![](bg7.png)
algorithm (1:8 ratio). The noise is due to spatial par-
tial derivatives that have a tendency to amplify minor
differences of optical flow.
Moving objects, like the bike and the white car in
the image sequence, are shown with darker red color
(meaning less threat) due to small relative velocity
with respect to the camera. This is an advantage of the
approach where estimation of looming is able to catch
the relevant threat of moving objects. This is clearly
an advantage of looming over conventional percep-
tion of depth.
5 CONCLUSIONS
Visual looming has been shown to be an important
cue for navigation and control tasks. This paper ex-
plores new ways for deriving and estimating visual
looming for general six-degrees-of-freedom motion.
The main contributions of the paper are:
1. We derived two novel analytical closed-form ex-
pressions for calculating looming for any six-
degree-of-freedom motion. These expressions in-
clude spatial derivatives of the motion field. This
approach can be applied to any relative motion be-
tween an observer and any visible point.
2. We showed the theoretical relationship of surface
normal to the values of looming.
3. We presented simulation results of the effect of
surface normals on values of calculated looming.
Quantitative calculations showed the relationship
between the angles of the surface normal relative
to the angle of the range vector and the related
effects on the accuracy of estimating looming val-
ues.
4. We demonstrated how to extract looming from op-
tical flow. The output of the RAFT model was
used to estimate looming values using expressions
that were derived in the paper.
It should also be emphasized that knowledge of range
to the 3D point, translation or rotation of the cam-
era (egomotion) is not required for the estimation of
looming and hence for autonomous navigation tasks.
ACKNOWLEDGMENTS
The authors thank Dr. Sridhar Kundur for many fruit-
ful discussion and suggestions as well as very detailed
comments and clarifications that led to meaningful
improvements of this paper. The authors also thank
Nikita Ostro and Benjamin Thaw for their thorough
review of this paper.
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