CONSTANT AFFINE VELOCITY PREDICTS THE 1 3 POWER-LAW OF PLANAR MOTION PERCEPTION AND GENERATION/

Numerous studies have shown that the power of 1/3 is important in rela ting Euclidean velocity to radius of curvature (R) in the generation a nd perception of planar movement, Although the relation between veloci ty and curvature is clear and very intuitive, no valid explanation for the specific 1/3 value has yet been found, We show that if instead of computing the Euclidean velocity we compute the affine one, a velocit y which is invariant to affine transformations, then we obtain that th e unique function of R which will give (constant) affine invariant vel ocity is precisely R(1/3), This means that the 1/3 power law, experime ntally found in the studies of hand-drawing and planar motion percepti on, implies motion at constant affine velocity, Since drawing/perceivi ng at constant affine velocity implies that curves of equal affine len gth will be drawn in equal time, we performed an experiment to further support this result, Results showed agreement between the 1/3 power l aw and drawing at constant affine velocity, Possible reasons for the a ppearance of affine transformations in the generation and perception o f planar movement are discussed. Copyright (C) 1996 Elsevier Science L td