Surface shape from the deformation of apparent contours

Abstract

This chapter has

• Related the geometry of apparent contours to the differential geometry of the visible surface and to the analysis of visual motion.

• Shown how the geometric properties of tangency and conjugacy allow the recovery of qualitative properties of the surface shape from a single view. These include surface orientation and the sign of Gaussian curvature.

• Shown how a moving monocular observer can recover an exact and complete description of the visible surface in the vicinity of a contour generator from the deformation of apparent contours. This requires the computation of spatio-temporal derivatives (up to second order) of the image and known viewer motion. The epipolar parameterisation of the spatio-temporal image and surface was introduced. Its advantages include that it allows all image contours to be analysed in the same framework. Image velocities allow the recovery of the contour generator while image accelerations allow the computation of surface curvature. A consequence of this is that the visual motion of curves can be used to detect extremal boundaries and distinguish them from rigid contour generators such as surface markings, shadows or creases.

• Shown how the relative motion of image curves (parallax-based measurements) can be used to provide robust estimates of surface curvature which are independent (and hence insensitive to) the exact details of the viewer's motion.