Gravesen, J., Lassen, B., Melnik, R.V.N., Picasso, B., Piche, R., Radulovic, N. and Wang, L.
Journal of Physics: Conf. Ser. (Special Issue: Mathematics for Industry in Denmark), 52, 46--57, 2006
An optical device is used to scan a cavity. In a single incident the scanner produces what can be considered a blurred image of the intersection curve between a plane and the cavity. Mathematically, the image represents an intensity function and that is obtained by integrating a certain kernel along the intersection curve. We suggest methods to determine the kernel and subsequently the intersection curve given the image. The methodology is tested with some success using an artificial, but realistic kernel and some synthetic images produced by this kernel.
Keywords: Inverse problems; optical distance measurements; medical imaging; shape-from-shading; intensity function; integral equations; Green's functions; nonlinear optimization