By Roberto Cipolla
This monograph is dedicated to the matter of inferring geometric information regarding arbitrarily curved surfaces from visible cues; it is a important challenge in machine imaginative and prescient with quick relevance for robotic manipulation and navigation.
The writer develops computational theories and methods concerning visible info coming up from viewer routine to the differential geometry of seen surfaces. The theories constructed were carried out and verified utilizing a real-time monitoring process in keeping with deformable contours. functions of the ideas to geometric modelling, situation avoidance, navigation, and item manipulation are presented.
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Additional resources for Active Visual Inference of Surface Shape
This is essentially the "aperture problem" for contours, considered either on the spherical perspective image q(s,t), or on the Gauss sphere n ( s , t ) , or between space curves on the surface r(s,t). The choice is arbitrary since the image contours are projections of different 3D space curves. 2 Epipolar parameterisatlon A natural choice of parameterisation (for both the spatio-temporal image and the surface), is the epipolar parameterisation defined by rt A p = 0. 33) The tangent to the t-parameter curve is chosen to be in the direction of the ray, p.
1) are now described. In particular this chapter presents: 1. A simple, computationally efficient method for accurately extracting image curves from real images and tracking their temporal evolution. This is an extension of tracking with snakes  - - energy minimising splines guided by "image forces" - - which avoids computing the internal energies by representing sections of curves as cubic B-splines. Moreover real-time processing (15 frames per second) is achieved by windowing and avoiding Gaussian smoothing.
2 Rate of parallax Following from the well-known results about motion parallax, we derive the central result of this section - - that the rate of parallax is a robust cue for surface curvature. 47) for normal curvature a t in terms of image acceleration was sensitive to viewer translational acceleration and rotational velocity and acceleration. If, instead, differences of image accelerations are used, the undesirable sensitivity vanishes. 7. Motion parallax and the robust estimation of surface curvature 43 The important point is that the two copies of this equation for the two positions i = 1, 2 can be subtracted, cancelling off the undesirable dependency on ~2, t2t and on Ut.
Active Visual Inference of Surface Shape by Roberto Cipolla