is a list of assumptions to take advantage of them. An explaination
explains either why the assumptions are reasonable or discusses
how this could be relaxed.
colors: All regions are untextured. This means
that any sudden change in color is a region boundary.
Constant shape: No
shape changes in size or shape. While this likely holds
for most real world objects, it may only hold locally for
depths : Regions are subsets of a fronto-parallel
plane. Thus there is a specific depth relating to each object
and a specific depth-ordering for the regions. Notice that
the depth ordering is the most important, so this assumption
can be relaxed in there is still a definite depth ordering.
calibration: Each frame can be connected to a specific
time in Mondrian Motion case and a specific horizontal location
in Mondrian Stereo.
colors: assumes that given any two pieces of the
same color, they are the same object. It may be relaxed
enough to say that two regions may have the same color as
long as they don't intersect.
shapes: All objects are convex. Obviously, this
needs to be relaxed for the code to be useful.
assumes that pixel boundaries are exactly where they look
to be—no approximation. This also means that all objects
need to have integer velocities and integer size, in pixels.
This can only hold in a "synthetic" Mondrian World.
Actual photographs need to assume that edges are only approximations
of where the edge actually is.
assumes no edges line up perfectly. This is useful for finding
T-junctions in the epigraph with only 3 frames. It also
is useful for finding standard T-Junctions in one frame.
velocities: Each region has a constant velocity.
In a real scene, this assumption will only hold over a couple
Bounded velocities: assumes
that nothing moves faster than a given value. This assumption
is reasonable since the frame rate can be set high in the
Mondrian Motion case, and the horizontal spacing can be
controlled in the Mondrian Stereo case.