On the Precision in Estimating the Location of Edges and Corners

Recently, in Rohr [13], we analyzed the systematiclocalization errors introduced by local operators for detectinggrey-value corners. These errors are inherently due to thedifferential structure of the operators and, in general, areenlarged by discretization and noise effects. Here, we take thestatistical point of view to analyze the localization errorscaused by noisy data. We consider a continuous image model thatrepresents the blur as well as noise introduced by an imagingsystem. In general, the systematic intensity variations arenonlinear functions of the location parameters. For this modelwe derive analytic results stating lower bounds for the locationuncertainty of image features. The lower bounds are evaluatedfor explicit edge and corner models. We show that the precisionof localization in general depends on the noise level, on thesize of the observation window, on the width of the intensitytransitions, as well as on other parameters describing thesystematic intensity variations. We also point out that theuncertainty lower bounds in localizing these image features canin principle be attained by fitting parametric models directlyto the image intensities. To give an impression of theachievable accuracy numerical examples are presented.