Mondrain Motion Assumptions

    Here 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.

  • Single 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 certain objects.
  • Single 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.
  • Known calibration: Each frame can be connected to a specific time in Mondrian Motion case and a specific horizontal location in Mondrian Stereo.
  • Unique 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.
  • Convex shapes: All objects are convex. Obviously, this needs to be relaxed for the code to be useful.
  • Exact positions: 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.
  • General Position: 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.
  • Fixed velocities: Each region has a constant velocity. In a real scene, this assumption will only hold over a couple frames.
  • 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.

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