Better geometric measurements based on photometric information

We propose new methods for estimating properties of analog objects in properly sampled multi-dimensional grey-scale images. The finite aperture of lenses ensures band limitation of the analog image and allows sampling. Many existing measurement procedures work on a binary object obtained by edge detection and thresholding. The ragged binary edge is disturbed by aliasing which cannot be repaired by smoothing. To solve this problem we propose methods that work directly on the grey-scale image. The grey-scale image contains accurate photometric information. Our new methods yield errors that are generally an order of magnitude better than the traditional binary ones. For applications where a smooth, constant edge height is a prerequisite we introduce erf-clipping. Erf-clipping is a point operation that shapes a linear edge region into a scaled error function. In contrast to thresholding it requires very mild oversampling