29 October 1996 Three-dimensional object recovery from two-dimensional images: a new approach
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This paper considers the work done by Thomas Marill in a series of papers on the recognition of two-dimensional wire- frame figures as 3D objects without the use of models. Marill discovered that if one minimizes the standard deviation of the angles found at each vertex of the figure, the likelihood of the computer interpretation of the figure matching the human interpretation is much higher than might be expected a priori. Here it is observed that the human mind's tendency to simplify inputs and find patterns even where there are none might be at least partly responsible for the observed phenomenon. It is conjectured that if this is indeed the case, it should be possible to get similar behavior from minimizing the standard deviation of other features. In particular, segment length presents itself as being an excellent choice of a test feature--it is very different from angles and is less computationally intensive. Thus another approach is considered: minimum standard deviation of segment magnitudes is explored in lieu of minimum standard deviation of angles. Marill's original experiment is then carefully repeated with several additional figure s that were deliberately chosen not to have all equal angles. The experiment is described in detail, and all the failures of Marill's algorithm are carefully studied and explained. The problem, of straight angles is touched upon and the difficulties of solving it as a special case are briefly discussed. A new program is the written to minimize the standard deviation of segment magnitudes instead of minimizing the standard deviation of angles. This program is run on the same test figures as the original algorithm. Its successes and failures are noted and explained, and its behaviors are studied. The results of the two algorithms zero then compared and the differences noted. It is of particular interest that the two algorithms have different areas of failure, suggesting that a combined algorithms should be able to produce better results than either one alone. This and some other avenues of future work are suggested. Finally, some comments about the basic behaviors of both algorithms are made.
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Eric Brown, Eric Brown, Patrick S. P. Wang, Patrick S. P. Wang, } "Three-dimensional object recovery from two-dimensional images: a new approach", Proc. SPIE 2904, Intelligent Robots and Computer Vision XV: Algorithms, Techniques,Active Vision, and Materials Handling, (29 October 1996); doi: 10.1117/12.256269; https://doi.org/10.1117/12.256269

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