Download A Primer of Statistics by Mary Phipps, Malcolm Quine PDF

By Mary Phipps, Malcolm Quine

ISBN-10: 1740096266

ISBN-13: 9781740096263

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In consequence, there are fewer sources of relatively long projected vertical lines in the world compared to sources of relatively long projected horizontal lines. 6B). 7B). Vertical lines are somewhat more likely to correspond to object surfaces than are lines oriented at 20–30◦ from vertical, simply because trees and other objects in the physical world more frequently extend along the vertical axis than they do along an axis oriented 20–30◦ away from vertical. As a result of the way that upright objects efficiently contend with gravity, the physical sources of relatively long linear projections at 20–30◦ from vertical are less probable than the sources of equally long vertical projections.

The black line, in contrast, indicates the cumulative probability distribution derived from a hypothetical distribution in which the probability of any given source is the same (see inset). B) The predicted perceptions of angle subtenses follow from the empirical ranks of angles in the cumulative probability distribution and are indicated by the gray curve; the dashed black line indicates the actual subtenses of the stimuli. 2A. (After Howe and Purves, 2005a) 44 Perceiving Geometry: Geometrical Illusions Explained by Natural Scene Statistics compared to its position in the geometrical space of 0 to 180◦ .

The pattern of cortical activity in response to two intersecting lines would, in this conception, reflect the empirical distribution of the real-world sources of the intersecting lines in the retinal image. 6A), the peaks of neuronal activity elicited would be shifted toward domains of orientation selectivity more orthogonal than those elicited by each line alone. In addition to providing a unified framework for understanding neuronal responses to both acute and obtuse angles, this prediction offers a new way of considering the relevant neurophysiology.

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