Three gradients and the perception of flat and curved surfaces

Abstract

Researchers of visual perception have long been interested in the perceived slant of a surface and in the gradients that purportedly specify it. Slant is the angle between the line of sight and the tangent to the planar surface at any point, also called the surface normal. Gradients are the sources of information that grade, or change, with visual angle as one looks from one's feet upward to the horizon. The present article explores three gradients--perspective, compression, and density--and the phenomenal impression of flat and curved surfaces. The perspective gradient is measured at right angles to the axis of tilt at any point in the optic array; that is, when looking down a hallway at the tiles of a floor receding in the distance, perspective is measured by the x-axis width of each tile projected on the image plane orthogonal to the line of sight. The compression gradient is the ratio of y/x axis measures on the projected plane. The density gradient is measured by the number of tiles per unit solid visual angle. For flat surfaces and many others, perspective and compression gradients decrease with distance, and the density gradient increases. We discuss the manner in which these gradients change for various types of surfaces. Each gradient is founded on a different assumption about textures on the surfaces around us. In Experiment 1, viewers assessed the three-dimensional character of projections of flat and curved surfaces receding in the distance. They made pairwise judgments of preference and of dissimilarity among eight stimuli in each of four sets. The presence of each gradient was manipulated orthogonally such that each stimulus had zero, one, two, or three gradients appropriate for either a flat surface or a curved surface. Judgments were made were made for surfaces with both regularly shaped and irregularly shaped textures scattered on them. All viewer assessment were then scaled in one dimension. Multiple correlation and regression on the scale values revealed that greater than 98% of the variance in scale values was accounted for by the gradients. For the flat surfaces a mean of 65% of the variance was accounted for by the perspective gradient, 28% by the density gradient, and 6% by the compression gradient. For curved surfaces, on the other hand, a mean of 96% of the variance was accounted for by the compression gradient, and less than 2% by either the perspective gradient or the density gradient.(ABSTRACT TRUNCATED AT 400 WORDS)