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Multi-scale optic flow
How can we find a dense optic flow field from a
motion sequence in 2D and 3D?
Many approaches are taken - gradient based (or
differential) - phase-based (or frequency
domain) - correlation-based (or area) -
feature-point (or sparse data) tracking.
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In the visual front-end retinal receptive fields
are organized in pairs, tuned to a specific
velocity and direction. The pairs arecoupled by
a delay cell, possibly the amacrine cell.
Neurons act as temporalcoincidence
detectors This leads to a redundantrepresentatio
n, all velocities and directionsare measuredat
all scales.
Reichardt detector
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Amacrine cellsare found nextto ganglion
cellbodies
Similar RF pairsare present inboth eyes
fordisparitydetection
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Calibration
We generate a test sequence with a warping vector
field, so we know the absolute displacement of
each pixel
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The isophote landscape of an image changes
drastically when we change our aperture size.
This happens when we move away or towards the
scene with the same camera. Left observation of
an image with ? 1 pix, isophotes L50 are
indicated. Right same observation at a distance
twice as far away. The isophotes L50 have now
changed.
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Two types of images need to be considered
Scalar images intensity is kept constant with
the divergence Density images intensity
dilutes with the divergence
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Multi-scale optic flow constraint equation
For scalar images
For density images
The velocity field is unknown, and this is what
we want to recover from the data. We like to
retrieve the velocity and its derivatives with
respect to x, y, z and t. We insert this
unknown velocity field as a truncated Taylor
series, truncated at first order.
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Multi-scale density flow in each pixel 8
equations of third order and8 unknowns
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Scale selection The condition number of the
coefficient matrix exhibits an optimumover scale
in many pixels, given the local density of
texture.
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Artificially created test image sequencefor
validation purposes
Scale selection map
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A. Suinesiaputra, UMCL / TUE, MICCAI 2002