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Direct Computation of Qualitative 3-D Shape and Motion Invariants
December 1991 (vol. 13 no. 12)
pp. 1236-1240

Structure from motion often refers to the computation of three-dimensional structure from a matched sequence of images. However, a depth map of a surface is difficult to compute and may not be a good representation for storage and recognition. Given matched images it is shown that the sign of the normal curvature in a given direction at a given point in the image can be computed from a simple difference of slopes of line segments in one image. Using this result, local surface patches can be classified as convex, concave, cylindrical, hyperbolic (saddle point), or planar. At the same time, the translational component of the optical flow, from which the focus of expansion can be computed, is obtained.

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Index Terms:
picture processing; pattern recognition; structure from motion; 3D shape invariants; 3D motion invariants; depth map; matched images; local surface patches; convex; concave; cylindrical; hyperbolic; saddle point; planar; optical flow; focus of expansion; pattern recognition; picture processing
D. Weinshall, "Direct Computation of Qualitative 3-D Shape and Motion Invariants," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 12, pp. 1236-1240, Dec. 1991, doi:10.1109/34.106997
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