Curvature formation in the visual cortex: How do we sample?

Does the human visual system sample shapes at discrete points? During adaptation, when the neurons are fatigued, one observes the underlying principles that were once less prominent than the fatigued features. Operating under deficit, these less prominent features expose the original contributions from the fatigued neurons that are now absent. An underlying lower-order neural process is thus, now revealed. In this paper, we conduct experiments using a modified version of the circle-polygon illusion to reveal the brains sampling pattern. The circle-polygon illusion produces polygonal percepts during adaptation when a static dark outline circle is pulsed at 2 Hz alternating with a gradient luminance circle. We define sampling as the edge length of the emergent polygon. We develop a reconstruction function that defines the edge length based on psychophysical responses. We perform two experiments. In the first experiment, we present circles of size [2,4,8,16] deg presented at eccentricity [0,1,2,4,8] deg in a cross design. In the second experiment, we modify the method of Sakurai (2014) and display arc lengths that are 1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8 and 1 (whole) of a circle, of size 4 and 8 deg, presented centrally. The observers report the edge length. We find that the stimulus size and presentation eccentricity, taken together, best explain the edge length reported by the users. The users, as a random effect, do not influence the mean of the edge length reported when considering the best model reported (size and eccentricity together). However, the users do influence edge length reported only when using mean eccentricity or eccentricity as the parameter influencing edge length. Arc lengths of a circle produce the same or similar edge lengths. The length of the curve does not play a significant role signifying that biological neurophysiology at an eccentricity controls the edge length formation. Using the influences on edge length, we define sampling as a sum of qualitative influences and a sampling function derived from Taylors polynomial using sampling values along the eccentricity grid. As we use the sampled values directly to reconstruct the function, we remove the need for recording directly from neurons and instead rely on behavioural responses to build the reconstruction function.