Tool Name	Resection (Terrestrial)
Tool ID	0
Library ID	imagery_photogrammetry
Version	1.0
Author(s)	HfT Stuttgart (c) 2013

Description

Single Image Spatial Resection (Terrestrial): from at least 3 image points with known coordinates, the Cardan angles of the image orientation and the coordinates of the perspective center are calculated by a least-squares adjustment. The Cardan angles refer to the following transformation between image coordinates (x_image) and global coordinates (X_Global):
x_image = R_1(omega) * R_2(kappa) * R_3(alpha) * X_Global
Here R_1, R_2, R_3 denote rotation matrices of a right-handed (passive) coordinate transformation.

The inputs consist of a point cloud containing the identical points with their pixel indices as additional attributes. The origin of pixels is in the lower left corner of the image. The interior orientation parameters of the camera is to be provided. These include Focal Length (mm), Pixel Size (um), Principal Point Offsets (pixels) and optionally the Radial Distortion Parameters. The distortion model being used is as follows:
x_d = x_u (1 - dR)
y_d = y_u (1 - dR)
where, dR = K1 * r_u ^ 2 + K2 * r_u ^ 4 + K3 * r_u ^ 6,
r_u ^ 2 = x_u ^ 2 + y_u ^ 2,
x_u, y_u are the undistorted (corrected) image coordinates in mm,
x_d, y_d are the distorted (observed) image coordinates in mm,
K1 is in [mm ^ -2], K2 is in [mm ^ -4], K3 is in [mm ^ -6].
Approximate coordinates in [m] for the Projection Center and the center of image are also to be provided.

Following the adjustment the results are written to a text file. The main contents of the text file are: for each iteration the Sum of Squared Residuals, the A-Posteriori Standard Deviation (Sigma Naught) and the Condition of Normal Matrix, and the final estimated exterior orientation parameters (Xc, Yc, Zc, Omega, Kappa, Alpha).

Optionally the Principal Point Offsets can be estimated. This requires at least 4 image points as input.

[Warning] The tool is dedicated to the terrestrial case which means the viewing direction must be sufficiently different from the vertical direction.
The estimation of Principal Point Offsets is not recommended if the condition of the Normal Matrix is less than 10 ^ -7.

Parameters

Name	Type	Identifier	Description	Constraints
Input
Measured Points (PC)	point cloud, input	POINTS	List of Measured Points as PC
Options
Focal Length (mm)	floating point number	F	Focal Length in mm	Default: 0.000000
Pixel Width (um)	floating point number	W	Pixel Width in micro meters	Default: 0.000000
Estimate Principal Point Offsets?	boolean	EST_OFFSETS	Do you wish to estimate Principal Point Offsets?	Default: 0
Principal Point Offset in X (pixels)	floating point number	ppX	Principal Point Offset in X	Default: 0.000000
Principal Point Offset in Y (pixels)	floating point number	ppY	Principal Point Offset in Y	Default: 0.000000
Provide Radial Distortion Parameters?	boolean	GIVE_DISTORTIONS	Do you wish to provide the Radial Distortion Parameters?	Default: 0
K1	floating point number	K1		Default: 0.000000
K2	floating point number	K2		Default: 0.000000
K3	floating point number	K3		Default: 0.000000
X	floating point number	Xc	Approximate Coordinate	Default: 0.000000
Y	floating point number	Yc	Approximate Coordinate	Default: 0.000000
Z	floating point number	Zc	Approximate Coordinate	Default: 0.000000
X	floating point number	Xt	Approximate Coordinate	Default: 0.000000
Y	floating point number	Yt	Approximate Coordinate	Default: 0.000000
Z	floating point number	Zt	Approximate Coordinate	Default: 0.000000
Output Text File	file path	OUTPUT FILE	The file to write the calculation results to.