Our new methods yield errors that are generally orders of magnitude better than the traditional binary ones. As an example we have chosen a microscope, an optical instrument for which diffraction limited optics are widely available. Many of the measurements in later chapters have been developed for application in quantitative microscopy. The image is acquired using an ideal sensor. Optics and camera are modeled to create synthetical images for test purposes.
Special attention is given to sampling theory.
Some frequently used image processing tools such as Gaussian filters, Gaussian derivatives and pillball filters are discussed. For applications where a smooth, constant edge height is a prerequisite we will 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. Chapter 3 deals with the systematic errors of second derivative operators applied to low-pass filtered curved edges.