Acronym or Symbols	Definition	Acronym or Symbols	Definition
DoF	depth of field	$K_i^{s,s_n}$	$i$-th radial distortion coefficient of the object plane at distance $s_n$ when the lens is focused at the distance of $s$
FoV	field-of-view	$K_i^{s,s_m}$	$i$-th radial distortion coefficient of the object plane at distance $s_m$ when the lens is focused at the distance of $s$
$p\left(\begin{array}{cc}{u}_{li}& v_{li}\end{array}\right)$	undistorted coordinates	$K_i^{s,s_k}$	$i$-th radial distortion coefficient of the object plane at distance $s_k$ when the lens is focused at the distance of $s$
$O_w{X}_w{Y}_w{Z}_w$	world coordinate system	$\delta P^{s,s_m}$	decentering distortion function in the defocused plane at the object distances of $s_m$ when the lens is focused at distance $s$
$ouv$	image coordinate system	$\delta P^{s,s_k}$	decentering distortion function in the defocused plane at the object distances of $s_k$ when the lens is focused at distance $s$
$O_C$	optical center	$\delta P^{s,s_n}$	decentering distortion function in the defocused plane at the object distances of $s_n$ when the lens is focused at distance $s$
$z^{\prime }$	scaling factor	$P^{s,s_n}$	$i$-th decentering distortion coefficient of the object plane at distance $s_n$ when the lens is focused at the distance of $s$
$\mathit{K}$	intrinsic parameter matrix	$P_i^{s,s_m}$	$i$-th decentering distortion coefficient of the object plane at distance $s_m$ when the lens is focused at the distance of $s$
CCD	Charge Coupled Device	$P_i^{s,s_k}$	$i$-th decentering distortion coefficient of the object plane at distance $s_k$ when the lens is focused at the distance of $s$
CMOS	Complementary Metal-Oxide Semiconductor	${\delta }_{max}$	maximum value of image distortion
$\mathit{M}$	transformation matrix	$r_{max}$	maximum distortion radius of the image
VCS	vision coordinate system	$I_l$	length of the image
$\mathit{R}$	rotation matrix	$I_h$	height of the image
$\mathit{T}$	translation matrix	${\delta }_{limited}$	minimum distortion value
$\left(\begin{array}{cc}{\overline{u}}_{li}& {\overline{v}}_{li}\end{array}\right)$	distorted coordinates	$r_{limited}$	minimum value of the image distortion radius
${\delta }_{u_{li}}$	distortion function of an image point in the $u$ direction	$n_p$	number of partitions
${\delta }_{v_{li}}$	the distortion function of an image point in the $v$ direction	${\delta }_{equ}$	distortion increment
$(u_0,v_0)$	distortion center	$\rho$	partition radius
$r$	distortion radius	$P_m$	point in VCS
$K_1$	first-order coefficient of radial distortion	$P_k$	point in VCS
$K_2$	second-order coefficient of radial distortion	${\mathsf{\Pi }}_m$	$m$-th object plane in the VCS
$P_1$	first-order coefficient of decentering distortion	${\mathsf{\Pi }}_k$	$k$-th object plane in the VCS
$P_2$	second-order coefficient of decentering distortion	${\mathsf{\Pi }}_n$	$n$-th object plane in the VCS
$\delta r_{\infty }$	radial distortion for a lens that is focused on plus infinity	${}^{g}K_i^{s,s_m}$	$i$-th order radial distortion coefficient in the $g$-th partition of object plane ${\mathsf{\Pi }}_m$
$\delta r_{-\infty }$	radial distortion for a lens that is focused on minus infinity	${}^{g}P_i^{s,s_m}$	$i$-th order decentering distortion coefficient in the $g$-th partition of object plane ${\mathsf{\Pi }}_m$
$m_s$	vertical magnification in the focal plane at object distance $s$	${}^{g}K_i^{s,s_k}$	$i$-th order radial distortion coefficient in the $g$-th partition of object plane ${\mathsf{\Pi }}_k$
$\delta r_{s_{}}$	lens radial distortion in the focal plane	${}^{g}P_i^{s,s_k}$	$i$-th order decentering distortion coefficient in the $g$-th partition of object plane ${\mathsf{\Pi }}_k$
$\delta r_{s_m}$	radial distortion in the focal plane when the lens is focused on the distance of $s_m$	${}^{g}K_i^{s,s_n}$	$i$-th order radial distortion coefficient in the $g$-th partition of object plane ${\mathsf{\Pi }}_n$
$\delta r_{s_k}$	radial distortion in the focal plane when the lens is focused on the distance of $s_k$	${}^{g}P_i^{s,s_n}$	$i$-th order decentering distortion coefficient in the $g$-th partition of object plane ${\mathsf{\Pi }}_n$
$f$	focal length	PnP	Perspective-n-Point
$K_i^s$	$i$-th radial distortion coefficient for focused object plane at distance $s$	$\theta$	angle between the regression line and the $u$ axis
$K_i^{s_m}$	$i$-th radial distortion coefficient when the lens is focused on the distance of $s_m$	$D$	average sum of squared distances from the points $\left(\begin{array}{cc}{u}_{li}& v_{li}\end{array}\right)$ to all the lines
$K_i^{s_k}$	$i$-th radial distortion coefficient when the lens is focused on the distance of $s_k$	$imR$	undistorted image
$\delta r_u$	component of the decentering distortion in $u$ direction	$imD$	distorted image
$\delta r_v$	component of the decentering distortion in $v$ direction	RMS	root mean square
$K^{s,s_p}$	radial distortion coefficient in the defocused plane with the depth of $s_p$ when the lens is focused at distance $s$	PSNR	Peak Signal-to-Noise Ratio
$g$	empirical coefficient	$MSE$	mean square error of the image before and after distortion correction
$K^{s_p}$	radial distortion coefficient in the focal plane at distance $s_p$	${\mathit{R}}_q$	rotation matrix in the $q$-th pose
$K^s$	radial distortion coefficient in the focal plane at distanced $s$	${\mathit{T}}_q$	translation matrix in the $q$-th pose
$\delta r^{s,s_n}$	radial distortion function of the object plane at distance $s_n$ when the lens is focused at the distance of $s$	${}^{g}K_i$	$i$-th order radial distortion coefficient in the $g$-th partition of the $q$-th pose
$\delta r^{s,s_m}$	radial distortion function of the object plane at distance $s_m$ when the lens is focused at the distance of $s$	${}^{g}P_j$	$j$-th order decentering distortion coefficient in the $g$-th partition of the $q$-th pose
$\delta r^{s,s_k}$	radial distortion function of the object plane at distance $s_k$ when the lens is focused at the distance of $s$	LM	Levenberg-Marquardt