  The paper investigates a hypothesis that our visual system groups visual cues
based on how they form a surface, or more specifically triangulation derived
from the visual cues. To test our hypothesis, we compare shape recognition with
three different representations of visual cues: a set of isolated dots
delineating the outline of the shape, a set of triangles obtained from Delaunay
triangulation of the set of dots, and a subset of Delaunay triangles excluding
those outside of the shape. Each participant was assigned to one particular
representation type and increased the number of dots (and consequentially
triangles) until the underlying shape could be identified. We compare the
average number of dots needed for identification among three types of
representations. Our hypothesis predicts that the results from the three
representations will be similar. However, they show statistically significant
differences. The paper also presents triangulation based algorithms for
reconstruction and recognition of a shape from a set of isolated dots.
Experiments showed that the algorithms were more effective and perceptually
agreeable than similar contour based ones. From these experiments, we conclude
that triangulation does affect our shape recognition. However, the surface
based approach presents a number of computational advantages over the contour
based one and should be studied further.
