Simulation of view. Part Three View geometry

^{1 Excursion in the eye - 2 Perception - 3 Geometry of view - 4 Eye tracking - 5 How to catch the eye - 6 Simulation of eye tracking}

This part is important for understanding the principles of eye tracking modeling, and for one applies knowledge of the work of the retina from the second post.

Visual acuity

5 types of visual acuity are known:

• Detection sharpness - detection of an object in the field of view, for example - points on a white background
• The severity of localization - the ability to determine whether two lines, the ends of which are in contact, the continuation of each other or one of them is shifted relative to another
• The sharpness of the resolution of the eye is the ability to perceive the boundary between discrete patterns that are not connected to each other (for example, how the fill pattern is clearly visible and how it is oriented)
• The acuteness of recognition is familiar to everyone who visited the oculist and picked up glasses with the help of the Golovin-Sivtsev table with letter recognition
• The acuteness of dynamism - the ability to discern movement

For the topic of modeling the most interesting are the first three types of sharpness.

A common parameter for all types of acuity is the angle of view that determines the magnitude of the projection of the stimulus on the retina. The angle of view is determined using elementary trigonometry, as
')


Where Is the desired angle, S is the linear size of the object, and D is the distance from the object to the retina.

The formula is applicable solely for an angle of view not exceeding 10 degrees and this is why: the region perceived by the central fossa of the retina corresponds to the greatest visual acuity. With a distance from the central fossa, the cone concentration per square millimeter decreases (but the number of rods increases, so night peripheral vision is sharper than directed), the sizes of receptive fields increase and visual acuity, including color perception sharply, decreases:


^{The diameter of the central fossa is 1 degree, the receptor diameter of the central fossa is 0.25 degrees, the location of the inner edge of the blind spot is 12 degrees to the nose, its size is 7.5 vertically and 5 horizontally.}

So, within these 10 degrees of maximum visual acuity, if you use the angle of view to determine sharpness, then the optimal values ​​for all types of sharpness are approximately equal and

• 0.5 seconds for sharp detection
• 2 seconds for fine tuning (quantification)

It is worth noting that although peripheral vision is inferior to foveal, but the edges of fuzzy stimuli perceived by peripheral vision seem to be clearer than they actually are.

Figure for evidence of a rapid decrease in visual acuity with increasing distance between the retinal stimulated area and the central fossa. Elements of the picture are arranged in such a way that when you fix the gaze at the central point, all the letters will be clearly visible. This happens because no matter how far the distance increases, the projection of each letter on the retina decreases, but the number of receptors that process the letter remains approximately the same:



In addition to the factor of the angular distance from the optical axis, the duration of fixation also has a significant effect on visual acuity: the longer the stimulus is considered, the more clearly it is visible .

Saccades

A reasonable question arises: why, with such a small optical angle of view, we perceive the world not as if looking through a folded newspaper, but much wider? The answer to this question are saccades.

Saccades. (from the French saccader - to pull) - these are jerky movements of the eyes, quickly looking from one object to another.

There are small saccades (less than 3 degrees of the field of view) and large (20 degrees or more). Saccades are movements of a ballistic type: they have a specific goal and direction, moreover, when moving the target object, the saccade will not interrupt and will not follow the object, but will end at the place where the object was previously (the effect “moved so fast that I did not have time to follow him ").

Saccades occur very quickly, usually the number of saccades is from 1 to 3 per second, but they are performed so quickly that they take no more than 10% of the total time.

Actually, the technology of eye tracking to the simulation of which I lead you is a technology of tracking saccades in the image of pupils taken by an infrared camera.

In addition to the saccades themselves, there are also microsaccades made when trying to keep a look in one place. Microsaccades are reflex eye movements for fractions of angular degrees in order to refresh the image on the retina.

The fact is, the retina works in such a way that it can only capture changes in the picture - i.e. the retina was originally invented only for the perception of movement .

For example, if you put on a contact lens and put a point on it, then the first time after the lens is put on, the point will be in sight and visible. After a few seconds, the point will no longer be perceived by the retina and will disappear from view. That is why nature had to make a patch in the form of microsacdes so that we could perceive static pictures.

Since microsaccades are a technical mechanism solely for the perception of static scenes, I will not say anything more about them because it goes beyond the scope of the post.

^{1 Excursion in the eye - 2 Perception - 3 Geometry of view - 4 Eye tracking - 5 How to catch the eye - 6 Simulation of eye tracking}