Table 2
Interpolation algorithms (IA) or subpixel minimum finding algorithms.
| Acronym | Name | Location of minimum |
|
|
||
| 2LS | 2D Least squares |
(x2,y2) where  |
| 2QI | 2D Quadratic interpolation |
(x2,y2) where  |
| 1LS | 1D Least squares | (x1,y1) using a2,a3,a4,a5 from 2LS above |
| 1QI | 1D Quadratic interpolation | (x1,y1) using a2,a3,a4,a5 from 2QI above |
Notes. Notation in the table refers to the elements,
si,j, of the submatrix s
of the correlation matrix centered on its sample minimum,
(imin,jmin),
the expression for a second order polynomial of two variables,
f(x,y) = a1 + a2x + a3x2 + a4y + a5y2 + a6xy,
and the location of its 1D minimum,
x1 = imin − a2 / 2a3;
y1 = jmin − a4 / 2a5
and its 2D minimum, 
; 
. The notation ⟨ · ⟩ i
denotes averaging over index
i ∈ {− 1,0,1} .
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