Camera parameter groups
TerraPhoto adjusts camera parameters in groups instead of solving all parameters at the same time with a single routine.
The Misalignment angles form one group that you can solve separately. This makes sense as the misalignment angles depend on the camera mount and thus, they change every time the camera is removed and reinstalled.
The second parameter group deals with the internal geometry of the camera. This group includes the Principal point and lens distortion. These parameters should not change as long you do not disassemble the camera and there is no internal movement of the parts inside the camera.
The third parameter group relates to Timing and Exposure problems. TerraPhoto provides some basic capabilities for solving timing issues manually but it is primarily written for data sets where image timing and raw positioning is good.
Heading, roll, and pitch misalignment values define the difference between the values reported by the inertial measurement unit (IMU) and the true camera orientation. These values represent how the camera is mounted into the aircraft and are not dependent on the internal structure of the camera as most of the other camera parameters. Heading describes the angle off from north direction, roll and pitch are the angles between a horizontal plane and the camera viewing direction across flight direction (roll - left/right rotation) and along flight direction (pitch - forward/backward rotation). The general camera viewing direction is known from the Orientation parameter of the camera definition. It is either down-looking (typically airborne cameras) or side-looking (typically mobile ground-based cameras).
If the values are completely unknown, you should try to derive initial values with the help of Camera Views. It is possible to achieve about 0.1 degree accuracy with this method.
To improve the misalignment values, you need to enter some tie points. See Chapter Working with Tie Points for detailed information. As soon as you have entered a few points, you can use the Output report command in the Tie points window in order to create a report which contains the optimal values. The application determines what misalignment values produce the smallest mismatch distances for the tie points and writes these values in the report.
The adjustment of the misalignment angles to optimal values is an iterative process. As soon as you have a handful of images well-defined with tie points (e.g. 5-6 ground tie points per image for airborne data), you should achieve fairly good misalignment angles. The more images are well-defined, the more stable the misalignment angles become until they do not change any more unless you make changes to other camera parameters.
Roll and pitch misalignment angles correlate highly with principal point x and y parameters for airborne data sets collected from one altitude above ground. For cameras in landscape orientation, a small change of the roll angle has almost the exact same effect as moving the principal point x position slightly. A small change of the pitch angle has almost the exact same effect as moving principal point y position.
For corridor projects, if images have been collected in only one survey direction, tie points provide a reliable solution only for the heading misalignment angle. Roll and pitch misalignment angles have a very small effect on the tie point matching in such data sets. In this case, camera views are the only way to verify roll and pitch misalignment angles.
Principal point and lens distortion
Principal point and lens distortion define how much the lens differs from a perfect spherical shape and what is the position of the CCD plate compared to the lens. The parameters define the internal geometry of the camera.
The values of the parameters should remain pretty stable from one mission to another. You should use a good calibration data set for deriving these values. An ideal data set is collected at a suitable calibration site, includes close to 100% overlap between images of different strips, and provides many clearly identifiable objects for placing tie points.
In order to solve principal point and lens distortion, you need to collect a good number of tie points that are well distributed over the raw images. In airborne missions, if the flight pattern is optimal with 100% overlap, Ground tie points for 20 images should be enough. If the images are captured with smaller overlap, tie points are needed in more images.
In mobile missions, tie lines of the type Straight line are best suited for solving the principle point z and the lens distortion with a Zero radius function. Good tie lines are placed along image edges and as long as possible. There should be a few Straight lines close to all four image edges.
The optimal values for principal point and lens distortion are computed by the Tools / Solve parameters command of the Camera dialog.
For Panoramic cameras, only principle point Y is defined. Principle point X and Z, as well as the lens distortion parameters are not available.
The lens distortion can be modeled as Zero radius function, Function or Balanced function which are very similar to each other. All three models include equations for radial distortions and for tangential distortions.
•Radial distortion of the Zero radius function model:
dx = -rx * ((A * (d2 - R2)) + (B * (d4 - R4)))
dy = -ry * ((A * (d2 - R2)) + (B * (d4 - R4)))
•Radial distortion of the Function model:
dx = -rx * ((A * d2) + (B * d4) + (C * d6))
dy = -ry * ((A * d2) + (B * d4) + (C * d6))
•Radial distortion of the Balanced function model:
dx = -rx * (K0 + (K1 * d2) + (K2 * d4))
dy = -ry * (K0 + (K1 * d2) + (K2 * d4))
•Tangential distortion of all three models:
dx = P1 * (d2 + 2.0*rx*rx) + 2 * P2 * rx * ry
dy = P2 * (d2 + 2.0*ry*ry) + 2 * P1 * rx * ry
•In all of the above equations:
dx is shift from original pixel to correct location
dy is shift from original pixel to correct location
rx is pixel coordinate relative to focal point
ry is pixel coordinate relative to focal point
d is pixel distance to focal point
A is Radial A3 setting
B is Radial A5 setting
C is Radial A7 setting
R is Zero radius setting
K0 is K0 setting
K1 is K1 setting
K2 is K2 setting
P1 is Tangential P1 setting
P2 is Tangential P2 setting
In addition to the three model above, the lens distortion can also be modeled as Homogenous function or Pix4d model.
•The Homogenous function does not include equations for radial distortions.
•Pix4d model is best suited for data pre-processed by Pix4d software. It is automatically selected if data is imported from Pix4d camera calibration files. The equations for distortion computation are provided in the Pix4d documentation.
Finally, the lens distortion can be modeled as a Grid of xy shift vectors. The correction vectors are expressed as 1/100th of a pixel.
The timing offset parameters take effect when you use Compute list command from the Images pulldown menu for creating a TerraPhoto image list. The values are zero if the time stamps in image timing files do not have a constant error.
There is no tool in TerraPhoto for directly solving timing offset problems. If you suspect a constant time offset, you can use a manually-driven strategy to find the best offset value. This simply involves that you test different timing offset values and determine what value results in the smallest mismatches for tie points. Whenever you change the timing offset, you have to optimize the pitch misalignment angle at the same time in order to compensate for the change.
Exposure is the time difference between the top and the bottom edge of an image. This relates to the time the shutter is open. Compute list command computes correction parameters based on trajectory positions (XYZ and HRP angles) at the moment of bottom of image and at the moment of top of image exposure.
