Faithful representation of similarities among three-dimensional shapes in human vision.

Efficient and reliable classification of visual stimuli requires that their representations reside a low-dimensional and, therefore, computationally manageable feature space. We investigated the ability of the human visual system to derive such representations from the sensory input-a highly nontrivial task, given the million or so dimensions of the visual signal at its entry point to the cortex. In a series of experiments, subjects were presented with sets of parametrically defined shapes; the points in the common high-dimensional parameter space corresponding to the individual shapes formed regular planar (two-dimensional) patterns such as a triangle, a square, etc. We then used multidimensional scaling to arrange the shapes in planar configurations, dictated by their experimentally determined perceived similarities. The resulting configurations closely resembled the original arrangements of the stimuli in the parameter space. This achievement of the human visual system was replicated by a computational model derived from a theory of object representation in the brain, according to which similarities between objects, and not the geometry of each object, need to be faithfully represented.

Projection structure of frog rhodopsin in two crystal forms.

Rhodopsin is the G protein-coupled receptor that upon light activation triggers the visual transduction cascade. Rod cell outer segment disc membranes were isolated from dark-adapted frog retinas and were extracted with Tween detergents to obtain two-dimensional rhodopsin crystals for electron crystallography. When Tween 80 was used, tubular structures with a p2 lattice (a = 32 A, b = 83 A, gamma = 91 degrees) were formed. The use of a Tween 80/Tween 20 mixture favored the formation of larger p22(1)2(1) lattices (a = 40 A, b = 146 A, gamma = 90 degrees). Micrographs from frozen hydrated frog rhodopsin crystals were processed, and projection structures to 7-A resolution for the p22(1)2(1) form and to 6-A resolution for the p2 form were calculated. The maps of frog rhodopsin in both crystal forms are very similar to the 9-A map obtained previously for bovine rhodopsin and show that the arrangement of the helices is the same. In a tentative topographic model, helices 4, 6, and 7 are nearly perpendicular to the plane of the membrane. In the higher-resolution projection maps of frog rhodopsin, helix 5 looks more tilted than it appeared previously. The quality of the two frog rhodopsin crystals suggests that they would be suitable to obtain a three-dimensional structure in which all helices would be resolved.