Our analysis suggests that this estimate of the maximum head turns is OK but we are interested in better approaches.

Eye turn.
Figure 7:Histogram showing average eye turn magnitude displayed to reach the end of the line being read for the near task.

Although we cannot know precisely where the wearer is looking at a given instant in the head-track trace we can infer the typical eye-rotations required at the start and end of each line. To do this we first calculate the maximum head rotation angle (taken as 2 twice the SD of the head turn data ~ 95%) and subtract this from the angle required to reach the end of the line (EOL). The difference between these two angles is the inferred eye-rotation. There are a number of assumptions in this trigonometric analysis as follows:

First, three eye-rotation values are calculated and the mean of these is taken as the eye turn value. The three individual values should correspond to the top, middle and bottom paragraphs. This calculation relies on the data being passed correctly into the sections of the recording run that correspond to head movements made when reading the three paragraphs. We chose to parse the data by paragraph because a number of wearers make significant head turns between paragraphs and this 'non-reading' head turn information should not be included in the head turn calculations. The parsing algorithm uses the head declination data (elevation) with Z (vertical) movements of the book to compute a relative velocity of these two movements (this velocity can be though of as face sweep across the page), high slopes seen in the vicinity of the 1/3 and 2/3 parts of the trace are assumed to be wearers moving to see the next paragraph. This algorithm appears to work very well but can be confounded by variable reading speed or very low head and book movement. We would are interested in better parsing algorithms.

Intermediate data

The intermediate task reading distance and eye-turn are considered below. We should point out that the external validity, the generalisability of the data to real life situations, is more questionable than the near reading task. Of the tasks that a wearer may engage in, the intermediate task is designed to simulate using a computer monitor. An A4 landscape page most closely resembles the geometry of a 15" monitor. The reader wishing to ponder this issue is directed to Figure 5. Unlike the near task, the intermediate data is not parsed when calculating the standard deviation of the head turn/Eye Turn data nor is any data discarded from the beginning and end of the run. We assume that the operator should press start when they hear the wearer start reading numbers and stop when they reach the last number so there is less ambiguity about when the wearer has started and finished reading.

Intermediate eye turns

We believe calculations to determine eye-turn may indicate that intermediate eye turn is less robust than the near eye turn data. We assume twice the standard deviation encompasses 95% of all eye turns and is therefore a good estimate of the maximum eye turn. As can be seen in Figure 8 the data looks more bi-modal than normally distributed. The 95% figure is based on assumptions of the normal distribution. On the other hand 2 x SD = 10.6 degrees which equates to 13.9 degree 95% cumulative point. The actual 95% cumulative point is 12.5 degrees, a 1.4 degree discrepancy, not enough to account for the -4 to -8 degree eye rotations. It is also possible that the dynamic nature of the intermediate task, reading widely spaced numbers, caused some subjects to over-shoot the end of line point.

In detail - Eye turn is calculated similar to the near eye turn, that is the maximum head rotation angle (taken as 2X the SD of the head turn data) is subtracted from the head turn angle required for the wearer to point their nose directly at the numbers at the ends of the line (EOL). The difference between these two angles is the inferred intermediate eye-rotation. There are a number of assumptions in this trigonometric analysis as follows: The distance between the head and transmitter cube is taken as the eye to page distance. The geometry of the intermediate stimulus is assumed to have numbers 140 mm either side of the central number on each line and the wearer is assumed to be central to the page and not off to one side. Eye turn values therefore reflect the predicted eye turns required at the beginning and end of each line in order to fixate the first and last number on the line.

Intermediate Eye turn.
Figure 8:Intermediate eye turn frequency histogram. Note: The negative values are possibly the result of subjects 'over shooting' the end of line or problems with the assumptions of a normal distribution with this data set.

Problems for MISG to consider

  • Near data parsing: What is the best method of parsing and filtering the data into that associated only with actual reading of the top, middle and bottom paragraphs.
  • Eye turn: What statistic or metric is the best estimate of the typical maximum head turn (and therefore eye-turn) at the end of each line for the near and intermediate tasks separately?
  • Alternatives: What ways are there to calculate maximum eye turn and average declination for each paragraph on the basis of the head and book position data.
  • Other data: What other things can we learn and or calculate from our data. [eye declination for a given paragraph, maximum eye turn for a given paragraph, reading distance, head turn, head declination, book angle, eye turn, eye declination). Is there anything to be learned from a power spectra or Fourier analysis?
  • Data compression: What is the minimum acceptable sample rate (we are using 10 Hz). What non-lossy data compression options are there?