By Roberto Cipolla
This monograph is dedicated to the matter of inferring geometric information regarding arbitrarily curved surfaces from visible cues; it is a relevant challenge in laptop imaginative and prescient with instant relevance for robotic manipulation and navigation. the writer develops computational theories and strategies referring to visible info bobbing up from viewer activities to the differential geometry of seen surfaces. The theories constructed were applied and verified utilizing a real-time monitoring method in keeping with deformable contours. purposes of the suggestions to geometric modelling, situation avoidance, navigation, and item manipulation are provided.
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Additional info for Active Visual Inference of Surface Shape (Lecture Notes in Computer Science)
The internal energy serves to maintain smoothness of the curve under changing external influences. 2) which is computed after convolution of the image with the derivative of a Gaussian kernel, VG(~r), of size (scale) o. Gaussian smoothing extends the search range of the snake by smearing out image edge features. The goal is to find the snake (contour) that minimises the total energy. This is achieved by the numerical solution of the elastic problem using techniques from variational calculus. The main step is the solution of a linear equation involving a banded matrix, typically in several hundred variables .
The physical constraints of tangency (all rays at a contour generator are in the surface's tangent plane) and conjugacv (the special relationship between the direction of the contour generator and the ray direction) provide powerful constraints on the local geometry of the surface being viewed and allow the recovery of surface orientation and the sign of Gaussian curvature directly from a single image of the contour generator, the apparent contour. 22 Chap. 2. 17) and the ray, p, must (by definition) lie in the tangent plane of the surface.
In such a case, it is sometimes possible to use the crude estimate to bootstrap a more precise visual ego-motion computation . However this requires an adequate number of identifiable corner features, which m a y not be available in an unstructured environment. Moreover, if the estimate is too crude the ego-motion c o m p u t a t i o n m a y fail; it is notoriously ill-conditioned . The alternative approach is to seek geometric cues that are much less sensitive to error in the motion estimate.