The paper discusses the interpretation of structure from motion, focusing on how 3-D structure and motion can be inferred from 2-D projections. It proposes a scheme that divides the image into groups of four elements, tests each group for a rigid interpretation, and combines the results. This method can correctly decompose scenes with arbitrary rigid objects in motion, recovering their 3-D structure and motion. The analysis is based on the "structure from motion" theorem, which states that the structure of four non-coplanar points is recoverable from three orthographic projections. The scheme is extended to perspective projections, and its psychological relevance is discussed. The paper also describes experiments showing that 3-D structure can be perceived from displays of unconnected elements in motion. A demonstration using two rotating cylinders showed that motion alone can be used to perceive structure, even when individual views are unrecognizable. The study highlights the challenges of interpreting structure from motion, including the ambiguity of the interpretation and the need for constraints like the rigidity assumption. The rigidity assumption is proposed as a key constraint for interpreting structure from motion. It suggests that any set of elements undergoing a two-dimensional transformation that can be uniquely interpreted as a rigid body moving in space should be interpreted as such. This assumption helps resolve the ambiguity of the interpretation and allows for the correct recovery of 3-D structure and motion. The paper also discusses the implementation of the scheme, showing that it can be applied to large collections of elements. The scheme involves dividing the image into groups of four elements, testing each group for a rigid interpretation, and combining the results. This approach is efficient and can handle large scenes with many elements. The paper further extends the analysis to perspective projections, showing that the rigidity assumption can be applied to these as well. It discusses the challenges of using perspective projections and how the polar-parallel method can be used to approximate results. The method involves treating small neighborhoods of the image as orthographic projections, allowing for the recovery of 3-D structure and motion. The psychological relevance of the scheme is also discussed, showing that principles similar to those underlying the polar-parallel method are used by the human visual system to infer structure from motion. The paper concludes that the rigidity assumption is a key factor in the interpretation of structure from motion, and that the proposed scheme is effective in recovering 3-D structure and motion from 2-D projections.The paper discusses the interpretation of structure from motion, focusing on how 3-D structure and motion can be inferred from 2-D projections. It proposes a scheme that divides the image into groups of four elements, tests each group for a rigid interpretation, and combines the results. This method can correctly decompose scenes with arbitrary rigid objects in motion, recovering their 3-D structure and motion. The analysis is based on the "structure from motion" theorem, which states that the structure of four non-coplanar points is recoverable from three orthographic projections. The scheme is extended to perspective projections, and its psychological relevance is discussed. The paper also describes experiments showing that 3-D structure can be perceived from displays of unconnected elements in motion. A demonstration using two rotating cylinders showed that motion alone can be used to perceive structure, even when individual views are unrecognizable. The study highlights the challenges of interpreting structure from motion, including the ambiguity of the interpretation and the need for constraints like the rigidity assumption. The rigidity assumption is proposed as a key constraint for interpreting structure from motion. It suggests that any set of elements undergoing a two-dimensional transformation that can be uniquely interpreted as a rigid body moving in space should be interpreted as such. This assumption helps resolve the ambiguity of the interpretation and allows for the correct recovery of 3-D structure and motion. The paper also discusses the implementation of the scheme, showing that it can be applied to large collections of elements. The scheme involves dividing the image into groups of four elements, testing each group for a rigid interpretation, and combining the results. This approach is efficient and can handle large scenes with many elements. The paper further extends the analysis to perspective projections, showing that the rigidity assumption can be applied to these as well. It discusses the challenges of using perspective projections and how the polar-parallel method can be used to approximate results. The method involves treating small neighborhoods of the image as orthographic projections, allowing for the recovery of 3-D structure and motion. The psychological relevance of the scheme is also discussed, showing that principles similar to those underlying the polar-parallel method are used by the human visual system to infer structure from motion. The paper concludes that the rigidity assumption is a key factor in the interpretation of structure from motion, and that the proposed scheme is effective in recovering 3-D structure and motion from 2-D projections.