By Roberto Cipolla
This monograph is dedicated to the matter of inferring geometric information regarding arbitrarily curved surfaces from visible cues; this can be a critical challenge in machine imaginative and prescient with fast relevance for robotic manipulation and navigation.
The writer develops computational theories and strategies touching on visible info bobbing up from viewer pursuits to the differential geometry of obvious surfaces. The theories built were applied and validated utilizing a real-time monitoring procedure in line with deformable contours. purposes of the ideas to geometric modelling, trouble avoidance, navigation, and item manipulation are presented.
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Extra info for Active Visual Inference of Surface Shape
Dependence on viewer motion is now limited to the velocity U. There is no dependence on viewer acceleration or rotational velocity. Hence the relative measurement should be much more robust. ) In the case that q0) is known to be a fixed surface reference point, with 1/t~ tl = 0, then A R = 1/t~ t2 so that the relative curvature A R constitutes an estimate, now much more robust, of the normal curvature ~t2 at the extremal boundary point q(~). 43) to obtain robust estimates of surface curvature. This is confirmed by the experiments of Chapter 3.
For a moving observer the viewer co-ordinate system is continuously moving with respect to the reference frame. The relationship between p and q can be conveniently expressed in terms of a rotation operator R(~) : p ----R(t)q. 16) where (as before) the subscripts denote differentiationwith respect to time and A denotes a vector product. 3 G e o m e t r i c properties of the contour generator and its projection We now establish why the contour generator is a rich source of information about surface geometry.
8. Summary 45 the inverse normal c u r v a t u r e 1/~; t must lie to be considered to be on a surface marking or a crease edge rather than an extremal boundary. 4 Qualitative shape Further robustness can be obtained by considering the ratio of relative curvatures. More precisely this is the ratio of differences in radii of curvature. Ratios of pairs of parallax based measurements can, in theory, be completely insensitive to viewer motion. n can be shown to be independent of the viewer motion and can be determined from spatio-temporal measurements on the image for a distinct point and apparent contour pair (Appendix C).