<p>Citing Muller et al’s, (1955) work on electronic displays, Eastman Kodak’s (1983) <em>Ergonomics Design for People at Work</em> states that people can discriminate 24 different absolute angles of inclination under optimum viewing conditions. This implies that an angle of 360/24 = 15 degrees can be readily classified as inclined rather than flat. </p>

<p>However, I’d say 15 degrees is probably overly conservative. It applies to discriminating one arbitrary angle of inclination from another when each is shown in isolation. Discriminating flat (0 degrees) from inclined is apparently a special case that is easier to do, as indicated by the <a href="https://cogsci.stackexchange.com/questions/7863/visual-identification-of-inclined-lines/7870#7870">study cited by Josh</a> where people quickly detected inclinations as small as 0.5 degrees. </p>

<p>Assuming you’re talking about imagery you create in the built environment (e.g., for an information display), there are often vertical and horizontal references to compare the line to (e.g., the edges of a page, the bezel of a monitor, the doorway to a room). In fact, the presence of such references probably defines what “flat” means (e.g., people will still call your first line above “flat” even if they cock their head a bit to look, or even if their respective tablets/laptops are in their laps and not completely level). So, in a built environment (and outside a field-dependence laboratory), detecting an inclined line often has a degree of relative discrimination that I expect helps a lot. As for detecting inclinations in the natural world, well, there’s a reason carpenters use levels.</p>

<p>If you’re building an information display (e.g., a graph), you can go to smaller angles by adding reference marks, as shown below. </p>

<p><img src="https://i.sstatic.net/GOIqi.jpg" alt="Static marks at each end of line"></p>

<p><img src="https://i.sstatic.net/70Tn9.jpg" alt="Static marks at each end of line"></p>

<p>This changes the viewers’ task from recognizing an inclination to recognizing vertical gap size. People can spot a gap as small as few arc-minutes of visual angle.</p>

<p>References:</p>

<p>Muller PF Jr, Sidorsky RC,  Slivinski AJ, Alluisi EA, &amp; Fitts PM
(1955). <em>The symbolic coding of information on cathode ray tubes and
similar displays</em> Technical Report 55-375. Wright Air Development Center, Wright-Patterson AFB, October.</p>

<p>Eastman Kodak Company (1983). <em>Ergonomic design for people at work</em>. New York: Van Norstrand.(<a href="http://books.google.ge/books?id=FSgcaAIoHu8C&amp;pg=PA230&amp;lpg=PA230&amp;dq=Ergonomic%20design%20for%20people%20at%20work%20pdf#v=onepage&amp;q&amp;f=false" rel="nofollow noreferrer">link</a>)</p>

CC BY-SA 3.0
2014-07-21T14:42:09.930Z
Wait, what? 15 degrees sounds like *a lot*. Am I missing something here? Are we talking the kind of degrees where 360 degrees equals a whole circle?
Speldosa
CC BY-SA 3.0
2014-07-21T14:42:41.170Z
Yeah, this doesn't fit with other research that has looked at this kind of perceptual judgment.
Josh
CC BY-SA 3.0
2014-07-21T19:23:57.913Z
There is some emphasis on "at first look" though; this may require a much larger angle than the JND for reliable detection without time limits.
Nick Stauner
CC BY-SA 3.0
2014-07-21T19:30:16.760Z
In the study referenced in my answer below, exposure time was 600ms.
Josh
CC BY-SA 3.0
2014-07-21T21:01:49.970Z
I believe the OP was concerned with detecting an inclined line in _isolation_, not detecting a change to an inclined line. I've edited my answer to clarify the application.
Michael Zuschlag
CC BY-SA 3.0
2014-07-21T21:14:37.743Z
The judgments in the study below were also in isolation. Stimuli were presented 5s apart and participants were comparing to their 'memory' of a horizontal line, not to another visually presented line.
Josh
CC BY-SA 3.0
2014-07-22T13:20:30.913Z
OK, you've convinced me. Helps that I tried a 0.5 degree inclination on my wife and she immediately detected it. Done more editing above.
Michael Zuschlag
CC BY-SA 3.0
2014-07-21T13:05:00.417Z
2014-07-22T13:27:05.327Z
2017-04-13T12:56:16.467Z
Michael Zuschlag
<p>Vogels and Orban (1985) asked subjects to complete several thousand angle judgments at near-principal angles (horizontal or vertical). They found that the just-noticeable difference (JND), the threshold at which people could reliably detect deviation from a horizontal line, was <strong>0.5 degrees</strong> after a 600ms exposure to the stimulus.</p>

<p>The real purpose of their study was to compare learning effects for judgments of deviations from principal orientations with judgments of deviations from oblique (diagonal) angles. They found that while people could double their sensitivity over extensive training to small changes in oblique angles, the principal angles showed no such learning effects, as you can see in this graph:</p>

<p><img src="https://i.sstatic.net/dC7jU.png" alt="results graph"></p>

<p>Additionally, the threshold for detection of changes from principal angles was about twice as good as the oblique angles, even after 5000 trials of practice discriminating oblique angles. </p>

<p><strong>Reference</strong></p>

<p>Vogels, R., &amp; Orban, G. A. (1985). The effect of practice on the oblique effect in line orientation judgments. <em>Vision research</em>, <em>25</em>(11), 1679-1687.</p>

CC BY-SA 3.0
2014-07-21T14:41:56.280Z
2014-07-21T19:31:12.527Z
2014-07-21T19:31:12.527Z
Josh
<p>Here is a straight line, which visually looks like a straight line:</p>

<p><img src="https://i.sstatic.net/uT5T3.jpg" alt="enter image description here"></p>

<p>At first look (lets say minimum 2–3 sec.) the line below looks straight, but after some time you can see that it is actually an inclined line. You need some time (more then 5–8 sec.) to classify that line as a inclined line.</p>

<p><img src="https://i.sstatic.net/yJflv.jpg" alt="enter image description here"></p>

<p>Here is an inclined line, which looks like an inclined line at first look:
<img src="https://i.sstatic.net/dCYo4.jpg" alt="enter image description here"></p>

<p><strong>Question:</strong> Is there any study that determines the minimum angle at which a line should be inclined to be visually classified at first look as an inclined line?</p>

<cognitive-psychology><perception><vision><categorisation>
What is the minimum angle off horizontal before a line visually appears inclined at first glance?
vasili111
# What is the minimum angle off horizontal before a line visually appears inclined at first glance?

(Asked by: username_0 on 2014-07-20)

Here is a straight line, which visually looks like a straight line:

![enter image description here](https://i.sstatic.net/uT5T3.jpg)

At first look (lets say minimum 2–3 sec.) the line below looks straight, but after some time you can see that it is actually an inclined line. You need some time (more then 5–8 sec.) to classify that line as a inclined line.

![enter image description here](https://i.sstatic.net/yJflv.jpg)

Here is an inclined line, which looks like an inclined line at first look:
![enter image description here](https://i.sstatic.net/dCYo4.jpg)

**Question:** Is there any study that determines the minimum angle at which a line should be inclined to be visually classified at first look as an inclined line?

**Tags:** cognitive-psychology, perception, vision, categorisation


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## 2 answers

### Answer by username_1 on 2014-07-21. Score: 3 | Accepted answer

Citing Muller et al’s, (1955) work on electronic displays, Eastman Kodak’s (1983) *Ergonomics Design for People at Work* states that people can discriminate 24 different absolute angles of inclination under optimum viewing conditions. This implies that an angle of 360/24 = 15 degrees can be readily classified as inclined rather than flat.

However, I’d say 15 degrees is probably overly conservative. It applies to discriminating one arbitrary angle of inclination from another when each is shown in isolation. Discriminating flat (0 degrees) from inclined is apparently a special case that is easier to do, as indicated by the [study cited by username_3](https://cogsci.stackexchange.com/questions/7863/visual-identification-of-inclined-lines/7870#7870) where people quickly detected inclinations as small as 0.5 degrees.

Assuming you’re talking about imagery you create in the built environment (e.g., for an information display), there are often vertical and horizontal references to compare the line to (e.g., the edges of a page, the bezel of a monitor, the doorway to a room). In fact, the presence of such references probably defines what “flat” means (e.g., people will still call your first line above “flat” even if they cock their head a bit to look, or even if their respective tablets/laptops are in their laps and not completely level). So, in a built environment (and outside a field-dependence laboratory), detecting an inclined line often has a degree of relative discrimination that I expect helps a lot. As for detecting inclinations in the natural world, well, there’s a reason carpenters use levels.

If you’re building an information display (e.g., a graph), you can go to smaller angles by adding reference marks, as shown below.

![Static marks at each end of line](https://i.sstatic.net/GOIqi.jpg)

![Static marks at each end of line](https://i.sstatic.net/70Tn9.jpg)

This changes the viewers’ task from recognizing an inclination to recognizing vertical gap size. People can spot a gap as small as few arc-minutes of visual angle.

References:

Muller PF Jr, Sidorsky RC, Slivinski AJ, Alluisi EA, & Fitts PM
(1955). *The symbolic coding of information on cathode ray tubes and
similar displays* Technical Report 55-375. Wright Air Development Center, Wright-Patterson AFB, October.

Eastman Kodak Company (1983). *Ergonomic design for people at work*. New York: Van Norstrand.([link](http://books.google.ge/books?id=FSgcaAIoHu8C&pg=PA230&lpg=PA230&dq=Ergonomic%20design%20for%20people%20at%20work%20pdf#v=onepage&q&f=false))

> **Comments:**
> **username_2**: Wait, what? 15 degrees sounds like *a lot*. Am I missing something here? Are we talking the kind of degrees where 360 degrees equals a whole circle?  
> **username_3**: Yeah, this doesn't fit with other research that has looked at this kind of perceptual judgment.  
> **username_4**: There is some emphasis on "at first look" though; this may require a much larger angle than the JND for reliable detection without time limits.  
> **username_3**: In the study referenced in my answer below, exposure time was 600ms.  
> **username_1**: I believe the OP was concerned with detecting an inclined line in _isolation_, not detecting a change to an inclined line. I've edited my answer to clarify the application.  
> **username_3**: The judgments in the study below were also in isolation. Stimuli were presented 5s apart and participants were comparing to their 'memory' of a horizontal line, not to another visually presented line.  
> **username_1**: OK, you've convinced me. Helps that I tried a 0.5 degree inclination on my wife and she immediately detected it. Done more editing above.  

---

### Answer by username_3 on 2014-07-21. Score: 4

Vogels and Orban (1985) asked subjects to complete several thousand angle judgments at near-principal angles (horizontal or vertical). They found that the just-noticeable difference (JND), the threshold at which people could reliably detect deviation from a horizontal line, was **0.5 degrees** after a 600ms exposure to the stimulus.

The real purpose of their study was to compare learning effects for judgments of deviations from principal orientations with judgments of deviations from oblique (diagonal) angles. They found that while people could double their sensitivity over extensive training to small changes in oblique angles, the principal angles showed no such learning effects, as you can see in this graph:

![results graph](https://i.sstatic.net/dC7jU.png)

Additionally, the threshold for detection of changes from principal angles was about twice as good as the oblique angles, even after 5000 trials of practice discriminating oblique angles.

**Reference**

Vogels, R., & Orban, G. A. (1985). The effect of practice on the oblique effect in line orientation judgments. *Vision research*, *25*(11), 1679-1687.


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