Physics of Digital Image Formation

Abstract

We begin our discussion of modeling by addressing why it is essential to consider two phenomena that play a role in image formation, influence the precision of landmark location, and have often been neglected in the past. These are the finite sensitive area of each pixel and the smoothing of the illuminance function introduced by diffraction. The detection of landmark location is an estimation problem, and the accuracy of any estimator is governed by the sensitivity of the data to changes in the quantity to be estimated. For landmark location, this is (∂J/∂ ^pP^∗ _o ) , where J ∈ R^Np×1 is the discrete analog intensity values of Np pixels used to estimate the landmark location, and ^pP^∗ _o ∈ R² is the true location of the landmark. The intensity values are organized as an N _p × 1 column vector so that the derivative (∂J/∂ ^pP^∗ _o ) is a 2-D array. For this discussion, the analog intensity values, J, are used rather than the digital image values, I, to avoid the complication of intensity quantization. Consideration of intensity quantization is deferred to Section 3.2.1.