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JEREMY
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Reconstructing Rectangular Polyhedra

From

Hand-Drawn Wireframe Sketches

Human observers are capable of interpreting hand drawn
sketches as three-dimensional objects, despite inconsistencies in
lengths, variability in angles, and unconnected vertices.

* Reconstruction of the simplest wireframe rectangular
polyhedral scene: a cube.
The first panel shows the original sketch, the following
panel shows the recovered surfaces.
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The current
system is an attempt to achieve such robust performance in the limited
domain of sketches of wireframe rectangular polyhedra. The first
version of this system reconstructed three-dimensional objects from
perfect drawings, in which all angles and line junctions are
consistent with projections of rectangular polyhedron. Ambiguities
which are inherent in such drawings are avoided by choosing a line
grammar which yields only a single interpretation.

* Reconstruction of a more complex wireframe sketch.*

Next,
reconstruction from imperfect drawings, in which all the line segments
were randomly perturbed, was then achieved by grouping line endpoints
into vertices while simultaneously restricting lines to particular
orientations, and recovering three-dimensional form from the corrected
line drawing.

*Reconstruction of an object with surfaces at three levels
in each dimension.*

Finally, when actual hand-drawn sketches were used as
input, we found that to successfully perform reconstruction the
constraints on line orientations had to be replaced with constraints
segment lengths and an additional three-dimensional point clustering
process was needed.

*The first complex polyhdron devised by friends in the
AI lab to challenge the system.*

*Another reconstruction with the same sort of theme.*

Because machine vision is an extremely difficult problem,
there is only so much that one can hope to solve with a single
problem. Therefore, to make this a tractable problem, some degree of
human assistance
is necessary in making it possible for the system to
successfully recover the desired object(s).

*Reconstruction of haphazardly drawn "right" angles
is made possible by allowing the recovered 3D lines to deviate from a
true rectangular polyhedron.*

*By relaxing the angular constrast of insisting on orthogonality,
the system is able to maintyain the relative distances indicated in the
original sketch.*

*Unless explicitly specified by attachment, as in the
above example, there is no way to determine relative depth of to polyhedra
in the same scene.*

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