Rapid, low -cost photogrammetry to monitor volcanic eruptions: an example
from Mount St. Helens, Washington, USA: Appendix 1.
Angela K. Diefenbach ∙ Juliet G. Crider ∙ Steve P. Schilling ∙ Daniel Dzurisin
Photogrammetric Analysis using PhotoModeler Pro v. 5
Camera Calibration
The Nikon D70 camera used in this study was calibrated by means of the camera
calibrator, a built-in extension of the photogrammetric software. Camera calibration was
performed under standard procedure from the user manual and in the same conditions as
operational use in the field (i.e., same focal length setting). A gridded target provided with the
software package was projected onto a wall using a slide projector. The grid comprised 100
uniformly spaced black dots, aligned in columns and rows, with four of the dots on the outer
edges outlined by symbols, representative of control points within the target. The target was
photographed from four camera locations. At each location, a photograph was taken in landscape
view and then the camera was rotated 90 degrees and a portrait view was taken. Images were
input into the calibration extension and camera interior orientation parameters were delivered in
an output text file that reported the overall calibration performance and object accuracy
represented by average root mean square (RMS) residuals. The Nikon D70 camera calibration
adjustment was performed successfully for all sets of photographs, with acceptable residuals of
the control points. According to the software documentation, a project with a good calibration
has a final error under 0.15 and marking residual error under 1.0 pixel. Camera calibration for
the Nikon D70 produced a final error of 0.077 and an overall RMS or marking residual of 0.311
pixels. Given these calibration checks, the Nikon D70 calibration file provided a quantitatively
accurate description of the camera interior orientation parameters necessary for a successful
project.
Image Processing
For each photogrammetry model, 4 to 7 images were used. The images were chosen
based on percentage of overlap, optimum angle of convergence (i.e. the angle of difference
between camera positions, at the time of image acquisition, relative to one another) and area of
the lava dome captured. The optimum angle between camera stations is between 45 to 90
degrees. We found the lowest acceptable angle of convergence to be 20 degrees. Exterior
orientation (camera location parameters) during image acquisition was not required. The
software calculated the three spatial coordinates and the three orientation angles of each camera,
or each camera position at which an image was taken, through resection, with the use of
identified reference points and ground control points (GCPs) (approximately 10 combined) in the
overlapping photographs.
Generation of a three-dimensional model required knowledge of the relative and absolute
orientation of the images as well as measurement of the positions of points in each image.
Relative orientation determined the projective centers of the images in an arbitrary spatial
coordinate system by measurement of at least 6 homologous points (tie points). In order to tie the
photographs together in arbitrary space and give the three-dimensional model correct, relative
dimensions, tie points were selected and identified in all images. For the purpose of this study,
tie points were points that resided in every image involved in a project. Tie points differ from
reference points in that the latter are shared between two or more images and are not required to
be seen in every image. On the other hand, each tie point must be seen in every photograph of
the project. This step required the most time because varying camera locations and angles made
identification of corresponding points in photographs difficult. Tie points were referenced with
the reference tool to identify the corresponding tie points throughout a series of photographs.
Absolute orientation was achieved by measurement of a minimum of 3 GCPs. In order to
construct a three-dimensional model in geographic space from images it is essential to know the
relationship between each image and the reference Cartesian coordinate system. A minimum of
two planimetric and three elevation points are needed to define a datum (geographic coordinate
system), but more control points are desirable to lower overall project error by increasing
accuracy and precision. Ideal controls were points tying frames together and surrounding the
volume of interest. The use of GCPs located in the field by differential GPS provides the highest
accuracy for control within a project compared to other methods, i.e. topographic maps, EDM
measurements and DEMs. Schilling et al. (2008) established a network of GCPs from campaign
GPS deployments at Mount St. Helens for vertical photogrammetry and GPS spiders (helicopter
deployable GPS units) were deployed on the growing dome and deforming glacier to establish
positions and monitor deformation at the time oblique photography was taken. Unfortunately,
few sets of oblique photographs contained visible GPS stations. For consistency between photo
sets, suitable control points for this project were well-defined natural features, clearly identifiable
on the photographs and on independently-created high-resolution DEMs (2 m). The same four
GCPs were used in each project to provide consistency and to accurately define the datum.
After GCPs and tie points were selected and orientations set, the software produced a
bundle block adjustment of each project that resulted in an accurately referenced threedimensional model of the study area. Once relative and absolute orientation was achieved,
reference points (selection of identical points between image pairs) were added to make models
of the dome during successive dates. This process involved the manual selection of identical
points on numerous images (minimum of two images for each point) that encompassed the area
of interest. Measurement and referencing between photos was done manually with the help of
epipolar lines or auto-drive referencing (a form of semi-automated referencing). In this mode,
when the source and destination images are oriented, the cursor and image will automatically
jump to the expected location of the point in the destination image, allowing the execution of the
final measurement to be done manually with a certain amount of aid provided by the software.
Reference point selection to construct DEMs of the evolving dome involved two steps:
(1) reference points were identified that outlined the perimeter of the area of interest, (2) point
clouds were created that filled in the area of interest. Qualitative review of each model was
intermittently checked in the 3D viewer tool provided with the software, which allowed the
operator to select and delete significant outliers in the models as well as pinpoint areas that
needed an increase in point density. The number of reference points and photographs used in
each DEM varied (Table). DEMs with high point densities were the result of one or more of the
following four conditions: (1) low flying altitude when photographs were taken, resulting in a
higher pixel resolution, which facilitated identification of common points, (2) at the date the
photographs were taken, the dome had more complex topography, requiring more points to
provide an accurate representation, (3) atmospheric interference (steaming at the vent) was
minimal, exposing the entire dome, or (4) photographs captured the entire growing dome.
Post-processing of the photogrammetry models for terrain models and volume
calculations was completed in ArcGIS 9.
Table. Dates of oblique photography with associated number of points and photographs used to
build each DEM.
Date of oblique
photography
11/20/2004
11/29/2004
01/03/2005
02/01/2005
02/22/2005
03/11/2005
04/10/2005
05/12/2005
06/15/2005
10/12/2005
05/30/2006
04/20/2007
Number of points used
in model
212
412
284
566
603
484
993
1795
798
580
415
380
Number of photographs
used in model
6
7
5
7
6
6
6
7
7
5
5
4
Note: Since the time of this writing, new versions of PhotoModeler Pro have been released.
Some new versions contain automated reference point selection tools. The above methodology
relates to the specific application of this software (specifically v. 5) for the study at Mount St.
Helens volcano and does not replace any manuals provided by EOS Systems, Inc. or serve as an
endorsement of the PhotoModeler Pro software.