By Walter Enders
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Accordingly, the subtense of any angle between 0◦ and 90◦ should be systematically enlarged in perception, whereas the subtense of angles between 90◦ and 180◦ should be reduced. 6C). 2 can also be explained in this framework. 2A). 7A). The orientation of this speciﬁc reference line was chosen because an inducing line at 60◦ is frequently used to demonstrate the tilt effect; the argument that follows, however, applies to an “inducing” line at any orientation. , a line rotated 30◦ from the reference line) is indicated by the dashed line in this distribution.
3A. 3 Analysis of the physical sources of straight-line projections in range images of fully natural scenes. A) Probability distributions of the occurrence of the physical sources of line stimuli. The probabilities of occurrence of the physical sources are plotted as functions of the projected length (l) of line stimuli orientated at four different orientations (θ). B) Cumulative probability distributions derived from the distributions in (A). The cumulative probability value for a given point x on the abscissa was obtained by calculating the area underneath the curve lying to the left of a line that corresponded to l = x in the relevant probability distribution in (A).
The cumulative probability value for a given point x on the abscissa was obtained by calculating the area underneath the curve lying to the left of a line that corresponded to l = x in the relevant probability distribution in (A). EMPIRICAL RANKING OF LINE LENGTHS Each of the probability distributions of the physical sources of lines derived in this way provides a basis for generating the empirical scale of line length pertinent to lines projected at a speciﬁc orientation. As described in the previous chapter, the purpose of this exercise is to indicate, with respect to any given line in an image, what percentage of the possible physical sources of a line projected in the same orientation generated projections shorter than the line stimulus at issue, and what percentage gave rise to longer line projections in the experience of human observers.