16.35. jitter_solve

The jitter_solve program takes as input several overlapping images and linescan and/or frame camera models in CSM format (such as for LRO NAC, CTX, HiRISE, Airbus Pleiades, DigitalGlobe, etc., Section 8.12) and adjusts each individual camera position and orientation in the linescan model to make them more consistent to each other and to the ground.

The goal is to reduce the effect of unmeasured perturbations in the linescan sensor as it acquires the data. This is quite analogous to what bundle_adjust does (Section 16.5), except that the latter tool has just a single position and orientation per camera, instead of a sequence of them.

Usage:

jitter_solve <images> <cameras> <input adjustments> \
  -o <output prefix> [options]

16.35.1. Ground constraints

Optimizing the cameras to reduce the jitter and make them self-consistent can result in the camera system moving away from the initial location or warping in any eventually produced DEM.

Hence, ground (and camera) constraints are very important. This tool uses several kinds of constraints. They are described below, and an example of comparing different ground constraints them is given in Section 16.35.7.

16.35.1.1. Intrinsic constraint

Triangulated ground points obtained from interest point matches are kept, during optimization, close to their initial values. This works well when the images have very good overlap. To use it, set a positive value to --tri-weight. An example is given in Section 16.35.6. See Section 16.35.14 for reference documentation.

16.35.1.2. Extrinsic constraint

This ties the triangulated ground points obtained from interest point matches to an external DEM, which may be at a lower resolution than the images. It is expected that this external DEM is well-aligned with the input cameras. This option is named --heights-from-dem, and it is controlled via --heights-from-dem-weight and --heights-from-dem-robust-threshold. How to perform alignment and use these options is shown in Section 16.35.5.

Only one of these two constraints can be used at a time. If both are specified, the intrinsic constraint will be used where the triangulated points are not above the provided DEM.

The intrinsic constraint is preferred. If desired to use the DEM constraint, specify a low weight and robust threshold (such as 0.05) and increase these only if desired to tighten the constraint.

16.35.1.3. Anchor points

The anchor points constraint also use a well-aligned external DEM, with important differences. These points are created based on pixels that are uniformly distributed over each image, not just where the images overlap, and can even go beyond the first and last image line. This ensures that the optimized poses do not oscillate where the images overlap very little or not at all.

This constraint works by projecting rays to the ground from the chosen uniformly distributed pixels, finding the anchor points where the rays intersect the DEM, then adding to the cost function to optimize reprojection errors (Section 12) for the anchor points. This complements the reprojection errors from triangulated interest point matches, and the external DEM constraint (if used).

Anchor points are strongly encouraged either with an intrinsic constraint or an external DEM constraint. Their number should be similar to the number of interest points, and it should be large if the poses are resampled very finely (see next section).

Anchor points can be used only with linescan cameras, so without frame cameras as inputs (Section 16.35.11).

The relevant options are --num-anchor-points, --num-anchor-points-per-tile, --anchor-weight, --anchor-dem, and --num-anchor-points-extra-lines. An example is given in Section 16.35.6.

16.35.2. Camera constraints

Jitter is believed to be caused by vibrations in the linescan camera as it acquires the image. If that is the case, the camera positions are likely accurate, and can be constrained to not move much, while the orientations can move more. This can be achieved by setting the option --translation-weight to a value on the order of 1.0 to 100.0, while keeping --rotation-weight at 0 or some other small value. These options are described in Section 16.35.14. See an example of using the translation weight in Section 16.35.7.

16.35.3. Resampling the poses

Often times, the number of tabulated camera positions and orientations in the CSM file is very small. For example, for Airbus Pleiades, the position is sampled every 30 seconds, while acquiring the whole image can take only 1.6 seconds. For CTX the opposite problem happens, the orientations are sampled too finely, resulting in too many variables to optimize.

Hence, it is strongly suggested to resample the provided positions and orientations before the solver optimizes them. Use the options: --num-lines-per-position and --num-lines-per-orientation. The estimated number of lines per position and orientation will be printed on screen, before and after resampling.

In the two examples below drastically different sampling rates will be used. Inspection of residual files (Section 16.35.13), and of triangulation errors (Section 11.4.1) and DEM differences after solving for jitter (Section 16.35.6) can help decide the sampling rate.

16.35.4. Interest point matches

Since solving for jitter is a fine-grained operation, modifying many positions and orientations along the satellite track, many dense and uniformly distributed interest points are necessary. It is suggested to create these with stereo, with the option --num-matches-from-disparity. An example is shown in Section 16.35.5.

The most accurate interest points are obtained when the images are mapprojected. This is illustrated in Section 16.35.6. The produced interest point matches will be, however, between the original, unprojected images, as expected by the solver.

If there are more than two images, it is good to have a lot of triplets among the interest point matches (features that show up in at least three images). Otherwise, the triangulated surface may decouple into disjoint pairwise triangulated surfaces (though this is less likely to happen with the --heights-from-dem option).

Plenty of triplets are usually generated with the option --num-matches-from-disparity, if this is invoked with stereo between first and second image, first and third, second and third, etc. The image that overlaps the most with other images should be used as the first one.

It is suggested to call jitter_solve with a large value of --max-pairwise-matches, such as 1000000, to ensure that all interest point matches are used, especially the triplets.

To determine if a triangulated point corresponds to a triplet of interest point matches, examine the produced *-pointmap.csv files. Their format is described in Section 16.35.13.

The dense interest point matches need to be copied from each output stereo directory to a location and with a naming convention such that they can be used by jitter_solve. That is illustrated in Section 16.35.6.

16.35.5. Example 1: CTX images on Mars

A CTX stereo pair will be used which has quite noticeable jitter. See Section 16.35.5.5 for a discussion of multiple images.

16.35.5.1. Input images

The pair consists of images with ids:

J03_045820_1915_XN_11N210W
K05_055472_1916_XN_11N210W

See Section 8.3 for how to prepare the image files and Section 8.12.2.1 for how to create CSM camera models.

All produced images and cameras were stored in a directory named img.

16.35.5.2. Reference datasets

The MOLA dataset from:

https://ode.rsl.wustl.edu/mars/datapointsearch.aspx

is used for alignment. The data for the following (very generous) longitude-latitude extent was fetched: 146E to 152E, and 7N to 15N. The obtained CSV file was saved as mola.csv.

A gridded DEM produced from this unorganized set of points is shipped with the ISIS data. It is gridded at 463 meters per pixel, which is quite coarse compared to CTX images, which are at 6 m/pixel, but it is good enough to constrain the cameras when solving for jitter. A clip can be cut out of it with the command:

gdal_translate -co compress=lzw -co TILED=yes              \
 -co INTERLEAVE=BAND -co BLOCKXSIZE=256 -co BLOCKYSIZE=256 \
 -projwin -2057237.6 1077503.1 -1546698.4 275566.33        \
 $ISISDATA/base/dems/molaMarsPlanetaryRadius0005.cub       \
 ref_dem_shift.tif

This one has a 190 meter vertical shift relative to the preferred Mars radius of 3396190 meters, which can be removed as follows:

image_calc -c "var_0-190" -d float32 ref_dem_shift.tif \
  -o ref_dem.tif

As a sanity check, one can take the absolute difference of this DEM and the MOLA csv file as:

geodiff --absolute --csv-format 1:lon,2:lat,5:radius_m \
  mola.csv ref_dem.tif

This will give a median difference of 3 meters, which is about right, given the uncertainties in these datasets.

16.35.5.3. Uncorrected DEM creation

Bundle adjustment is run first:

bundle_adjust                               \
  --ip-per-image 20000                      \
  --max-pairwise-matches 1000000            \
  --tri-weight 0.05                         \
  --tri-robust-threshold 0.1                \
  --camera-weight 0                         \
  --remove-outliers-params '75.0 3.0 20 20' \
  img/J03_045820_1915_XN_11N210W.cal.cub    \
  img/K05_055472_1916_XN_11N210W.cal.cub    \
  img/J03_045820_1915_XN_11N210W.cal.json   \
  img/K05_055472_1916_XN_11N210W.cal.json   \
  -o ba/run

The triangulation weight was used to help the cameras from drifting. Outlier removal was allowed to be more generous (hence the values of 20 pixels above) as perhaps due to jitter some triangulated points obtained from interest point matches may not project perfectly in the cameras.

Here we chose to use a large value for --max-pairwise-matches and we will do the same when solving for jitter below. That is because jitter-solving is a finer-grained operation than bundle adjustment, and a lot of interest point matches are needed.

Stereo is run next. The local_epipolar alignment (Section 6.1) here did a flawless job, unlike affineepipolar alignment which resulted in some blunders.

parallel_stereo                           \
  --bundle-adjust-prefix ba/run           \
  --stereo-algorithm asp_mgm              \
  --num-matches-from-disparity 40000      \
  --alignment-method local_epipolar       \
  img/J03_045820_1915_XN_11N210W.cal.cub  \
  img/K05_055472_1916_XN_11N210W.cal.cub  \
  img/J03_045820_1915_XN_11N210W.cal.json \
  img/K05_055472_1916_XN_11N210W.cal.json \
  stereo/run
point2dem --errorimage stereo/run-PC.tif

Note how above we chose to create dense interest point matches from disparity. They will be used to solve for jitter. We used the option --num-matches-from-disparity. See Section 16.35.4 for more details.

See Section 6 for a discussion about various speed-vs-quality choices for stereo. Close to the poles a polar stereographic projection may be preferred in point2dem (Section 16.52).

This DEM was aligned to MOLA and recreated, as:

pc_align --max-displacement 400           \
  --csv-format 1:lon,2:lat,5:radius_m     \
  stereo/run-DEM.tif mola.csv             \
  --save-inv-transformed-reference-points \
  -o stereo/run-align
point2dem stereo/run-align-trans_reference.tif

The value in --max-displacement may need tuning (Section 16.49).

This transform was applied to the cameras, to make them aligned to MOLA (Section 16.49.14):

bundle_adjust                                                \
  --input-adjustments-prefix ba/run                          \
  --initial-transform stereo/run-align-inverse-transform.txt \
  img/J03_045820_1915_XN_11N210W.cal.cub                     \
  img/K05_055472_1916_XN_11N210W.cal.cub                     \
  img/J03_045820_1915_XN_11N210W.cal.json                    \
  img/K05_055472_1916_XN_11N210W.cal.json                    \
  --apply-initial-transform-only                             \
-o ba_align/run

16.35.5.4. Solving for jitter

Then, jitter was solved for, using the aligned cameras:

jitter_solve                               \
  img/J03_045820_1915_XN_11N210W.cal.cub   \
  img/K05_055472_1916_XN_11N210W.cal.cub   \
  img/J03_045820_1915_XN_11N210W.cal.json  \
  img/K05_055472_1916_XN_11N210W.cal.json  \
  --input-adjustments-prefix ba_align/run  \
  --max-pairwise-matches 1000000           \
  --match-files-prefix stereo/run-disp     \
  --num-lines-per-position    1000         \
  --num-lines-per-orientation 1000         \
  --max-initial-reprojection-error 20      \
  --translation-weight 0                   \
  --rotation-weight 0                      \
  --heights-from-dem ref_dem.tif           \
  --heights-from-dem-weight 0.05           \
  --heights-from-dem-robust-threshold 0.05 \
  --num-iterations 50                      \
  --anchor-weight 0                        \
  --tri-weight 0                           \
-o jitter/run

It was found that using about 1000 lines per pose (position and orientation) sample gave good results, and if using too few lines, the poses become noisy. Dense interest point matches appear necessary for a good result, though perhaps the number produced during stereo could be lowered.

The constraint relative to the reference DEM is needed, to make sure the DEM produced later agrees with the reference one. Otherwise, the final solution may not be unique, as a long-wavelength perturbation consistently applied to all obtained camera trajectories may work just as well.

Here we set --rotation-weight 0 and --translation-weight 0. These are camera constraints, and at least a positive position (translation) constraint is normally recommended. See Section 16.35.2.

The model states (Section 8.12.6) of optimized cameras are saved with names like:

jitter/run-*.adjusted_state.json

Then, stereo can be redone, just at the triangulation stage, which is much faster than doing it from scratch. The optimized cameras were used:

parallel_stereo                                                 \
  --prev-run-prefix stereo/run                                  \
  --stereo-algorithm asp_mgm                                    \
  --alignment-method local_epipolar                             \
  img/J03_045820_1915_XN_11N210W.cal.cub                        \
  img/K05_055472_1916_XN_11N210W.cal.cub                        \
  jitter/run-J03_045820_1915_XN_11N210W.cal.adjusted_state.json \
  jitter/run-K05_055472_1916_XN_11N210W.cal.adjusted_state.json \
  stereo_jitter/run
  point2dem --errorimage stereo_jitter/run-PC.tif

To validate the results, first the triangulation (ray intersection) error (Section 16.52) was plotted, before and after solving for jitter. These were colorized as:

colormap --min 0 --max 10 stereo/run-IntersectionErr.tif
colormap --min 0 --max 10 stereo_jitter/run-IntersectionErr.tif

The result is below.

Fig. 16.3 The colorized triangulation error (max shade of red is 10 m) before and after optimization for jitter.

Then, the absolute difference was computed between the sparse MOLA dataset and the DEM after alignment and before solving for jitter, and the same was done with the DEM produced after solving for it:

geodiff --absolute                                  \
  --csv-format 1:lon,2:lat,5:radius_m               \
  stereo/run-align-trans_reference-DEM.tif mola.csv \
  -o stereo/run

geodiff --absolute                                  \
  --csv-format 1:lon,2:lat,5:radius_m               \
  stereo_jitter/run-DEM.tif mola.csv                \
  -o stereo_jitter/run

Similar commands are used to find differences with the reference DEM:

geodiff --absolute ref_dem.tif                \
  stereo/run-align-trans_reference-DEM.tif -o \
  stereo/run
colormap --min 0 --max 20 stereo/run-diff.tif

geodiff --absolute ref_dem.tif                \
  stereo_jitter/run-DEM.tif                   \
  -o stereo_jitter/run
colormap --min 0 --max 20 stereo_jitter/run-diff.tif

Plot with:

stereo_gui --colorize --min 0 --max 20 \
   stereo/run-diff.csv                 \
   stereo_jitter/run-diff.csv          \
   stereo/run-diff_CMAP.tif            \
   stereo_jitter/run-diff_CMAP.tif     \
   stereo_jitter/run-DEM.tif           \
   ref_dem.tif

DEMs can later be hillshaded.

Fig. 16.4 From left to right are shown colorized absolute differences of (a) jitter-unoptimized but aligned DEM and MOLA (b) jitter-optimized DEM and MOLA (c) unoptimized DEM and reference DEM (d) jitter-optimized DEM and reference DEM. Then, (e) hillshaded optimized DEM (f) hillshaded reference DEM . The max shade of red is 20 m difference.

It can be seen that the banded systematic error due to jitter is gone, both in the triangulation error maps and DEM differences. The produced DEM still disagrees somewhat with the reference, but we believe that this is due to the reference DEM being very coarse, per plots (e) and (f) in the figure.

16.35.5.5. Using multiple images

At a future time an analysis can be done where more images for that area are used. The following overlap with the above pair quite well:

B19_016902_1913_XN_11N210W
F04_037367_1929_XN_12N211W
N14_067737_1928_XI_12N210W
P06_003347_1894_XI_09N210W

Bundle adjustment can be run on all of them, and pairwise DEMs can be created from the pairs with a convergence angle between 10 and 30 degrees (bundle_adjust saves the list of convergence angles).

Then, the obtained DEMs could be merged with dem_mosaic, which will hopefully result in a solid high-resolution reference DEM due to jitter canceling out. Then, jitter could be solved either simultaneously for all these, or in pairs, and the logic in the earlier example could be repeated, but with a higher quality reference DEM.

See Section 16.35.4 for how to create interest point matches when taking into account that multiple images are used.

16.35.6. Example 2: WorldView-3 DigitalGlobe images on Earth

Jitter was successfully solved for a pair of WorldView-3 images over a mountainous site in Grand Mesa, Colorado, US.

This is a much more challenging example than the earlier one for CTX, because:

• Images are much larger, at 42500 x 71396 pixels, compared to 5000 x 52224 pixels for CTX.

• The jitter appears to be at much higher frequency, necessitating using 50 image lines for each position and orientation to optimize rather than 1000.

• Many dense interest point matches and anchor points are needed to capture the high-frequency jitter Many anchor points are needed to prevent the solution from becoming unstable at earlier and later image lines.

• The terrain is very steep, which introduces some extraneous signal in the problem to optimize.

We consider a datatset with two images named 1.tif and 2.tif, and corresponding camera files 1.xml and 2.xml, having the exact DigitalGlobe linescan model.

16.35.6.1. Bundle adjustment

Bundle adjustment was invoked first to reduce any gross errors between the cameras:

bundle_adjust                               \
  -t dg                                     \
  --ip-per-image 10000                      \
  --tri-weight 0.1                          \
  --tri-robust-threshold 0.1                \
  --camera-weight 0                         \
  --remove-outliers-params '75.0 3.0 20 20' \
  1.tif 2.tif                               \
  1.xml 2.xml                               \
  -o ba/run

A lot of interest points were used, and the outlier filter threshold was generous, since because of trees and shadows in the images likely some interest points may not be too precise but they could still be good.

16.35.6.2. Mapprojection

Because of the steep terrain, the images were mapprojected onto the Copernicus 30 m DEM (Section 6.1.7.1). We name that DEM ref.tif. (Ensure the DEM is relative to WGS84 and not EGM96, and convert if necessary; see Section 6.1.7.2.)

Fig. 16.5 The Copernicus 30 DEM for the area of interest. Some of the topographic signal, including cliff edges and trees will be noticeable in the error images produced below.

Mapprojection of the two images (Section 6.1.7):

proj="+proj=utm +zone=13 +datum=WGS84 +units=m +no_defs"
for i in 1 2; do
  mapproject -t rpc                         \
  --nodes-list nodes_list.txt               \
  --tr 0.4                                  \
  --t_srs "$proj"                           \
  --bundle-adjust-prefix ba/run             \
  ref.tif ${i}.tif ${i}.xml ${i}.map.ba.tif
done

16.35.6.3. Stereo

Stereo was done with the asp_mgm algorithm. It was very important to use --subpixel-mode 9. Using --subpixel-mode 1 was resulting in subpixel artifacts which were dominating the jitter. Mode 3 (or 2) would have worked as well but it is a lot slower. It also appears that it is preferable to use mapprojected images than some other alignment methods as those would result in more subpixel artifacts which would obscure the jitter signal which we will solve for.

The option --max-disp-spread 100 was used because the images had many clouds (Section 5.4).

A large number of dense matches from stereo disparity will be created, to be used later to solve for jitter.

parallel_stereo                                \
  -t dgmaprpc                                  \
  --max-disp-spread 100                        \
  --nodes-list nodes_list.txt                  \
  --ip-per-image 10000                         \
  --stereo-algorithm asp_mgm                   \
  --subpixel-mode 9                            \
  --processes 6                                \
  --alignment-method none                      \
  --num-matches-from-disparity 60000           \
  --keep-only '.exr L.tif F.tif PC.tif .match' \
  1.map.tif 2.map.tif 1.xml 2.xml              \
  run_1_2_map/run                              \
  ref.tif

proj="+proj=utm +zone=13 +datum=WGS84 +units=m +no_defs"
point2dem --tr 0.4 --t_srs "$proj" --errorimage \
  run_1_2_map/run-PC.tif

16.35.6.4. Alignment

Align the stereo DEM to the reference DEM:

pc_align --max-displacement 100           \
  run_1_2_map/run-DEM.tif ref.tif         \
  --save-inv-transformed-reference-points \
  -o align/run
proj="+proj=utm +zone=13 +datum=WGS84 +units=m +no_defs"
point2dem --tr 0.4 --t_srs "$proj" align/run-trans_reference.tif

It is suggested to hillshade and inspect the obtained DEM and overlay it onto the hillshaded reference DEM. The geodiff command (Section 16.23) can be used to take their difference.

Apply the alignment transform to the bundle-adjusted cameras, to align them with the reference terrain:

bundle_adjust                                         \
  --input-adjustments-prefix ba/run                   \
  --match-files-prefix ba/run                         \
  --skip-matching                                     \
  --initial-transform align/run-inverse-transform.txt \
  1.tif 2.tif 1.xml 2.xml                             \
  --apply-initial-transform-only                      \
  -o align/run

16.35.6.5. Solving for jitter

Copy the produced dense interest point matches for use in solving for jitter:

mkdir -p dense
cp run_1_2_map/run-disp-1.map__2.map.match \
  dense/run-1__2.match

See Section 16.35.4 for a longer explanation regarding interest point matches.

Solve for jitter:

jitter_solve                           \
  1.tif 2.tif                          \
  1.xml 2.xml                          \
  --input-adjustments-prefix align/run \
  --match-files-prefix dense/run       \
  --num-iterations 10                  \
  --max-pairwise-matches 1000000       \
  --max-initial-reprojection-error 10  \
  --robust-threshold 0.2               \
  --tri-weight 0.1                     \
  --tri-robust-threshold 0.1           \
  --translation-weight 0               \
  --rotation-weight 0                  \
  --num-lines-per-position    50       \
  --num-lines-per-orientation 50       \
  --num-anchor-points 40000            \
  --num-anchor-points-extra-lines 500  \
  --anchor-dem ref.tif                 \
  --anchor-weight 1.0                  \
-o jitter/run

The robust threshold was set to 0.2 because the jitter signal is rather weak. This allows the optimization to focus on this signal and not on the larger errors due to the steep terrain.

Here we set --rotation-weight 0 and --translation-weight 0. These are camera constraints, and at least a positive position (translation) constraint is normally recommended. See Section 16.35.2.

Fig. 16.6 The pixel reprojection errors per triangulated point (first row) and per anchor point (second row) before and after (left and right) solving for jitter. Blue shows an error of 0, and red is an error of at least 0.3 pixels.

It can be seen in Fig. 16.6 that after optimization the jitter (oscillatory pattern) goes away, but the errors per anchor point do not increase much. The remaining red points are because of the steep terrain. See Section 16.35.13 for description of these output files and how they were plotted.

16.35.6.6. Redoing mapprojection and stereo

(See also section Section 16.35.6.7 for a more efficient approach in ASP 3.3.0 or later.)

Mapproject the optimized CSM cameras:

proj="+proj=utm +zone=13 +datum=WGS84 +units=m +no_defs"
for i in 1 2; do
  mapproject -t csm                     \
    --nodes-list nodes_list.txt         \
    --tr 0.4 --t_srs "$proj"            \
    ref.tif ${i}.tif                    \
    jitter/run-${i}.adjusted_state.json \
    ${i}.jitter.map.tif
done

Run stereo:

parallel_stereo                                        \
  --max-disp-spread 100                                \
  --nodes-list nodes_list.txt                          \
  --ip-per-image 20000                                 \
  --stereo-algorithm asp_mgm                           \
  --subpixel-mode 9                                    \
  --processes 6                                        \
  --alignment-method none                              \
  --keep-only '.exr L.tif F.tif PC.tif map.tif .match' \
  1.jitter.map.tif 2.jitter.map.tif                    \
  jitter/run-1.adjusted_state.json                     \
  jitter/run-2.adjusted_state.json                     \
  stereo_jitter/run                                    \
  ref.tif

point2dem --tr 0.4 --t_srs "$proj"                     \
  --errorimage                                         \
  stereo_jitter/run-PC.tif

16.35.6.7. Reusing a previous run

In ASP 3.3.0 or later, the mapprojection need not be redone, and stereo can resume at the triangulation stage (Section 6.1.7.8). This saves a lot of computing. The commands in the previous section can be replaced with:

parallel_stereo                                        \
  --max-disp-spread 100                                \
  --nodes-list nodes_list.txt                          \
  --ip-per-image 20000                                 \
  --stereo-algorithm asp_mgm                           \
  --subpixel-mode 9                                    \
  --processes 6                                        \
  --alignment-method none                              \
  --keep-only '.exr L.tif F.tif PC.tif map.tif .match' \
  --prev-run-prefix run_1_2_map/run                    \
  1.map.tif 2.map.tif                                  \
  jitter/run-1.adjusted_state.json                     \
  jitter/run-2.adjusted_state.json                     \
  stereo_jitter/run                                    \
  ref.tif

point2dem --tr 0.4 --t_srs "$proj"                     \
  --errorimage                                         \
  stereo_jitter/run-PC.tif

Note how we used the old mapprojected images 1.map.tif and 2.map.tif, the option --prev-run-prefix pointing to the old run, while the triangulation is done with the new jitter-corrected cameras.

16.35.6.8. Validation

The geodiff command (Section 16.23) can be used to take the absolute difference of the aligned DEM before jitter correction and the one after it:

geodiff --float --absolute align/run-trans_reference-DEM.tif \
  stereo_jitter/run-DEM.tif -o stereo_jitter/run

See Fig. 16.7 for results.

Fig. 16.7 The colorized triangulation error (Section 11.4.1) before and after solving for jitter, and the absolute difference of the DEMs before and after solving for jitter (left-to-right). It can be seen that the oscillatory pattern in the intersection error is gone, and the DEM changes as a result. The remaining signal is due to the steep terrain, and is rather small.

16.35.7. Example 3: Airbus Pleiades

In this section we will solve for jitter with Pleiades linescan cameras. We will investigate the effects of two kinds of ground constraints: --tri-weight and --heights-from-dem (Section 16.35.1). The first constraint tries to keep the triangulated points close to where they are, and the second tries to tie them to a reference DEM. Note that if these are used together, the first one will kick in only in regions where there is no coverage in the provided DEM.

In both cases we use a somewhat strong camera position constraint (--translation-weight) as it is believed that it is vibrations in camera orientations which cause the jitter.

The conclusion is that if the two kinds of ground constraints are weak, and the reference DEM is decent, the results are rather similar. Likely the intrinsic --tri-weight constraint is preferred, unless desired to pull the solution towards the reference DEM. Some user judgment is needed in choosing the type of constraint and its weight, depending on the circumstances.

16.35.7.1. Creation of terrain model

The site used is Grand Mesa, as in Section 16.35.6, and the two recipes also have similarities.

First, a reference DEM (Copernicus) for the area is fetched, and adjusted to be relative to WGS84, creating the file ref-adj.tif (Section 6.1.7.1).

Let the images be called 1.tif and 2.tif, with corresponding Pleiades exact linescan cameras 1.xml and 2.xml. Since the GSD specified in these files is about 0.72 m, this value is used in mapprojection of both images (Section 6.1.7):

proj="+proj=utm +zone=13 +datum=WGS84 +units=m +no_defs"
  mapproject --processes 4 --threads 4 \
  --tr 0.72 --t_srs "$proj"            \
  --nodes-list nodes_list.txt          \
  ref-adj.tif 1.tif 1.xml 1.map.tif

and same for the other image.

Since the two mapprojected images agree very well with the hillshaded reference DEM when overlaid in stereo_gui (Section 16.64), no bundle adjustment was used.

Stereo was run:

outPrefix=stereo_map_12/run
parallel_stereo                      \
  --max-disp-spread 100              \
  --nodes-list nodes_list.txt        \
  --ip-per-image 10000               \
  --num-matches-from-disparity 90000 \
  --stereo-algorithm asp_mgm         \
  --subpixel-mode 9                  \
  --processes 6                      \
  --alignment-method none            \
  1.map.tif 2.map.tif                \
  1.xml 2.xml                        \
  $outPrefix                         \
  ref-adj.tif                        \

DEM creation:

proj="+proj=utm +zone=13 +datum=WGS84 +units=m +no_defs"
point2dem --t_srs "$proj" \
  --errorimage            \
  ${outPrefix}-PC.tif

Colorize the triangulation (ray intersection) error, and create some image pyramids for inspection later:

colormap --min 0 --max 1.0 ${outPrefix}-IntersectionErr.tif
stereo_gui --create-image-pyramids-only \
  --hillshade ${outPrefix}-DEM.tif
stereo_gui --create-image-pyramids-only \
  ${outPrefix}-IntersectionErr_CMAP.tif

Fig. 16.8 Left to right: One of the input images, the produced hillshaded DEM, and the reference Copernicus DEM.

It can be seen in Fig. 16.8 (center) that a small portion having snow failed to correlate. That is not a showstopper here. Perhaps adjusting the image normalization options in Section 17 may resolve this.

16.35.7.2. Correcting the jitter

The jitter can clearly be seen in Fig. 16.9 (left). There seem to be about a dozen oscillations. Hence, jitter_solve will be invoked with one position and orientation sample for each 500 image lines, which results in about 100 samples for these, along the satellite track. Note that earlier we used --num-matches-from-disparity 90000 which created about 300 x 300 dense interest point matches for these roughly square input images. These numbers usually need to be chosen with some care.

Copy the dense interest point matches found in stereo, using the convention expected later by jitter_solve:

mkdir -p matches
/bin/cp -fv stereo_map_12/run-disp-1.map__2.map.match \
  matches/run-1__2.match

See Section 16.35.4 for a longer explanation regarding interest point matches.

Solve for jitter with the intrinsic --tri-weight constraint. Normally, the cameras should be bundle-adjusted and aligned to the reference DEM, and then below the option --input-adjustments-prefix should be used, but in this case the initial cameras were accurate enough, so these steps were skipped.

jitter_solve                               \
  1.tif 1.tif                              \
  2.xml 2.xml                              \
  --match-files-prefix matches/run         \
  --num-iterations 10                      \
  --max-pairwise-matches 1000000           \
  --max-initial-reprojection-error 20      \
  --robust-threshold 0.5                   \
  --tri-weight 0.1                         \
  --tri-robust-threshold 0.1               \
  --num-lines-per-position    500          \
  --num-lines-per-orientation 500          \
  --num-anchor-points 40000                \
  --num-anchor-points-extra-lines 500      \
  --translation-weight 10.0                \
  --rotation-weight 0.0                    \
  --anchor-dem ref-adj.tif                 \
  --anchor-weight 0.1                      \
  -o jitter_tri/run

The translation weight is set to 10.0, which is rather high. This multiplies the differences of initial and optimized camera centers in the optimization problem, with no robust threshold, so this should not let the camera centers move much, giving a chance to the camera orientations to do most of the work. The rotation weight is set to 0.0, so the quaternions can move freely, subject to the ground and pixel reprojection error constraints. See also Section 16.35.2.

Next, we invoke the solver with the same initial data, but with a constraint tying to the reference DEM, with the option --heights-from-dem ref-adj.tif. Since the difference between the created stereo DEM and the reference DEM is on the order of 5-10 meters, we will use --heights-from-dem-weight 0.05 and --heights-from-dem-robust-threshold 0.05. The reference DEM weight times its uncertainty better be less 1.0, to make it comparable to pixel reprojection error or less.

The pixel reprojection error --robust-threshold value is 0.5, which is larger than the DEM constraint robust threshold used here, at 0.05. So, pixel reprojection errors will be given higher priority than errors to ground. Therefore, we want the solution to be first of all self-consistent, and only then consistency with the ground will be attempted.

Fig. 16.9 Stereo intersection error (Section 11.4.1) before solving for jitter (left), after solving for it with the --tri-weight constraint (middle) and with the --heights-from-dem constraint (right). Blue = 0 m, red = 1 m.

It can be seen in Fig. 16.9 that any of these constraints can work at eliminating the jitter.

Fig. 16.10 Absolute difference of the stereo DEMs before and after solving for jitter. Left: with the --tri-weight constraint. Right: with the --heights-from-dem constraint. Blue = 0 m, red = 1 m.

It is very instructive to examine how much the DEM changed as a result. It can be seen in Fig. 16.10 that the reference DEM constraint changes the result more. Likely, a smaller value of the weight for that constraint could have been used.

16.35.8. ASTER cameras

ASTER (Section 8.17) is a very good testbed for studying jitter because there are millions of free images over a span of 20 years, with many over the same location, and the images are rather small, on the order of 4,000 - 5,000 pixels along each dimension.

16.35.8.1. Setup

In this example we worked on a rocky site in Egypt with a latitude 24.03562 degrees and longitude of 25.85006 degrees. Dozens of cloud-free stereo pairs are available here. The jitter pattern, including its frequency, turned out to be quite different in each the stereo pair we tried, but the solver was able to minimize it in all cases.

Fetch and prepare the the data as documented in Section 8.17.1. Here we will work with dataset AST_L1A_00301062002090416_20231023221708_3693.

A reference Copernicus DEM can be downloaded per Section 6.1.7.1. Use dem_geoid to convert the DEM to be relative to WGS84.

16.35.8.2. Initial stereo and alignment

We will call the two images in an ASTER stereo pair out-Band3N.tif and out-Band3B.tif. This is the convention used by aster2asp (Section 16.2), and instead of out any other string can be used. The corresponding cameras are out-Band3N.xml and out-Band3B.xml. The reference Copernicus DEM relative to WGS84 is ref.tif.

Bundle adjustment:

bundle_adjust -t aster          \
  --aster-use-csm               \
  --camera-weight 0.0           \
  --tri-weight 0.1              \
  --tri-robust-threshold 0.1    \
  --num-iterations 50           \
  out-Band3N.tif out-Band3B.tif \
  out-Band3N.xml out-Band3B.xml \
  -o ba/run

Not using -t aster will result in RPC cameras being used, which would lead to wrong results. We used the option --aster-use-csm. This saves the adjusted cameras in CSM format (Section 8.12.6), which is needed for the jitter solver. Then the produced .adjust files should not be used as they save the adjustments only.

Stereo was done with mapprojected images. The reference DEM was blurred a little as it is at the resolution of the images, and then any small misalignment between the images and the DEM may result in artifacts:

dem_mosaic --dem-blur-sigma 2 ref.tif -o ref_blur.tif

Mapprojection in local stereographic projection:

proj='+proj=stere +lat_0=24.0275 +lon_0=25.8402 +k=1 +x_0=0 +y_0=0 +datum=WGS84 +units=m +no_defs'
mapproject -t csm                       \
 --tr 15 --t_srs "$proj"                \
  ref_blur.tif out-Band3N.tif           \
  ba/run-out-Band3N.adjusted_state.json \
  out-Band3N.map.tif

The same command is used for the other image. Both must use the same resolution in mapprojection (option --tr).

It is suggested to overlay and inspect in stereo_gui (Section 16.64) the produced images and the reference DEM and check for any misalignment or artifacts. ASTER is quite well-aligned to the reference DEM.

Stereo with mapprojected images (Section 6.1.7) and DEM generation is run. Here the asp_mgm algorithm is not used as it smears the jitter signal:

parallel_stereo                         \
  --stereo-algorithm asp_bm             \
  --subpixel-mode 1                     \
  --max-disp-spread 100                 \
  --num-matches-from-disparity 100000   \
  out-Band3N.map.tif out-Band3B.map.tif \
  ba/run-out-Band3N.adjusted_state.json \
  ba/run-out-Band3B.adjusted_state.json \
  stereo_bm/run                         \
  ref_blur.tif

point2dem --errorimage --t_srs "$proj" \
  --tr 15 stereo_bm/run-PC.tif         \
  --orthoimage stereo_bm/run-L.tif

We chose to use option --num-matches-from-disparity to create a large and uniformly distributed set of interest point matches. That is necessary because the jitter that we will solve for has rather high frequency.

Fig. 16.11 Produced DEM, orthoimage and intersection error. The correlation algorithm has some trouble over sand, resulting in holes. The jitter is clearly visible. The color scale on the right is from 0 to 10 meters.

The created DEM is brought in the coordinate system of the reference DEM. This results in a small shift in this case, but it is important to do this each time before solving for jitter.

  pc_align --max-displacement 50          \
  stereo_bm/run-DEM.tif ref.tif           \
  -o stereo_bm/run-align                  \
  --save-inv-transformed-reference-points

point2dem --t_srs "$proj" --tr 15 \
  stereo_bm/run-align-trans_reference.tif

One has to be careful with the value of --max-displacement that is used (Section 16.49).

Take the difference with the reference DEM after alignment:

geodiff stereo_bm/run-align-trans_reference-DEM.tif \
  ref.tif -o stereo_bm/run

The result of this is shown in Fig. 16.14. Apply the alignment transform to the cameras (Section 16.49.14):

bundle_adjust -t csm                        \
  --initial-transform                       \
  stereo_bm/run-align-inverse-transform.txt \
  --apply-initial-transform-only            \
  out-Band3N.map.tif out-Band3B.map.tif     \
  ba/run-out-Band3N.adjusted_state.json     \
  ba/run-out-Band3B.adjusted_state.json     \
  -o ba_align/run

It is important to use here the inverse alignment transform, as we want to map from the stereo DEM to the reference DEM, and the forward transform would do the opposite, given how pc_align was invoked.

If the produced difference of DEMs shows large residuals consistent with the terrain, one should consider applying more blur to the reference terrain and/or redoing mapprojection and stereo with the now-aligned cameras, and see if this improves this difference.

16.35.8.3. Solving for jitter

Copy the dense match file to follow the naming convention for unprojected images:

mkdir -p jitter
cp stereo_bm/run-disp-out-Band3N.map__out-Band3B.map.match \
  jitter/run-out-Band3N__out-Band3B.match

The naming convention for the output match file above is <prefix>-<image1>__<image2>.match, where the image names are without the directory name and extension.

Here it is important to use a lot of match points and a low value for --num-lines-per-orientation and same for position, because the jitter has rather high frequency.

Solve for jitter with the aligned cameras:

jitter_solve out-Band3N.tif out-Band3B.tif        \
  ba_align/run-run-out-Band3N.adjusted_state.json \
  ba_align/run-run-out-Band3B.adjusted_state.json \
  --max-pairwise-matches 1000000                  \
  --num-lines-per-position 100                    \
  --num-lines-per-orientation 100                 \
  --max-initial-reprojection-error 20             \
  --translation-weight 1000                       \
  --rotation-weight 0                             \
  --num-iterations 10                             \
  --robust-threshold 0.25                         \
  --match-files-prefix jitter/run                 \
  --heights-from-dem ref.tif                      \
  --heights-from-dem-weight 0.1                   \
  --heights-from-dem-robust-threshold 0.1         \
  -o jitter/run

The DEM weight constraint was set to 0.1, as the image GSD is 15 meters, and this value multiplied by 0.1 becomes comparable to a pixel, which is the unit of the pixel reprojection error in the camera. For an unreliable DEM this should be less.

We used --robust-threshold 0.25 as the reprojection error due to jitter is a fraction of a pixel (as seen in Fig. 16.12). The DEM robust threshold was set to be less than --robust-threshold, to prioritize pixel reprojection errors.

The camera positions were constrained with a high value of --translation-weight, as it is assumed that the jitter is in the camera orientations.

Fig. 16.12 Pixel reprojection errors (Section 16.35.13) before (left) and after (right) solving for jitter. Compare with the ray intersection error in Fig. 16.13.

Then, parallel_stereo and point2dem can be run again, with the new cameras created in the jitter directory. The --prev-run-prefix option can be used to reuse the previous run (Section 16.35.6.7).

Fig. 16.13 The ray intersection error before (left) and after (right) solving for jitter. The scale is in meters.

Fig. 16.14 The signed difference between the ASP DEM and the reference DEM, before (left) and after (right) solving for jitter. The scale is in meters. It can be seen that the jitter pattern is gone.

16.35.9. Jitter with synthetic cameras and orientation constraints

The effectiveness of jitter_solve can be validated using synthetic data, when we know what the answer should be ahead of time. The synthetic data can created with sat_sim (Section 16.57). See a recipe in Section 16.57.7.

For example, one may create three linescan images and cameras, using various values for the pitch angle, such as -30, 0, and 30 degrees, modeling a camera that looks forward, down, and aft. One can choose to not have any jitter in the images or cameras, then create a second set of cameras with pitch (along-track) jitter.

Then, jitter_solve can be used to solve for the jitter. It can be invoked with the images not having jitter and the cameras having the jitter.

It is suggested to use the roll and yaw constraints (--roll-weight and --yaw-weight, with values on the order of 1e+5), to keep these angles in check while correcting the pitch jitter.

The --heights-from-dem option should be used as well, to tie the solution to the reference DEM.

We found experimentally that, if the scan lines for all the input cameras are perfectly parallel, then the jitter solver will not converge to the known solution. This is because the optimization problem is under-constrained. If the scan lines for different cameras meet at, for example, a 6-15 degree angle, and the lines are long enough to offer good overlap, then the “rigidity” of a given scan line will be able to help correct the jitter in the scan lines for the other cameras intersecting it, resulting in a solution close to the expected one.

See a worked-out example for how to set orientation constraints in Section 16.35.11. There, frame cameras are used as well, to add “rigidity” to the setup.

16.35.10. Constraining direction of jitter with real cameras

For synthetic cameras created with sat_sim (Section 16.57), it is assumed that the orbit is a straight segment in projected coordinates (hence an ellipse if the orbit end points are at the same height above the datum). It is also assumed that such a camera has a fixed roll, pitch, and yaw relative to the satellite along-track / across-track directions, with jitter added to these angles (Section 16.57.4, and Section 16.57.6).

For a real linescan satellite camera, the camera orientation is variable and not correlated to the orbit trajectory. The jitter_solve program can then constrain each camera sample being optimized not relative to the orbit trajectory, but relative to initial camera orientation for that sample.

That is accomplished by invoking the jitter solver as in Section 16.35.9, with the additional option --initial-camera-constraint. See the description of this option in Section 16.35.14.

This option is very experimental and its effectiveness was only partially validated.

This option can be used with synthetic cameras as well. The results then will be somewhat different than without this option, especially towards orbit end points, where the overlap with other cameras is small.

16.35.11. Mixing linescan and frame cameras

This solver allows solving for jitter using a combination of linescan and frame (pinhole) cameras, if both of these are stored in the CSM format (Section 8.12).

For now, this functionality was validated only with synthetic cameras created with sat_sim (Section 16.57). In this case, roll and yaw constraints for the orientations of cameras being optimized are supported, for both linescan and frame cameras.

Here is a detailed recipe.

Consider a DEM named dem.tif, and an orthoimage named ortho.tif. Let x be a column index in the DEM and y1 and y2 be two row indices. These will determine path on the ground seen by the satellite. Let h be the satellite height above the datum, in meters. Set, for example:

x=4115
y1=38498
y2=47006
h=501589
opt="--dem dem.tif
  --ortho ortho.tif
  --first $x $y1 $h
  --last  $x $y2 $h
  --first-ground-pos $x $y1
  --last-ground-pos  $x $y2
  --frame-rate 45
  --jitter-frequency 5
  --focal-length 551589
  --optical-center 2560 2560
  --image-size 5120 5120
  --velocity 7500
  --save-ref-cams"

Create nadir-looking frame images and cameras with no jitter:

sat_sim $opt                  \
  --save-as-csm               \
  --sensor-type pinhole       \
  --roll 0 --pitch 0 --yaw 0  \
  --horizontal-uncertainty    \
  "0.0 0.0 0.0"               \
  --output-prefix jitter0.0/n

Create a forward-looking linescan image and camera, with no jitter:

sat_sim $opt                  \
  --sensor-type linescan      \
  --square-pixels             \
  --roll 0 --pitch 30 --yaw 0 \
  --horizontal-uncertainty    \
  "0.0 0.0 0.0"               \
  --output-prefix jitter0.0/f

Create a forward-looking linescan camera, with no images, with pitch jitter:

sat_sim $opt                  \
  --no-images                 \
  --sensor-type linescan      \
  --square-pixels             \
  --roll 0 --pitch 30 --yaw 0 \
  --horizontal-uncertainty    \
  "0.0 2.0 0.0"               \
  --output-prefix jitter2.0/f

The tool cam_test (Section 16.9) can be run to compare the camera with and without jitter:

cam_test --session1 csm    \
  --session2 csm           \
  --image jitter0.0/f.tif  \
  --cam1  jitter0.0/f.json \
  --cam2  jitter2.0/f.json

This will show that projecting a pixel from the first camera to the ground and then projecting it back to the second camera will result in around 2 pixels of discrepancy, which makes sense give the horizontal uncertainty set above and the fact that our images are at around 0.9 m/pixel ground resolution.

To reliably create reasonably dense interest point matches between the frame and linescan images, first mapproject (Section 16.38) them:

for f in jitter0.0/f.tif                    \
         jitter0.0/n-1[0-9][0-9][0-9][0-9].tif; do
    g=${f/.tif/} # remove .tif
    mapproject --tr 0.9                     \
      dem.tif ${g}.tif ${g}.json ${g}.map.tif
done

This assumes that the DEM is in a local projection in units of meter. Otherwise the --t_srs option should be set.

Create the lists of images, cameras, then a list for the mapprojected images and the DEM. We use individual ls command to avoid the inputs being reordered:

dir=ba
mkdir -p $dir
ls jitter0.0/f.tif                        >  $dir/images.txt
ls jitter0.0/n-1[0-9][0-9][0-9][0-9].tif  >> $dir/images.txt

ls jitter0.0/f.json                       >  $dir/cameras.txt
ls jitter0.0/n-1[0-9][0-9][0-9][0-9].json >> $dir/cameras.txt

ls jitter0.0/f.map.tif                       >  $dir/map_images.txt
ls jitter0.0/n-1[0-9][0-9][0-9][0-9].map.tif >> $dir/map_images.txt
ls dem.tif                                   >> $dir/map_images.txt

Run bundle adjustment to get interest point matches:

parallel_bundle_adjust                           \
    --processes 10                               \
    --nodes-list nodes_list.txt                  \
    --num-iterations 10                          \
    --tri-weight 0.1                             \
    --camera-weight 0                            \
    --translation-weight 1000                    \
    --rotation-weight 0                          \
    --auto-overlap-params "dem.tif 15"           \
    --min-matches 5                              \
    --remove-outliers-params '75.0 3.0 20 20'    \
    --min-triangulation-angle 5.0                \
    --ip-per-tile 500                            \
    --max-pairwise-matches 6000                  \
    --image-list $dir/images.txt                 \
    --camera-list $dir/cameras.txt               \
    --mapprojected-data-list $dir/map_images.txt \
    -o ba/run

Here we assumed a minimum triangulation convergence angle of 15 degrees between the two sets of cameras (Section 8.1). See Section 8.16 for how to set up the computing nodes needed for --nodes-list.

We could have used a ground constraint above, but since we only need the interest points and not the camera poses, it is not necessary.

Solve for jitter with a ground constraint. Use roll and yaw constraints, to ensure movement only for the pitch angle:

jitter_solve                                 \
    --num-iterations 10                      \
    --translation-weight 10000               \
    --rotation-weight 0.0                    \
    --max-pairwise-matches 3000              \
    --clean-match-files-prefix               \
      ba/run                                 \
    --roll-weight 10000                      \
    --yaw-weight 10000                       \
    --max-initial-reprojection-error 100     \
    --tri-weight 0.05                        \
    --tri-robust-threshold 0.05              \
    --num-anchor-points 10000                \
    --num-anchor-points-extra-lines 5000     \
    --anchor-dem dem.tif                     \
    --anchor-weight 0.05                     \
    --heights-from-dem dem.tif               \
    --heights-from-dem-weight 0.05           \
    --heights-from-dem-robust-threshold 0.05 \
    jitter0.0/f.tif                          \
    jitter0.0/n-images.txt                   \
    jitter2.0/f.json                         \
    jitter0.0/n-cameras.txt                  \
    -o jitter_solve/run

Here we used --max-pairwise-matches 3000 as the linescan camera has many matches with each frame camera image, and there are many such frame camera images. A much larger number would be used if we had only a couple of linescan camera images and no frame camera images.

The initial cameras were not bundle-adjusted and aligned to the reference DEM, as they were good enough. Normally one would use them as input to jitter_solve with the option --input-adjustments-prefix.

Then, we set --translation-weight 10000 to keep the camera centers fixed as in this case we only want to modify the camera orientations.

Notice that the nadir-looking frame images are read from a list, in jitter0.0/n-images.txt. This file is created by sat_sim. All the images in such a list must be acquired in quick succession and be along the same satellite orbit portion, as the trajectory of all these cameras will be used to enforce the roll and yaw constraints.

A separate list must be created for each such orbital stretch, then added to the invocation above. The same logic is applied to the cameras for these images.

There is a single forward-looking image, but it is linescan, so there are many camera samples for it.

The forward-looking camera has jitter, so we used its version from the jitter2.0 directory, not the one in jitter0.0.

This solver does not create anchor points for the frame cameras. There are usually many such images and they overlap a lot, so anchor points are not needed as much as for linescan cameras.

16.35.12. Solving for jitter with a linescan and frame rig

In this example we consider a rig that is made of linescan and frame camera. These sensors are positioned in the same location and look in the same direction. The linescan sensor acquires a single very long image line at a high rate, while the frame camera records a rectangular image of much smaller dimensions and at a lower rate. They both experience the same jitter.

The end result is a wide and tall linescan image and many smaller frame images that overlap with each other and the linescan image. The “rigid” frame camera images are used to correct the jitter in the rig.

Synthetic data for this example can be produced as in Section 16.35.11. The sat_sim invocations for linescan and frame cameras are the same except using different sensor dimensions and sensor type.

A straightforward application of the jitter-solving recipe in Section 16.35.11 will fail, as it is not possible to triangulate properly the points seen by the two cameras. The following adjustments are suggested:

• Use --forced-triangulation-distance 500000 for both bundle adjustment and jitter solving (use here the value of the camera height above the terrain). This will result in triangulated points even when the rays are parallel or even a little divergent (during optimization these points will get refined, so the above value need not be perfectly known).

• Instead of --heights-from-dem use the option --reference-dem in jitter_solve, with associated options --reference-dem-weight and --reference-dem-robust-threshold. See Section 16.35.14 for details.

• Use --match-files-prefix instead of --clean-match-files-prefix in jitter_solve, as maybe bundle adjustment filtered out too many good matches with small convergence angle.

• Use --min-triangulation-angle 1e-10 in both bundle adjustment and jitter solving, to ensure we don’t throw away features with small convergence angle, as that will be almost all of them.

Here’s the command for solving for jitter, and the bundle adjustment command that creates the interest point matches is similar.

jitter_solve                               \
    --forced-triangulation-distance 500000 \
    --min-matches 1                        \
    --min-triangulation-angle 1e-10        \
    --num-iterations 10                    \
    --translation-weight 10000             \
    --rotation-weight 0.0                  \
    --max-pairwise-matches 50000           \
    --match-files-prefix ba/run            \
    --roll-weight 10000                    \
    --yaw-weight 10000                     \
    --max-initial-reprojection-error 100   \
    --tri-weight 0.05                      \
    --tri-robust-threshold 0.05            \
    --num-anchor-points-per-tile 100       \
    --num-anchor-points-extra-lines 5000   \
    --anchor-dem dem.tif                   \
    --anchor-weight 0.01                   \
    --reference-dem dem.tif                \
    --reference-dem-weight 0.05            \
    --reference-dem-robust-threshold 0.05  \
    data/nadir_frame_images.txt            \
    data/nadir_linescan.tif                \
    data/nadir_frame_cameras.txt           \
    data/nadir_linescan.json               \
    -o jitter/run

The weights and thresholds above can be increased somewhat if the input DEM is reliable and it is desired to tie the solution more to it.

When the linescan sensor is much wider than the frame sensor, the anchor points should be constrained to the shared area of the produced images, to have the same effect on both sensors. That is accomplished with the option --anchor-weight-image.

16.35.13. Output files

The optimized CSM model state files (Section 8.12.6), which reduce the jitter and also incorporate the initial adjustments as well, are saved in the directory for the specified output prefix.

This program saves, just like bundle_adjust (Section 16.5.8), two .csv error files, before and after optimization. Each has the triangulated world position for every feature being matched in two or more images, the mean absolute residual error (pixel reprojection error in the cameras, Section 12) for each triangulated position, and the number of images in which the triangulated position is seen. The files are named:

{output-prefix}-initial_residuals_pointmap.csv

and:

{output-prefix}-final_residuals_pointmap.csv

Such CSV files can be colorized and overlaid with stereo_gui (Section 16.64.6) to see at which pixels the residual error is large.

These files are very correlated to the dense results produced with stereo (the DEM and intersection error, respectively, before and after solving for jitter), but the csv files can be examined before stereo runs, which can take many hours.

If anchor points are used, the coordinates of each anchor point and the norm of the pixel residual at those points are saved as well, to:

{output-prefix}-initial_residuals_anchor_points.csv

and:

{output-prefix}-final_residuals_anchor_points.csv

These have almost the same format as the earlier file. The key distinction is that each anchor point corresponds to just one pixel, so the last field from above (the count) is not present.

When being optimized, the reprojection errors of anchor points are multiplied by the anchor weight. In this file they are saved without that weight multiplier, so they are in units of pixel.

These can be plotted and colorized in stereo_gui as well, for example, with:

stereo_gui --colorize --min 0 --max 0.5   \
  --plot-point-radius 2                   \
  {output-prefix}-final_residuals_anchor_points.csv

Note that the initial pointmap.csv file created with the --heights-from-dem option reflects the fact that the triangulated points have had their heights set to the DEM height, which can be confusing. Yet in the final (optimized) file these points have moved, so then the result makes more sense. When using the --tri-weight option the true initial triangulated points and errors are used.

16.35.14. Command-line options for jitter_solve

-o, --output-prefix <filename>

Prefix for output filenames.

-t, --session-type <string>

Select the stereo session type to use for processing. Usually the program can select this automatically by the file extension, except for xml cameras. See Section 16.47.3 for options.

--robust-threshold <double (default:0.5)>

Set the threshold for robust cost functions. Increasing this makes the solver focus harder on the larger errors.

--min-matches <integer (default: 30)>

Set the minimum number of matches between images that will be considered.

--max-pairwise-matches <integer (default: 10000)>

Reduce the number of matches per pair of images to at most this number, by selecting a random subset, if needed. This happens when setting up the optimization, and before outlier filtering. It is suggested to set this to a large number, such as one million, to avoid filtering out too many matches. It may be reduced only if the number of images is large and the number of matches becomes unsustainable.

--num-iterations <integer (default: 100)>

Set the maximum number of iterations.

--parameter-tolerance <double (default: 1e-8)>

Stop when the relative error in the variables being optimized is less than this.

--input-adjustments-prefix <string>

Prefix to read initial adjustments from, written by bundle_adjust. Not required. Cameras in .json files in ISD or model state format can be passed in with no adjustments.

--num-lines-per-position

Resample the input camera positions and velocities, using this many lines per produced position and velocity. If not set, use the positions and velocities from the CSM file as they are.

--num-lines-per-orientation

Resample the input camera orientations, using this many lines per produced orientation. If not set, use the orientations from the CSM file as they are.

--tri-weight <double (default: 0.0)>

The weight to give to the constraint that optimized triangulated points stay close to original triangulated points. A positive value will help ensure the cameras do not move too far, but a large value may prevent convergence. Does not apply to GCP or points constrained by a DEM via --heights-from-dem. This adds a robust cost function with the threshold given by --tri-robust-threshold. The suggested value is 0.1 to 0.5 divided by the image ground sample distance.

--tri-robust-threshold <double (default: 0.1)>

Use this robust threshold to attenuate large differences between initial and optimized triangulation points, after multiplying them by --tri-weight.

--heights-from-dem <string>

If the cameras have already been bundle-adjusted and aligned to a known DEM, in the triangulated points obtained from interest point matches replace their heights above datum with the ones from this DEM before optimizing them, and then constrain them via --heights-from-dem-weight and --heights-from-dem-robust-threshold. See Section 12.2.1.5.

--heights-from-dem-weight <double (default: 0.5)>

How much weight to give to keep the triangulated points close to the DEM if specified via --heights-from-dem. This value should be about 0.1 to 0.5 divided by the image ground sample distance, as then it will convert the measurements from meters to pixels, which is consistent with the pixel reprojection error term.

--heights-from-dem-robust-threshold <double (default: 0.5)>

The robust threshold to use keep the triangulated points close to the DEM if specified via --heights-from-dem. This is applied after the point differences are multiplied by --heights-from-dem-weight. It should help with attenuating large height difference outliers. It is suggested to make this equal to --heights-from-dem-weight.

--match-files-prefix <string (default: “”)>

Use the match files from this prefix. Matches are typically dense ones produced by stereo or sparse ones produced by bundle adjustment.

--clean-match-files-prefix <string (default: “”)>

Use as input match files the *-clean.match files from this prefix.

--max-initial-reprojection-error <integer (default: 10)>

Filter as outliers triangulated points project using initial cameras with error more than this, measured in pixels. Since jitter corrections are supposed to be small and cameras bundle-adjusted by now, this value need not be too big.

--num-anchor-points <integer (default: 0)>

How many anchor points to create tying each pixel to a point on a DEM along the ray from that pixel to the ground. These points will be uniformly distributed across each input image. Only applies to linescan cameras. See also --anchor-weight and --anchor-dem.

--num-anchor-points-per-tile <integer (default: 0)>

How many anchor points to create per 1024 x 1024 image tile. They will be uniformly distributed. Useful when images of vastly different sizes (such as frame and linescan) are used together. See also --anchor-weight and --anchor-dem.

--anchor-weight <double (default: 0.0)>

How much weight to give to each anchor point. Anchor points are obtained by intersecting rays from initial cameras with the DEM given by --heights-from-dem. A larger weight will make it harder for the cameras to move, hence preventing unreasonable changes.

--anchor-dem <string (default: “”)>

Use this DEM to create anchor points.

--num-anchor-points-extra-lines <integer (default: 0)>

Start placing anchor points this many lines before first image line and after last image line.

--quat-norm-weight <double (default: 1.0)>

How much weight to give to the constraint that the norm of each quaternion must be 1. It is implicitly assumed in the solver that the quaternion norm does not deviate much from 1, so, this should be kept positive.

--rotation-weight <double (default: 0.0)>

A higher weight will penalize more deviations from the original camera orientations. This adds to the cost function the per-coordinate differences between initial and optimized normalized camera quaternions, multiplied by this weight, and then squared. No robust threshold is used to attenuate this term. See also Section 16.35.2.

--translation-weight <double (default: 0.0)>

A higher weight will penalize more deviations from the original camera positions. This adds to the cost function the per-coordinate differences between initial and optimized camera positions, multiplied by this weight, and then squared. No robust threshold is used to attenuate this term. See also Section 16.35.2.

--roll-weight <double (default: 0.0)>

A weight to penalize the deviation of camera roll orientation as measured from the along-track direction. Pass in a large value, such as 1e+5. This is best used only with linescan cameras created with sat_sim (sat_sim).

--yaw-weight <double (default: 0.0)>

A weight to penalize the deviation of camera yaw orientation as measured from the along-track direction. Pass in a large value, such as 1e+5. This is best used only with linescan cameras created with sat_sim (sat_sim).

--initial-camera-constraint

When constraining roll and yaw, measure these not in the satellite along-track/across-track/down coordinate system, but relative to the initial camera poses. This is experimental. Internally, the roll weight will then be applied to the camera pitch angle (rotation around camera y axis), because the camera coordinate system is rotated by 90 degrees in the sensor plane relative to the satellite coordinate system. The goal is the same, to penalize deviations that are not aligned with satellite pitch.

--reference-dem <string>

If specified, intersect rays from matching pixels with this DEM, find the average, and constrain during optimization that rays keep on intersecting close to this point. This works even when the rays are almost parallel, but then consider using the option --forced-triangulation-distance. See also --reference-dem-weight and --reference-dem-robust-threshold.

--reference-dem-weight <double (default: 1.0)>

Multiply the xyz differences for the --reference-dem option by this weight. This is being tested.

--reference-dem-robust-threshold <double (default: 0.5)>

Use this robust threshold for the weighted xyz differences with the --reference-dem option. This is being tested.

--weight-image <string (default: “”)>

Given a georeferenced image with float values, for each initial triangulated point find its location in the image and closest pixel value. Multiply the reprojection errors in the cameras for this point by this weight value. The solver will focus more on optimizing points with a higher weight. Points that fall outside the image and weights that are non-positive, NaN, or equal to nodata will be ignored. See Section 12.3.2 for details.

--anchor-weight-image <string (default: “”)>

Weight image for anchor points. Limits where anchor points are placed and their weight. Weights are additionally multiplied by --anchor-weight. See also --weight-image.

--min-triangulation-angle <degrees (default: 0.1)>

The minimum angle, in degrees, at which rays must meet at a triangulated point to accept this point as valid. It must be a positive value.

--forced-triangulation-distance <meters>

When triangulation fails, for example, when input cameras are inaccurate, artificially create a triangulation point this far ahead of the camera, in units of meters. Some of these may be later filtered as outliers.

--overlap-limit <integer (default: 0)>

Limit the number of subsequent images to search for matches to the current image to this value. By default try to match all images.

--match-first-to-last

Match the first several images to last several images by extending the logic of --overlap-limit past the last image to the earliest ones.

--threads <integer (default: 0)>

Set the number threads to use. 0 means use the default defined in the program or in ~/.vwrc. Note that when using more than one thread and the Ceres option the results will vary slightly each time the tool is run.

--cache-size-mb <integer (default = 1024)>

Set the system cache size, in MB, for each process.

-h, --help

Display the help message.

-v, --version

Display the version of software.