Panoramic Imaging: Sensor-Line Cameras and Laser Range-Finders

List of Symbols

Image notations

EP	panoramic image (two-dimensional image)
EPi	the ith panoramic image, for integer i, when multiple panoramic images are considered at the same time
EPL, EPR	the left or the right panoramic image in the stereo image case
M	planar matrix image width in pixels
W	panoramic image width in pixels
H	image height in pixels
(xo, yo)	image center (measurements, in real numbers)
(ic, jc)	image center (pixel position, in integers)

Parameters of rotating sensor-line camera

τ	CCD size or pixel size (in micrometers, assuming square CCD cells)
f	camera's focal length (in millimeters)
v	camera's vertical field of view
R	off-axis distance (in meters)
ω	principal angle (i.e., the camera's viewing angle)
γ	angular unit (i.e., angular distance between adjacent projection centers)

Stereo analysis

d	image disparity in pixels
θ	angular image disparity

A scene's range of interest (RoI)

D1	radius of the RoI's inner cylindrical frontier (in meters)
D2	radius of the RoI's outer cylindrical frontier (in meters)
V1	height of the RoI's inner cylindrical frontier (in meters)
H1	distance between the camera's optical center and the RoI's inner cylindrical frontier with respect to the camera's viewing direction (in meters)

Coordinate systems

W	origin of world coordinate system
O	origin of sensor coordinate system
C	origin of camera coordinate system
(X, Y, Z)	coordinates in a 3D Euclidean coordinate system
(x, y ...