Derivation of Invariant Properties of Geons
Viewpoint invariance: The viewpoint invariance of geons derives from their being distinguished by three nonaccidental properties (NAPs) of contours that do not change with orientation in depth:
- Whether the contour is straight or curved,
- The vertex that is formed when two or three contours coterminate (that is, end together at the same point), in the image, i.e., an L (2 contours), fork (3 contours with all angles < 180°), or an arrow (3 contours, with one angle > 180°), and
- Whether a pair of contours is parallel or not (with allowance for perspective). When not parallel, the contours can be straight (converging or diverging) or curved, with positive or negative curvature forming a convex or concave, envelope, respectively (see Figure below).
NAPs can be distinguished from metric properties (MPs), such as the degree of non-zero curvature of a contour or its length, which do vary with changes in orientation in depth.
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