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When a person is spying from around a corner with only one eye, it's rather easy to ignore the other eye's image, since it's probably much darker, because one usually spies around a corner standing close to a wall.
But if both eyes get equally bright visual input, it takes some effort to try and stay focused on just one of them. What processes in human body allow such action?
Short answer
Image blur on the retina is the most important monocular cue for lens accommodation.
Background
Focussing of an image on the retina is mediated by the lens. Re-shaping of the lens to focus the image on the retina is called accommodation. In general , the main cues for focussing are retinal disparity and blur, and to a lesser extent proximal cues such as looming, motion parallax and overlay of contours.
When looking with two eyes (binocularly) at an object, retinal disparity is by far the most important depth cue for accommodation. The two eyes look at an object from slightly different angles, so they get slightly different views of it. This difference is the disparity (imperfect match) between the two views. The visual system normally fuses these two images into a single perception and converts the disparity between the two images into perception of depth (Source: Indiana university).
When only one eye is available (monocular focussing), use of retinal disparity isn't possible, and retinal blur becomes the most important factor for lens accommodation. When an image is out of focus, its representation on the retina is blurry. By adjusting the shape of the lens the visual system adjusts the image projection to bring it into focus such that blur is minimized (Horwood & Riddell, 2008). Looming (incoming object becomes apparently bigger), motion parallax (objects further away move slower across the field of view) and overlay of contours (objects closer by obscure things further away) also provide monocular cues for accommodation.
