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 relevant challenge in desktop imaginative and prescient with rapid relevance for robotic manipulation and navigation.
The writer develops computational theories and methods touching on visible info coming up from viewer events to the differential geometry of obvious surfaces. The theories built were carried out and proven utilizing a real-time monitoring procedure in keeping with deformable contours. purposes of the concepts to geometric modelling, situation avoidance, navigation, and item manipulation are presented.
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Extra info for Active Visual Inference of Surface Shape
2. 17) and the ray, p, must (by definition) lie in the tangent plane of the surface. n = 0. 18) This allows the recovery of the surface orientation n (defined up to a sign) directly from a single view p(s, to) using the direction of the ray and the tangent to the apparent (image) contour paps n - i p ps-----A ]. 19) This result is also valid for projection on to the plane. It is a trivial generalisation to perspective projection of the well-known observation of Barrow and Tenenbanm [16, 17]. 2 Conjugate generator direction relationship of ray and contour The tangency conditions constrain the contour generator to the tangent plane of the surface.
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). 34)). This result is important because it demonstrates the possibility of obtaining robust inferences of surface geometry which are independent of any assumption of viewer motion.
The reason for the insensitivity of relative curvature measurements is that global additive errors in motion m e a s u r e m e n t are cancelled out. 9) are q ( s i , t ) , i = 1, 2 (which we will abbreviate to q(i), i = 1, 2) and which have 42 Chap. 2. 35): ['] ql i) = [(U A q(i)) A q(i)] ~ _ f~ A q(i). 53) Clearly depth can only be recovered accurately if rotational velocity ~2 is known. The dependence on rotational velocity is removed if, instead of using raw image motion qt, the difference of the image motions of a pair of points, q 0 ) q ( 2 ) , is used.
Active Visual Inference of Surface Shape by Roberto Cipolla