|5.2 Understanding the GIANT Printout-listing|
|As indicated in Section 5.1, the Project.LST file contains
the GIANT output listing which contains the printout of the least-squares adjustment.
While the listing is fully annotated and, for the most part self explanatory, some remarks
are offered in this section to assist with the understanding and interpretation of the
The contents of the GIANT printout-listing file will vary depending upon the configuration of the switches described in Section 3.5. The user is advised to review that section to consider the various options available and their effect on the GIANT printout listing. This section will describe the printout-listing file as if all optional switches were active and the maximum possible amount of information was directed to the file.
Generally speaking, the GIANT printout listing contains five sections:
|5.2.1 Record of Adjustment Option and Switch Settings|
|All GIANT printout-listing files begin with a listing of
the adjustment options and switch settings. This includes such information as the
coordinate system type (geographic or rectangular), semi-axis lengths for the reference
ellipsoid when geographic coordinate systems are used and interpretation of the
orientation angles. Statistical flags listed include whether error propagation is
selected, if the unit variance is to be computed and image residual listings and their
threshold. Settings for the application of the three refraction models are indicated.
Finally it is indicated whether the results of the adjustment (triangulated ground
coordinates and/or adjusted camera station parameters) will be saved to files or not.
The user is strongly encouraged to carefully review this page to ensure that the adjustment truly reflects the desired configuration.
|5.2.2 Input Data Echo|
| The second section of the GIANT printout listing
contains an echo of the input data. For large projects, echoing the input data can lead to
a voluminous listing file. If the real interest of the adjustment is only the triangulated
ground coordinates, it may be advisable to echo the input data only during the initial
adjustment debugging stages to confirm its correctness, and then disable it during final
runs. Alternately, limiting the classes of input data that is echoed can control listing
file size. Review Section 3.5 for possible configurations of input data echoing.
When all input data is selected for inclusion, GIANT will send it to the printout-listing file in the following order:
Camera System Parameters, Photo Group Parameters and Error Warnings will always be included regardless of the configuration of input or output switches.
As suggested, it may be judicious in the initial, debugging phases of the adjustment, to carefully review the echoed input data. This probably pertains more to the camera system parameters and the group parameters, as they tend to have more of a global impact on the adjustment outcome than the image, frame and control data do. In a, say, 200 frame adjustment, the volume of image and frame data preclude the careful examination of it all. Moreover, the image plate coordinates do not tend to lend themselves to intuitive checking. As it turns out, GIANT provides statistical measures elsewhere in the output that will help to point out or suggest if there may be problems in the input frame or image data. Regarding the input ground control data, once again the data volume may discourage its careful inspection. A quick check of the control points' flags that distinguish full from horizontal from vertical control may, however, be warranted.
A nomenclature note pertains to the camera system parameters and the photo group's parameters. When the self-calibration options or GPS antenna offset options are selected, the printout listing will contain the specification of two switches: an updating switch and an exclusion switch. These flags reflect the Modifiable and Adjust switches of the model parameters, respectively. If, for instance, the GPS antennas component's were set to be adjustable, but not modifiable, then the printout-listing would indicate an Exclusion Switch Off and the Update Switch Off. The Exclusion switch behaves in a manner converse to the Adjust Switch: when a parameter is to be excluded from adjustment, its Exclusion Switch is On, while also being set to Do not adjust.
The final section of the input data listing is a set of error warnings. GIANT searches for and reports about the following five conditions, along with the corresponding frame, image or control point information to identify the violating item:
If GIANT detects none of these conditions, the section will not appear. All of these conditions justify an edit of the appropriate file(s) of the input data stream and a subsequent run of GIANT with the edited data.
|5.2.3 Per-Iteration Adjustment Summary|
| This section appears regardless of the
configuration of input and output switches. The specific numbers presented on a
per-iteration basis for the corrections to the frame positions and attitudes do not lend
themselves to intuitive analysis. In a general sense they should collectively decrease. It
could happen that some individual values increase while others decrease over the course of
the iterations. Theoretically, however, under error-free adjustment conditions the
corrections should eventually converge to zeroes. It is not a cause for alarm if this does
Certain things should be consciously noted from this section of the printout listing. The user should first check to see if the number of iterations reached the maximum allowable, as specified in Section 3.7. If this is the case, the adjustment may not have had sufficient time to converge to its final solution. If the number of iterations is less than the maximum specified, the iteration has either diverged or converged to a solution, although there is no assurance it has converged to a correct solution. Only a thorough consideration of other statistical measures in the printout listing will permit the user to ascertain if the final, convergent solution is an acceptable one.
The provisional weighted sum of squares is printed for each iteration. It is not necessarily a cause for concern, if during an iteration, this number increases. If it increases for two consecutive iterations, however, GIANT considers that there is a problem with the adjustment and terminates. In such a case, the input data stream should be carefully re-checked for accuracy of its content. If all verification tests passed successfully, then file structure is unlikely to be a cause of the divergence. Under error-free adjustment conditions, this number would, given a sufficient number of iterations, eventually be expected to converge to some constant value. The sufficient number of iterations may exceed the maximum number as described in the previous paragraph, and is unlikely to be the same from one project to the next. It is important to bear in mind that GIANT's definition of a convergent adjustment is one in which the change (either increase or decrease) in the provisional weighted sum of squares is less than the percentage specified under Convergence Criteria as described in Section 3.7.
|5.2.4 Statistical Information|
|The GIANT printout listing supplies several statistical
measures to aid the user in assessing the quality of the bundle adjustment or to locate
errors, should they be present. This discussion of the statistical measures will proceed
according to the order in which they are encountered in the printout-listing file.
The first statistical measure presented is the Triangulated Ground Point Residuals. This section will be present only if in the adjustment there were image residuals that exceeded the user-specified threshold. Section 3.6 discussed the setting of this threshold value. This information is generally useful in the location of bad image measurements. Presumably, the user will select a threshold whose value that, when exceeded, is likely to be indicative of a suspect image measurement. The threshold value should be a measure of what is judged to be an anomalous violation of the organization's measuring precision. For every image residual that exceeds the threshold, GIANT will list the corresponding ground point and all of the frames on which the image was measured. The violating readings will appear beneath the identification of the frame on which the reading was made. Numerous conditions can be detected from this information. Violations of several images on a specific frame could suggest errors related to the frame. Repeated violations by the same image might suggest an error in the ground control file. The careful inspection of this information is strongly advised during the assessment of an adjustment.
Aerotriangulation Statistics appear next in the printout listing. These statistics contain the specification of the weighted sums of squares of residuals, itemized according to observation type: auxiliary parameters (self-calibration and GPS antenna positions); photo positions and attitudes; ground point coordinates; image coordinates. Generally speaking, the image measurements make the largest contribution simply because they are the largest in number. Specific guidance for interpreting this information is not possible. Rather, the user will, with experience, gain a sense for what contributions might be expected for the different components and be able to recognize anomalies. An anomalous contribution would strongly indicate a concern with the corresponding set of observations. The degree of freedom (redundancy) is given, followed by the A posteriori variance of unit weight and standard deviation of unit weight. The variance is the quotient of the total weighted sum of squares and the degrees of freedom. It is often judged to be the single number that encapsulates the quality of the adjustment. Conventionally, an a posteriori variance of unit weight close to one has been judged to indicate a successful adjustment. While there is some statistical defense to this thinking, it is considered a better advice for the user to study all available statistical measures to get a fully integrated overview of the adjustment's behavior before deciding upon the quality of the adjustment.
Special note should be made of the standard deviation of unit weight. It will be used to scale all of the standard deviations and covariance matrices presented in the balance of the printout-listing, if the user specified use of the computed unit variance. See Section 3.6 to review the effects and implications of this selection. In each of the sections where adjusted parameters are presented (Section 5.2.5 below) either standard deviations or covariance matrices always accompany adjusted parameters. When a covariance matrix is given, the standard deviation can be determined from the square root of the corresponding diagonal element of the matrix. For instance, in the covariance matrix of the Triangulated Camera Stations, the square root of the first diagonal element is the standard deviation of the first coordinate (longitude or X) of the triangulated camera station. The square root of the second diagonal element is the standard deviation of the second coordinate (latitude or Y) of the triangulated camera station, and so on. As described in Section 3.6, the standard deviation should be considered to characterize the uncertainty in the calculated value of the parameter. Standard deviations are generally thought to be precision, or internal accuracy measures. Small standard deviations do not necessarily indicate accuracy.
For the two sets of adjusted parameters, Triangulated Camera Stations and Triangulated Ground Coordinates, GIANT presents Summary Statistics. These statistics give, for each general parameter class (camera station longitude, latitude, etc.) the average, maximum and root mean square (RMS) correction applied to the class of parameter. Careful inspection should be made of the maximum values, where large values may indicate an area of concern.
Whereas the standard deviations can be viewed as indicators of precision, the final section of the printout-listing file contains the Corrections Applied to Ground Control, which can be considered an indicator of accuracy. This information is sometimes also referred to as "Goodness of Fit" or "Misclosure". Since ground control points have known coordinates, they can be judged as true or error-free values. For these points, GIANT can apply the adjusted camera station parameters to the image measurements and compute coordinates for these points. Differences between the computed values and the known values can reflect the difference between the adjustment and reality (assuming the image measurements have no errors). Large values in Corrections to Ground Control should be investigated as indicating problems with ground control coordinates.
|5.2.5 Presentation of Adjusted Parameters|
|The final component of the GIANT printout-listing file is the presentation of the adjusted parameters. There can be up to four sets of adjusted parameters presented here in order of their appearance in the listing: Self-Calibration Camera Models, GPS Antenna Offsets, Triangulated Camera Stations, Triangulated Ground Points. As reported earlier, standard deviations or covariance matrices are reported with all adjusted parameters when error propagation has been requested. In and of themselves adjusted values of parameters offer little in the way of assessing the quality of the adjustment or assistance in error detection.|