The interpretation of structure from motion

The interpretation of structure from motion is examined from a computional point of view. The question addressed is how the three dimensional structure and motion of objects can be inferred from the two dimensional transformations of their projected images when no three dimensional information is conveyed by the individual projections. The following scheme is proposed: (i) divide the image into groups of four elements each; (ii) test each group for a rigid interpretation; (iii) combine the results obtained in (ii). It is shown that this scheme will correctly decompose scenes containing arbitrary rigid objects in motion, recovering their three dimensional structure and motion. The analysis is based primarily on the ʻstructure from motion’ theorem which states that the structure of four non-coplanar points is recoverable from three orthographic projections. The interpretation scheme is extended to cover perspective projections, and its psychological relevance is discussed.

[1]  H. Wallach,et al.  The kinetic depth effect. , 1953, Journal of experimental psychology.

[2]  H. Wallach,et al.  Circles and derived figures in rotation. , 1956, The American journal of psychology.

[3]  J. Gibson Optical motions and transformations as stimuli for visual perception. , 1957, Psychological review.

[4]  G. E. Mueser,et al.  Accuracy in reconstructing the arrangement of elements generating kinetic depth displays. , 1960, Journal of experimental psychology.

[5]  Green Bf Figure coherence in the kinetic depth effect. , 1961 .

[6]  G. Johansson PERCEPTION OF MOTION AND CHANGING FORM: A study of visual perception from continuous transformations of a solid angle of light at the eye , 1964 .

[7]  J. Hay,et al.  Optical motions and space perception: an extension of Gibson's analysis. , 1966, Psychological review.

[8]  W A Hershberger,et al.  Comment on "apparent reversal (oscillation) of rotary motion in depth". , 1967, Psychological review.

[9]  Gunnar Johansson,et al.  Perceived rotary motion from changes in a straight line , 1968 .

[10]  William Epstein,et al.  Perceived angle of oscillatory motion , 1968 .

[11]  J J Gibson,et al.  What gives rise to the perception of motion? , 1968, Psychological review.

[12]  C. Hofsten,et al.  Spatial determinants of depth perception in two-dot motion patterns , 1972 .

[13]  E. Sture Eriksson,et al.  Distance perception and the ambiguity of visual stimulation: A theoretical note , 1973 .

[14]  G. Johansson,et al.  Visual Perception of Bending Motion , 1973, Perception.

[15]  G. Johansson Visual perception of biological motion and a model for its analysis , 1973 .

[16]  Claes von Hofsten,et al.  Visual perception of motion in depth: Application of a vector model to three-dot motion patterns , 1973 .

[17]  E. S. Eriksson A theory of veridical space perception , 1974 .

[18]  Claes von Hofsten Proximal velocity change as a determinant of space perception , 1974 .

[19]  Jerry Lee Potter,et al.  The extraction and utilization of motion in scene description. , 1974 .

[20]  G. Johansson Visual motion perception. , 1975, Scientific American.

[21]  W. Hershberger,et al.  Perceived orientation in depth from line-of-sight movement , 1976 .

[22]  S. Ullman The Interpretation of Visual Motion , 1979 .