Effect of point-spread functions on geometric measurements in computer vision.

Abstract

The point-spread function (PSF) of an imaging system can affect the precision to which geometric features can be measured in digital images. It is shown that the PSF alone, when larger than a certain size relative to the sampling rate, does not cause a loss of precision, but actually improves the precision to which features can be measured. Quantization of the samples in an image is the limiting factor on precision. How much the precision is limited in the face of quantization depends on the size and shape of the PSF. The theory of locales is used extensively to compute bounds on precision as a function of PSF size and shape. Many geometric feature models are considered although almost all of the emphasis is on analysis of the unit step edge. It is shown for the step edge that the size of a PSF has more influence on precision than its shape. The size for which optimal precision occurs is ∼0.7 pixels in "radius". Bounds on precision are also shown for the case of a fixed rectangular sampling PSF with a variable-sized optical PSF and for the case where electronic components introduce asymmetry into the PSF. A method for objective comparison of imaging system PSFs is demonstrated. Other factors influencing precision, including unknown scene contrast and noise, are briefly examined. To illustrate the utility of the results, an experiment is presented showing that approximation of a PSF by a Gaussian PSF results in little loss of precision. Another illustrative experiment shows how the orientation precision of several widely-used first derivative operators are affected by the PSF and shows how the template coefficients can be found to optimize orientation precision for a given PSF.