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Three experiments investigated anisotropic perception of visual angle outdoors. In Experiment 1, scales for vertical and horizontal visual angles ranging from 20 degrees to 80 degrees were constructed with the method of angle production (in which the subject reproduced a visual angle with a protractor) and the method of distance production (in which the subject produced a visual angle by adjusting viewing distance). In Experiment 2, scales for vertical and horizontal visual angles of 5 degrees-30 degrees were constructed with the method of angle production and were compared with scales for orientation in the frontal plane. In Experiment 3, vertical and horizontal visual angles of 3 degrees-80 degrees were judged with the method of verbal estimation. The main results of the experiments were as follows: (1) The obtained angles for visual angle are described by a quadratic equation, theta' = a + b theta + c theta 2 (where theta is the visual angle; theta', the obtained angle; a, b, and c, constants). (2) The linear coefficient b is larger than unity and is steeper for vertical direction than for horizontal direction. (3) The quadratic coefficient c is generally smaller than zero and is negatively larger for vertical direction than for horizontal direction. And (4) the obtained angle for visual angle is larger than that for orientation. From these results, it was possible to predict the horizontal-vertical illusion, over-constancy of size, and the moon illusion.

Anisotropic perception of visual angle: Implications for the horizontal-vertical illusion, overconstancy of size, and the moon illusion