Discriminating the volume of motion-defined solids

Abstract

We investigated the ability of human observers to discriminate an important global 3-D structural property, namely volume, of motion-defmed objects. Weused convex transparent wire-frame objects consisting of about 12planar triangular facets. Two objects, vertically separated by 7°, were shown simultaneously on a computer display. Both revolved at 67°/sec around a common vertical axis through their centers of mass. Observers watched the objects monocularly for an average ofthree full rotations before they responded. We measured volume discrimination as a function of absolute volume (3-48 crn''; 1 m viewing distance) and shape (cubes, rods, and slabs of different regularity). Wefound that (1) volume discrimination performance can be described by Weber's law, (2) Weber fractions depend strongly on the particular combination of shapes used (regular shapes, especially cubes, are easiest to compare, and similar shapes are easier to compare than different shapes), and (3) humans use a representation of volume that is more veridical and stable in the sense of repeatability than a strategy based on the average visible (2-D) area would yield.The volume of a solid object is one of its most fundamental structural features. It determines the space the object occupies and can give some indication of its mass. We use our visual sense continuously to make judgments of volume (and mass): Which piece of meat is larger? Do I have as much lemonade as she has? Can I lift this object? Will this pile of clothes fit into that suitcase? And so on. How do we go about making these judgments? It is highly probable that we use all sorts ofexperience and prior knowledge. This will not be very helpful, however, when we are dealing with unfamiliar objects. Observing the objects from different viewpoints will help us to gain a better 3-D impression. This paper reports on the human ability to discriminate the volumes ofvarious objects when these objects are rotating in front of the observer. The rotation lets the observer see all sides ofthe objects and make use ofstructurefrom-motion computations to determine the 3-D structure of the objects. We varied the size and shape of the objects and measured the veridicality and reproducibility of volume comparisons.There has been some previous research in this area, but it has mainly involved the use of stationary, real objects. Lauer (1929) asked subjects to compare spheres, cubes, prisms, spherical sectors, and spherical segments, and found that shape does affect estimates of volume (e.g., the volumes of cubes were overestimated relative to spheres). He also concluded that disparity of dimensions within an ob- ject was critical, because the volumes of elongated prisms were overestimated relative to cube-like prisms, and the volumes of flat spherical segments were underestimated relative to higher segments. Brunswik (1934Brunswik ( , 1956) mentioned an unpublished study by Stevenson on a similar theme. In this study prisms of various elongations were compared with cubes ofvarious sizes. Subjects were g...