This file explains the contents of the supplementary material for the WACV 2021 submission 'Cinematic-L1 Video Stabilization with a Log-Homography Model'.

=== l1_stabilization_supplement.pdf

l1_stabilization_515_supplement.pdf provides more detail on the derivative calculations,
point-delta linearization, area and sidelength gradients, third-order
Markov property for windowed L1, and keystone-translation relationship,
as well as additional plots. It also contains a Results section providing
details about and interpretations of our supplementary videos.


=== fountain-tripod-smooth-l1.mp4

Compares L1 stabilization, Gaussian
smoothing, and virtual tripod stabilization for a short video. Virtual
tripod introduces distortion and parallax, and Gaussian smoothing only
removes the high-frequency motion, while L1 stabilization yields a
constant-velocity pan followed by a ‘tripod’ segment with minimal
distortion.


=== river-l1.mp4

Demonstrates L1 stabilization on a longer, more complex
video. The L1 stabilized video contains tripod-like segments, as well as
constant-velocity horizontal pans, with smooth transitions between them.
The z-axis rotation and y-translation are reduced or eliminated in the
panning segments.


=== dog-l1-saliency-comparison.mp4

Demonstrates L1 stabilization with
saliency constraints or centering objective on a video with a tracked
object (the dog). Default L1 produces a smooth pan, but the dog goes out
of frame toward the end of video (due to crop). The saliency constraint
adjusts the trajectory to keep the dog in frame. The centering objective
keeps the dog approximately centered to the extent possible given other
constraints.


=== fountain-l1-affine.mp4, fountain-l1-affine-uncropped.mp4, wakatipu-l1-affine.mp4

Contrast stabilization with our log-homography L1 model with a simpler version of our method restricted to affinities (cropped and uncropped versions). Detail in Supplement A.2. wakatipu-l1-affine.mp4 also shows our method's behavior on a very shaky video, as discussed in Supplement A.5.


== grundmann-gleicher4.mp4, grundmann-sam1.mp4, grundmann-lf-juggle.mp4, grundmann-sany0025.mp4

Comparisons to the method of Grundmann et al., as detailed in Supplement A.3. 

Note that Grundmann et al. employ a hybrid 'residual motion suppression' approach, wherein similarity transforms are used in the convex formulation, and full homographies are used in post-process to clean up the residual keystone wobble. Unfortunately, this post-processing step can consume a large amount of crop over and above the fraction allowed in the optimization. Our results are generally similar to those of Grundmann et al. in terms of smoothness, but our method can more rigorously satisfy crop and other constraints. This is most apparent in grundmann-gleicher4.mp4, where Grundmann et al.'s result, which is supposed to have 30% crop fraction, actually has a much smaller field-of-view due to the homography post-processing, while our method is able to satisfy the crop constraint. For the remaining three videos, which do not have severe keystone, Grundmann et al.'s method does not seriously overconsume crop; our results are visually fairly similar to for these less-challenging videos.


=== fountain-ablation-derivatives.mp4, fountain-ablation-innovations.mp4, fountain-crop-compare.mp4

Video corresponding to ablation study; detail in Supplement A.4.


=== slow-pan-windowed.mp4

Failure case of windowed-L1 when the window is very short. Further detail in 'Windowing' section of Supplement A.5.


All videos are in MP4 format using the H.264 codec.







