Reconstructing Rectangular Polyhedra
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.

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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