Abstract
Reconstructing the missing parts of a curve has been
the subject of much computational research, with applications in image inpainting, object synthesis, etc. Different
approaches for solving that problem are typically based on
processes that seek visually pleasing or perceptually plausible completions. In this work we focus on reconstructing the
underlying physically likely shape by utilizing the global
statistics of natural curves. More specifically, we develop
a reconstruction model that seeks the mean physical curve
for a given inducer configuration. This simple model is both
straightforward to compute and it is receptive to diverse additional information, but it requires enough samples for all
curve configurations, a practical requirement that limits its
effective utilization. To address this practical issue we explore and exploit statistical geometrical properties of natural curves, and in particular, we show that in many cases
the mean curve is scale invariant and oftentimes it is extensible. This, in turn, allows to boost the number of examples
and thus the robustness of the statistics and its applicability. The reconstruction results are not only more physically
plausible but they also lead to important insights on the reconstruction problem, including an elegant explanation why
certain inducer configurations are more likely to yield consistent perceptual completions than others