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 vital challenge in machine imaginative and prescient with fast relevance for robotic manipulation and navigation. the writer develops computational theories and strategies referring to visible info coming up from viewer events to the differential geometry of obvious surfaces. The theories built were applied and established utilizing a real-time monitoring approach in response to deformable contours. purposes of the recommendations to geometric modelling, predicament avoidance, navigation, and item manipulation are offered.
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Extra resources for Active Visual Inference of Surface Shape (Lecture Notes in Computer Science)
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. 59). This result corresponds to the following intuitive idea.
The use of spherical projection (rather than planar), which has previously proven to be a powerful tool in structure-from-motion  , makes it feasible to extend tile theory of Giblin and Weiss  to allow for perspective. Its simplicity arises from the fact that there are no special points on the image surface, whereas the origin of the perspective plane is special and the consequent loss of symmetry tends to complicate mathematical arguments. 2). 11) where n is the surface normal. 11) defines both the contour generator and the apparent contour.
As before with r(s,t), the parameterisation is underdetermined but that will be fixed later. 4 Viewer and reference co-ordinate systems Note that p is the direction of the light ray in the fixed reference/world frame for R 3. It is determined by a spherical image position vector q (the direction of the ray in the camera/viewer co-ordinate system) and the orientation of the camera co-ordinate system relative to the reference frame. For a moving observer the viewer co-ordinate system is continuously moving with respect to the reference frame.
Active Visual Inference of Surface Shape (Lecture Notes in Computer Science) by Roberto Cipolla