# The ICICS/CS Reading Room

## UBC CS TR-92-25 Summary

- No on-line copy of this technical report is available.

- The Rapid Recovery of three-Dimensional Orientation from Line Drawings, September 1992 R. A. Rensink, 188 pages
A computational theory is developed that explains how line drawings of
polyhedral objects can be interpreted rapidly and in parallel at early
levels of human vision. The key idea is that a time-limited process can
correctly recover much of the three-dimensional structure of these
objects when split into concurrent streams, each concerned with a single
aspect of scene structure.

The work proceeds in five stages. The first extends the framework of
Marr to allow a process to be analyzed in terms of resource limitations.
Two main concerns are identified: (i) reducing the amount of nonlocal
information needed, and (ii) making effective use of whatever
information is obtained. The second stage traces the difficulty of line
interpretation to a small set of constraints. When these are removed,
the remaining constraints can be grouped into several relatively
independent sets. It is shown that each set can be rapidly solved by a
separate processing stream, and that co-ordinating these streams can
yield a low-complexity ``approximation'' that captures much of the
structure of the original constraints. In particular, complete recovery
is possible in logarithmic time when objects have rectangular corners
and the scene-to-image projection is orthographic. The third stage is
concerned with making good use of the available information when a fixed
time limit exists. This limit is motivated by the need to obtain
results within a time independent of image content, and by the need to
limit the propagation of inconsistencies. A minimal architecture is
assumed, viz., a spatiotopic mesh of simple processors. Constraints are
developed to guide the course of the process itself, so that candidate
interpretations are considered in order of their likelihood. The fourth
stage provides a specific algorithm for the recovery process, showing
how it can be implemented on a cellular automaton. Finally, the theory
itself is tested on various line drawings. It is shown that much of the
three-dimensional structure of a polyhedral scene can indeed be
recovered in very little time. It also is shown that the theory can
explain the rapid interpretation of line drawings at early levels of
human vision.

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