How Accurate Is the Logic-Based Filter?

doi:10.1117/3.677549.ch3

Book: Logic-based Nonlinear Image Processing

Author(s): Stephen Marshall

Published: 2006

https://doi.org/10.1117/3.677549.ch3

Author Affiliations +

Abstract

In most practical situations, even the optimal filter within a finite window is unable to recover the original image exactly. However, the remaining error will be the smallest possible for that window. Returning to the observations for the simple example shown in Fig. 2.8, it can be seen that for the line of the table discussed, x=(1,0,1) , the output of the filter was set to 1. While this gave the correct output value for four of the pixels, it still left one in error. In general, each input x will make a contribution to the error equivalent to the smaller of the two values of N 0 or N 1 . The error from each input may be totaled to give the overall filter error.