About NTU300

National Taiwan University Random-dot Stereograms (NTU RDS) 300 sec-of-arc

A popular tool for visual screening of pre-school and school children in Taiwan

Ai-Hou Wang, M.D., Ph.D.

Dr. Song-Yang Wei asked me about the origins of NTU300, so here’s a review.

The random-dot stereogram (RDS) was invented in 1960 by Dr. Bela Julesz at Bell Labs. It is an invention, not a discovery, because RDS did not exist in the universe before.

Another "invention" in 1960 was the ruby laser. There was no laser light in the universe; Einstein predicted the possibility of coherent light, which led to the emergence of the first physical laser in 1960.

In 1982, during my ophthalmology residency, Dr. Luke L-K Lin used Titmus and TNO for stereopsis tests. Titmus belongs to contour stereograms, the 3D images (like a fly) are visible to one eye; TNO, on the other hand, is a random-dot stereogram, where the hidden image (like a butterfly) cannot be seen with either eye. Small angle esotropia and anisometropia may not be detected through the Titmus test, but they are impossible to pass TNO Stereotest.

Clinically, the most criticized aspect of using random-dot stereograms to test stereopsis is that everyday environments do not resemble the scenarios presented by random-dot patterns. At most, one might encounter some similar situation while searching for a small bird or a cicada in the bushes. However, after a period of clinical experience, we have learned that random-dot stereopsis tests are indeed a useful tool for diagnosing and screening strabismus and amblyopia.

The mechanisms of stereopsis in contour stereograms and random-dot stereograms are different: in contour stereopsis, such as Titmus, the right eye sees a fly and the left eye also sees a fly. The brain recognizes that the flies in the two eyes fall at different coordinates, there exists a disparity, which is converted into depth perception, resulting in a 3D sensation. In random-dot stereopsis, such as TNO, neither the right eye nor the left eye sees a butterfly initially; after the images from both eyes fuse together, the butterfly emerges. But what are the two eyes fusing? The only possibility is the fusion of random-dot textures. After the random-dot textures from both eyes are combined, the brain detects the hidden disparity and then decodes the butterfly.

This is a random-dot pattern used in NTU300, consisting of 320x240 pixels (picture elements) with 50% density. The so-called texture refers to the patterns formed by the clustering of black dots in some areas and white dots in others.

I was very interested in creating my own random-dot stereograms. At that time, the personal computer I used was Apple II. I utilized several existing software tools, relying on graphic shifts and logical operations between two images (AND, OR, NOT, XOR). I prepared two random-dot images at 50% density, one for the foreground and one for the background, along with a black-and-white image that I wanted to embed into the random-dot stereogram. I designed a step-by-step process that allowed me to create a random-dot stereogram with those three elements.

This process was presented at the 1986 ISA (International Strabismological Association) conference in Rome – "Random-dot stereogram made with personal computer - ISA V Rome 1986."

Here is a step-by-step process for creating random-dot stereograms that you can refer to:

https://ahwang.url.tw/WebArticles/Creating%20RDS%20step-by-step-English.htm.

The program prepares two random-dot patterns at 50% density and one black-and-white figure to be embedded. The program can automatically generate a random-dot stereogram that conceals this figure.

Creating Random-dot Stereogram: Step-by-Step.ppt

(Powerpoint file. It cannot be played on Google Drive. Please download and play on your computer.)

Creating Random-dot Stereogram: Step-by-Step.exe

(Windows executable file. It cannot be played on Google Drive. Please download and run on the computer with Windows operating system.)

(You may need to temporarily disable "Real-time Scan" in your antivirus software.)

The Apple II had a very slow operating speed, and the resolution of the graphics was low, with a width of only 320 pixels. The minimum disparity between the left and right eye half-stereograms in a random-dot stereogram is one pixel. If displayed on a 15-inch screen, the width is 12 inches (1 foot) (30.48 cm) and the height is 9 inches. This means that the horizontal span of 320 pixels corresponds to 30.48 cm. Using the formula 30.48/320/distance x 180/pi x 60 x 60 = 300”, we calculate that if the visual angle of a pixel is 300 sec-of-arc (or 5 min-of-arc), the test distance should be 65 cm.

If printed on a 4x6 inch photo, the width is 6 inches (15.24 cm) and the height is 4 inches. The horizontal span of 320 pixels corresponds to 15.24 cm. Using the same calculation, at a test distance of 33 cm, the visual angle of one pixel will be 300 sec-of-arc.

For this commonly used NTU300 printed on 6x4 inch photos, to be precise, test distance of 33 cm would give a stereopsis of exactly 300 sec-of-arc.

During the IBM PC era, Dr. Ji-Hau Jan (deceased) recommended using QuickBASIC 4.0, and later QuickBASIC 4.5, to create NTU stereograms. He wrote many subroutines to help speed up program execution and developed various other computer tools for ophthalmic use.

Dr. Luke Lin once hoped I could create a 150” stereogram. Given the resolution limits, as calculated earlier, a stereogram on a 6x4 inch photo needs to be tested at a distance of 66 cm (33 x 2 cm) to achieve a 150” stereopsis. Test distance of 66 cm seems too long and not very convenient for clinical use.

Small angle esotropia would potentially pass the contour stereograms like Titmus, but can never pass the random-dot stereopsis test of 300”. We thus think random-dot stereogram is much more sufficient for visual screening than contour stereograms.

The early computers limited our use of more pixels, which could be seen as a fortunate constraint. If too many pixels were used, the random-dot stereogram might become difficult to read. The left image shows the 320x240 pixels, 50% density random-dot pattern used in NTU300, while the right image shows a random-dot pattern of 1280x960 pixels. An excessively high resolution makes the texture of the random-dot pattern less distinct, resulting in a blurry appearance. With fewer texture available for the two eyes to fuse, the information needed to disclose the disparity is also reduced, making the stereogram harder to read.

If we want to use high resolution random-dot patterns to achieve finer stereopsis, we need to remove the high spatial frequency components (details) in each half-stereogram. We convolve digitally the half-stereogram several times to remove high spatial frequency while keeping the low spatial frequency components, to facilitate the fusion between two eyes.

Convolution should be performed as the final step in creating a stereogram. If convolution is performed earlier than the logical operations, monocular cues will appear that defies the very nature of random-dot stereograms. Dr. Shao-Ming Yan(deceased) of the Beijing Naval Hospital in mainland China created a new version of a random-dot stereograms (left). You’ll find monocular cues of the hidden figure they tried to bury within the stereogram (right).

The figures embedded in the random-dot stereogram are essentially monochromatic. The left and right half-stereograms are composed of black and white dots. To separate the right and left eye, the white and black dots of the right half-stereogram are overlaid with blue and black color, to be seen by the right eye wearing blue lens; the white and black dots of the left half-stereogram are overlaid with red and black color, to be seen by the left eye wearing red lens. This type of binocular dissociation using red and blue or red and green colors is called anaglyph.

TNO uses red and green for binocular dissociation. We have tried red and green, to find that the effect is not as good as red and blue (actually, cyan) dissociation. Computer colors are composed of red, green, and blue (R, G, B). Each color has 256 levels of intensity (0-255). Red-green dissociation uses red (255, 0, 0) and green (0, 255, 0), while red-blue dissociation uses red (255, 0, 0) and blue (0, 255, 255). The left figure shows red-green dissociation, and the right figure shows red-blue dissociation.

The right half-stereogram is overlaid with cyan, and the left half-stereogram is overlaid with red. The two half-stereograms are superimposed together with logical OR operation. The pixels of the combined figure have four colors: white, cyan, red and black (see figure).

The background of two half-stereograms should also be slightly spaced apart. Otherwise, the identical texture of the left and right backgrounds will be completely overlapped, resulting in only black and white dots, and the hidden figure will be revealed as monocular cue (left figure). Our experience suggests a minimum of three or four dots apart are needed to avoid this monocular cue. Similarly, the embedded figures of two half-stereograms should not be too close together, otherwise the monocular cue will be revealed (right figure).

Depth = 5 pixels = (+5 pixels) – (0 pixels) Depth = 4 pixels = (0 pixels) – (-4 pixels)

Initially, I shifted the right half-stereogram two points to the left and the left half-stereogram two points to the right. This crossed backgrounds looks floating above the real paper plane, and the embedded figure goes even higher above the paper plane. The two eyes need to converge more to fuse, making it more difficult for people of weaker convergence to read (left image). The current version shifts the right half-stereogram two points to the right and the left half-stereogram two points to the left. It requires less convergence to fuse, and thus easier to read. After fusion, the background appears to recess back, lower than the real paper plane (right image).

Depth = 2 pixels = (+6 pixels) – (+4 pixels) Depth = 2 pixels = (-2 pixels) – (-4 pixels)

In addition to the six pairs of stereograms of 480", 240", 120", 60", 30", and 15" for detailed quantification of stereopsis, the TNO Stereotest has three 33 min-of-arc (1980 sec-of-arc) stereograms for learning and screening.

The NTU300 is of one pixel disparity. We tried to mimic TNO 33 min-of-arc in our NTU stereograms. The closest one is 7 pixels disparity, of stereopsis of 300x7 = 2100 sec-of-arc = 35 min-of-arc. We abbreviate it as NTU35, or more precisely, NTU35’, or NTU2100”.

Viewing an NTU 300 sec-of-arc stereogram (NTU300”), the figure appears 1 pixel above the background (relative height), and the background is 4 pixels below the paper plane (absolute height). Therefore, the figure is 3 pixels below the paper plane (absolute height). We write this as Depth = 1 pixel = (-3 pixels) – (-4 pixels). Most people simply feel the figure comes above the background, but if they observe carefully the relative depth of the figure to the surface of the paper, they will discover that the figure is actually below the surface. About the 35 min-of-arc NTU stereogram (NTU35' or NTU2100"), the figure rises 7 pixels above the background (relative height). While the background is 4 pixels below the paper plane (absolute height), the figure is 3 pixels above the paper plane (absolute height). We write this as Depth = 7 pixels = (3 pixels) – (-4 pixels). Most people will just notice that the figure rises significantly above the background, much higher than that of NTU300. However, if they observe carefully the relative depth to the paper plane, they will find that the figure is above the paper plane, while the background is below the paper plane.

Based on the method described in https://ahwang.url.tw/WebArticles/Creating%20RDS%20step-by-step-English.htm, we created and share four interesting random-dot stereograms below:

Logo of Universal Eye Center Depth 1 pixel = (-3 pixels) – (-4 pixels)

Arthur Jampolsky (AJ) 100^th birthday Depth 7 pixels = (+3 pixels) – (-4 pixels)

‘Eye’ in Chinese Depth 7 pixels = (+3 pixels) – (-4 pixels)

Checkerboard Depth 7 pixels = (+3 pixels) – (-4 pixels)

We initially took pictures of the computer screen, laminating the photographs into five cards, front and back (left figure). Later, with the development of digital photo processing, we printed photos directly from the computer files. We worked with the Kodak store to adjust the CMYK (Cyan, Magenta, Yellow, Key/Black) color palette, and the color and clarity of NTU300 were significantly improved (right figure).

Dr. Luke Lin referenced the name of TMC color vision test book from Tokyo Medical College and named our random-dot stereograms NTU (National Taiwan University) random-dot stereopsis test (NTU RDS). Luke screened preschoolers and schoolchildren with NTU RDS of 300 sec-of-arc disparity, hence the familiar ‘NTU300’.

TNO is a random-dot stereotest produced by Netherlands. It includes three 33' (=1980") stereograms for learning and screening, and six pairs for quantitative test. The quantitative stereograms are of 480", 240", 120", 60", 30", and 15".

If we would like to create a 15 sec-of-arc stereogram like TNO on a 6x4-inch photo, meaning the visual angle of each pixel must be as small as 15 sec-of-arc, how many pixels are needed at a testing distance of 40 cm? The calculation is as follows:

6 x 2.54 / n / 40 x 180/pi x 60 x 60 = 15" à n = 5239 pixels

In other words, a 6x4-inch photo would require 5239 x 3493 pixels to produce a 15 sec-of-arc stereogram. For comparison, NTU's resolution is only 320x240 pixels! We haven't even attempted such a high resolution yet. A 6-inch width contains 5239 pixels, close to 900 dpi (dots per inch). It requires a high-end printer to achieve that. Think that it has already been published and sold by Netherlands in the 1970~80s!s

Stereopsis testing, like visual acuity testing, measures spatial resolution, both measured in visual angles.

Visual acuity that can resolve 1 min-of-arc is considered Snellen 1.0; visual acuity that can only resolve 2 min-of-arc is considered Snellen 0.5. "NTU 300" means there’s a disparity of 300 sec-of-arc, or 5 min-of-arc, between the half-stereograms of the two eyes; "NTU 35" means there's a 35 min-of-arc, or 2100 sec-of-arc disparity, between the half-stereograms of the two eyes.

During clinical testing, if a patient can't see the embedded shape, we ask him/her to move forward to see if they can get it. Just like if they can't answer on visual acuity testing, they might get it by moving forward. The increased visual angle at nearer distance allows them to see it.

The note "NTU300(+) at 20 cm" in the medical record means that the patient can only resolve the 300 sec-of-arc stereogram of regular test distance of 33 cm when they move forward to 20 cm. His/her stereopsis is thus 300 x 33 / 20 = 495 seconds. Clinical testing doesn't necessarily require such precise numbers. This test result tell us that this patient's stereopsis is worse than 300 sec-of-arc, but it’s not too bad to require the NTU 35 min-of-arc testing. During subsequent follow-up visits, if he/she can pass the NTU300 at 35-40 cm, it indicates his/her stereopsis has improved.

Creating NTU stereograms was part of my doctoral dissertation, which involved comparing the stereopsis threshold of NTU300 and TNO stereotest.

Patients with normal stereopsis or complete stereopsis blind, that is, those who passed TNO 60 sec-of-arc and those who failed TNO 33 min-of-arc, could not be used to verify the threshold.

We identified a small number of patients with moderate stereopsis, whose stereopsis are not perfect [TNO 60(-)] nor stereopsis blind [TNO 33(-)]. The comparison showed an exact match between the stereopsis threshold of NTU300 and TNO stereotest: 6 patients who passed TNO 33 min-of-arc or TNO 480 sec-of-arc but failed TNO 240 sec-of-arc also failed NTU 300 sec-of-arc; 2 patients who passed TNO 240 sec-of-arc but failed TNO 120 sec-of-arc also passed NTU 300 sec-of-arc (see the table).

Dr. Luke Lin implemented the "Precursor Program to Promote Visual Screening for Preschool Children in Taiwan" commissioned by Department of Health (now Ministry of Health and Welfare) from 1990 to 1994, and recommended that visual screening include two items: (1) distance vision and (2) NTU300.

Since 2000, Health Promotion Administration, Ministry of Health and Welfare has been implementing a comprehensive screening program for preschool children using (1) distance vision and (2) NTU300. During this period, Dr. Shu-Mei Li once questioned why NTU300 was used for stereopsis screening? What authority does NTU300 have? Dr. Luke Lin then asked me to apply for a patent for NTU300 (see figure).

A few years later, the annual patent fee skyrocketed. Our patent wasn't originally oriented toward profit, and at the time, National Taiwan University didn't provide subsidy for patent maintenance, we therefore stopped to renew the patent.

NTU300 screens primarily for small angle esotropia, anisometropia, and other forms of unilateral amblyopia.

During school visual screenings, children with amblyopia, unable to see the vision chart with the worse eye, often remove the patch covering their good eye to peek, and thus miss the screening (a false negative). But these children, with a significant difference of the best corrected visual acuity between two eyes, won’t be able to pass the NTU300 screening.

For large angle esotropia, parents naturally would take their children to ophthalmologist by themself, which is not included in the screening purpose.

If pass the NTU300 test, we will reply on the school's vision report "normal stereopsis". I personally think 300 sec-of-arc is sufficient as normal stereopsis clinically.

TNO stereotest has three 33" RDS’s for learning and screening. Besides that there are quantification tests of 480", 240", 120", 60", 30", and 15". Most people would pass 60", yet fail 30" and 15". With so many steps, I don’t think it will give more clinical information than NTU300 test alone.

In outpatient examinations, the use of the NTU35’ (=2100") in addition to the NTU300" is as following:

If fail NTU 35", we will report "abnormal stereoscopic perception." Two conditions which will pass NTU35' yet fail NTU300" are esophoria and anisometropia, which are considered as “subnormal stereopsis”. We explain to the parents that their child's stereopsis is not good enough, but is not completely absent (there's room for improvement).

For Hyperopia + ET the stereopsis may gradually return to normal after wearing glasses.

X(T) post-operatively may show some DVD and subnormal stereopsis, but hopefully it will gradually improve to NTU300"(+).

National Taiwan University Random-dot Stereogram (NTU RDS)

NTU300" NTU35' (or NTU2100")

Left side shows 300 second-of-arc, 1-pixel disparity NTU RDS (NTU300”) and the right side shows 35 minute-of-arc, 7-pixels disparity NTU RDS (NTU35’) (or NTU2100”).

The Computer division of Universal Eye Center expanded NTU RDS into a cross-platform program, https://www.eyedoctor.com.tw/Stereopsis_Screening/, which can be run on web browsers under various operating systems such as Windows, iOS, Android, and macOS etc.

We had once proposed that Health Promotion Administration (HPA), Ministry of Health and Welfare switch to the computer version of NTU300 for visual screenings for preschoolers and schoolchildren. First, the testing process is more engaging; second, it eliminates the pollution concerns of the photo-based NTU300. The HPA hopes to have medical schools/medical centers lead the effort, and this idea has not been implemented yet.

Another problem is the red-blue lens issue. Each brand of monitor uses different phosphors, and some screen colors don't match perfectly the color of red-blue lenses.

I designed this grid pattern to checkout that. The grid should appear as horizontal stripes through blue lens and vertical stripes through red lens.

The less ghost image the better. The less ghost image it will be easier to read the red-blue dissociated anaglyphs on the screen.

Usually, blue lens is fine, but red lens is harder to get rid of the ghost image.

I currently use an Acer monitor, and the red and blue lenses do a very good job of separating the left and right eye images.

This is a 3' x 6', 2mm thick sheet of acrylic, cut into 5x5cm red and blue lenses and stick them together. The colors are adequate for anaglyph viewing.

One idea is to distribute this nice red-blue acrylic lens to everyone in need. You can hold it directly in front of your eyes to see the anaglyph, or you can take it apart and ask the optician to cut the acrylic lenses to fit them onto the glasses frame.

If you're taking the NTU300 screening online, another option for red-blue glasses is to purchase on Shopee. Please note: the right eye is blue lens and the left eye is red lens.

To test the NTU300"/NTU35" please also print a card or photo for the preverbal children (ages 2.5 to 3.5) to select with their hands the shape they see (see the picture). The NTU300”/NTU35’ can typically be tested two or three months earlier than the E chart of visual acuity test.

When testing NTU clinically, after answering two or three questions correctly, I like to cover the patient's left eye with a patch and ask, "Can't you see the triangle with your right eye?" Then, I cover the right eye and ask, "Can't you see the triangle with your left eye either?... You only have two eyes, so if you can't see the triangle with either eye, where does the triangle come from?" Keep covering the right eye, then switch to the next stereopsis question and ask, "You can't answer that, right?"

Use this program to explain that stereopsis is a kind of binocular vision and cannot be seen with one eye only. At the same time, observe whether the child is curious about not being able to see shapes with either eye, and whether they have a scientific traits.

Compared to the card version of NTU, testing NTU on computer screen allows you to perform the patch test described above, making it much more fun.

Please try https://www.eyedoctor.com.tw/Stereopsis_Screening/. The applause and cheers at the end suggest that children undergoing the screening will be eager to try it out after watching their classmates taking the test, and the test will be completed quickly and joyfully. (I haven't actually tested it myself. Can anyone help me test it and report back?)

After testing stereopsis, we explain to parents: "Even if both eyes have 1.0 vision, they won't pass the stereopsis test if they have esotropia or cross-eyes."

"We depict visual function simply with three parameters: the visual acuity of each eye, and the stereopsis of the two eyes working together."

The computer division of Universal Eye Center has developed a cross-platform program for stereopsis testing. Besides static stereopsis tests of NTU300” and NTU35’ there are programs for motion stereopsis (Binocular Depth-from-Motion, BDFM) tests.

Stereopsis test – https://www.eyedoctor.com.tw/Stereopsis/

Stereopsis screening – https://www.eyedoctor.com.tw/Stereopsis_Screening/