# Vision modeling. Part three. Geometry of vision

1 Excursion to the eye - 2 Perception - 3 Geometry of vision - 4 Eye tracking - 5 How to catch a look - 6 Modeling eye tracking

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

## Visual acuity

There are 5 types of visual acuity known:
• Acuity of detection - detection of an object in the field of view, for example, points on a white background
• Acuity of localization - the ability to determine whether two lines whose ends are in contact are extensions of each other or whether one of them is offset relative to the other
• The sharpness of the resolution of the eye is the ability to perceive the border between discrete, unrelated patterns (for example, how the fill pattern is clearly visible and how it is oriented)
• Acuity of recognition - familiar to everyone who visited the optometrist and picked up glasses using the Golovin-Sivtsev table with recognition of letters
• The acuity of dynamism - the ability to distinguish movement

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

A parameter common to all types of acuity is the angle of view that determines the magnitude of the projection of the stimulus onto the retina. The angle of view is determined using elementary trigonometry,

where 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 that is why:the greatest visual acuity corresponds to the region perceived by the central fossa of the retina. When moving away from the central fossa, the concentration of cones per square millimeter decreases (but the number of rods increases, therefore night peripheral vision is sharper than directed), the sizes of receptive fields increase, and from this visual acuity, including the color perception sharpness decreases:

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

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

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

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

Figure for evidence of a rapid decrease in visual acuity with increasing distance between the stimulated portion of the retina and the central fossa. The elements of the picture are arranged in such a way that when fixing the gaze at the central point, all the letters will be clearly visible. This is because no matter how 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 angular distance from the optical axisthe duration of fixation also has a significant effect on visual acuity: the longer the stimulus is examined, the more clearly it is visible .

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

Saccades. (from the French saccader - to yank) - these are abrupt eye movements that quickly move your eyes 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 ballistic-type movements: 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 earlier (the effect “moved so fast that I didn’t have time to follow him ”).

Saccades take place very quickly, as a rule, the number of saccades is from 1 to 3 per second, but they are so fast that they take no more than 10% of the total time.

Actually, the eye tracking technology to the modeling of which I am leading you to is a technology for tracking saccades by the image of the pupils captured by an infrared camera.

In addition to the saccades themselves, there are also micro-saccades made when trying to keep a glance in one place. Microsaccades are reflex eye movements at fractions of an angular degree in order to update 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 will be visible. After a few seconds, the point ceases to be perceived by the retina and disappears from the field of view. That is why nature had to make a patch in the form of micro saccades, so that we could perceive static pictures.

Since micro-saccades are a technical mechanism solely for the perception of static scenes, I won’t tell anything more about them because it goes beyond the scope of the post.

1 Eye tour - 2 Perception - 3 Geometry of vision - 4 Eye tracking - 5 How to catch a look - 6 Modeling eye tracking