Global shape versus local feature: An angle illusion

We have shown previously that the precision of angle judgments depends strongly on the global stimulus configuration: discrimination thresholds for angles that form part of isosceles triangles are up to 3 times lower than for those that form part of scalene triangles [Kennedy, G. J., Orbach, H. S., & Loffler, G. (2006). Effects of global shape on angle discrimination. VisionResearch, 46(8-9), 1530-1539]. Here, we investigated whether or not the perceived size of an angle (accuracy) is also affected by the overall shape of which it forms a part. Observers compared the relative sizes of angles contained in isosceles triangles with those of angles in scalene triangles and points of subjective equality were determined. For a reference angle of 60 degrees , angles embedded in isosceles triangles were judged to be on average 14 degrees larger than angles embedded in scalene triangles. This result is largely independent of the reference angle, triangle orientation and triangle size. Moreover, the effect is present whether or not triangles of different shapes enclose the same area, whether or not the side of the triangle opposite the angle is present and whether the triangle is outlined or defined by dots at its vertexes. In sum, our results provide evidence for a novel illusion where an angle embedded in an isosceles triangle is judged substantially larger than the same angle embedded in a scalene triangle. This finding demonstrates that mechanisms for computing angles are sensitive to the context within which angles are presented.