centroiding

Centroiding is a procedure to estimate the position of the center of a localized signal in an image or signal set. It is widely used to determine the coordinates of point-like sources such as stars, fluorescent beads, or particles, by exploiting the symmetry of their intensity distribution.

In a discrete image, the centroid coordinates are computed as x̄ = Σx I(x,y) / Σ I(x,y) and ȳ = Σy I(x,y) / Σ I(x,y), where I is the intensity at pixel (x,y). Subtraction of background and noise weighting improve accuracy. More generally, centroiding can be framed as the first moments of the intensity distribution or as a weighted average. For subpixel accuracy, methods such as fitting a model PSF (often a 2D Gaussian) or performing a weighted least-squares fit yield positions beyond pixel centers.

Common methods include: simple intensity-weighted centroid; center of mass after background subtraction; and model-based centroiding through PSF fitting, which is more robust at low signal-to-noise but computationally heavier.

Applications: astronomy for star catalogs, fluorescence microscopy and super-resolution localization (e.g., PALM/STORM) to determine molecular positions, particle tracking and velocimetry, metrology and autofocus systems that require precise localization.

Considerations: accuracy depends on signal-to-noise ratio, sampling, PSF, and background estimation; close or overlapping sources require deblending or multiple-source fitting; noise and detector effects can bias estimates.