Influence of thresholding on centroid statistics: full analytical description

Abstract

The centroid method is a common procedure for subpixel location that is applied to a large number of optical sensors. In practice, it is always accompanied by thresholding algorithms used to eliminate undesirable background that may decrease precision. We present a full analytical description of the interaction between centroiding and thresholding applied over an intensity distribution corrupted by additive Gaussian noise. An in depth analysis of the most outstanding statistical properties of this relation (mean and variance) is also presented by means of simulated and experimental data. This work provides fundamental concepts to the designers of sensors that are based on centroid measurements to allow them to use thresholding correctly before centroid computation.

Confocal microscopy of colloidal particles: Towards reliable, optimum coordinates

“…Most notable is particle image velocimetry (PIV) [53], in which roughly-Gaussian shaped (correlation) peaks are located [83][84][85][86][87] with some using more sophisticated procedures, such as the three-point estimator (Section 4.2.1) [53,87] or iterative procedures [88]. They also include discussions on the accuracy of centroiding [76] as well as the presence of noise [89][90][91]. The centroiding method was first applied to two-dimensional projections of colloidal samples by Murray and Grier [43], and then refined in the classical paper by Crocker and Grier [47], which also forms the basis for the routines by Weeks [52].…”

Low-cost precision rotary index calibration

“…Interference-type patterns, resulting from laser light interaction with the grating surface, are clearly visible about the center of the beam. The accuracy of the centroid position tracking algorithm has been studied and generally accepted to be dependent on the type and level of noise present in the image 9 . A good estimate of the accuracy is normally taken to be 1/10th of the detector's pixel spacing.…”

Changes of ocular aberrations with gaze

“…There is also an extrinsic fluctuation contributing to the measured changes, due to random eye movements, different initial pupil positioning between measurement series (Davies et al. , 2003), and measurement noise due to the centroiding algorithms and the detector noise (Ares and Arines, 2001, 2004). Our results (see ) show that there is a high inter‐series variability of aberrations for a fixed gaze, which diminishes the signal‐to‐noise ratio for the detection of gaze‐related aberration changes.…”