By Roberto Cipolla
This monograph is dedicated to the matter of inferring geometric information regarding arbitrarily curved surfaces from visible cues; it is a critical challenge in machine imaginative and prescient with instant relevance for robotic manipulation and navigation.
The writer develops computational theories and strategies pertaining to visible details bobbing up from viewer activities to the differential geometry of seen surfaces. The theories constructed were carried out and confirmed utilizing a real-time monitoring process in line with deformable contours. purposes of the concepts to geometric modelling, problem avoidance, navigation, and item manipulation are presented.
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Extra info for Active Visual Inference of Surface Shape
5). 6 T h e geodesic c u r v a t u r e of a curve on a sphere is s o m e t i m e s called the apparent c u r v a t u r e . It m e a s u r e s how the curve is c u r v i n g in the imaging surface. It is equal to the c u r v a t u r e of t h e perspective projection onto a plane defined by the ray direction. 7The curvature, a, and the F r e n e t - S e r r e t normal, N , for a space curve "y(s) are given by (, p103): a N = ('Ys A "Yss) A "Ys/ ["Is[4, The n o r m a l c u r v a t u r e is the m a g n i t u d e of the c o m p o n e n t of teN in the direction of the surface n o r m a l (here p since p ( s , to) is a curve on the image sphere); the geodesic c u r v a t u r e is the m a g n i t u d e of the c o m p o n e n t in a direction p e r p e n d i c u l a r to the surface n o r m a l and the curve t a n g e n t (in this case Ps).
G. 4b). 0=0 The special case /9 = 0 occurs when the ray p lies along an asymptotic direction on the surface. The tangent to the contour generator and the ray are parallel - asymptotic directions are self-conjugate. 5). Conjugacy is an important relation in differential geometry and vision. As well as determining the direction of a contour generator, it also determines the direction of a self-shadow boundary in relation to its light source . 4 Static properties of apparent contours It is now well established that static views of extremal boundaries are rich sources of surface geometry [17, 120, 36, 85].
The main results are summarised below followed a description and simple derivation. 4 Since, generically, there is only one direction conjugate to any o t h e r direction, this p r o p e r t y m e a n s t h a t a c o n t o u r g e n e r a t o r will n o t intersect itself. Chap. 2. 4: In which direction does the contour generator run? (a) An example in which the direction of the contour generator is determined by the direction of the ray. For any point on a sphere the contour generator will run in a perpendicular direction to the ray.