Curve Reconstruction via the Global Statistics of Natural Curves
This work addresses curve reconstruction for applications like image inpainting and object synthesis, but it is incremental as it builds on existing statistical methods by exploiting scale invariance and extensibility to improve robustness.
The authors tackled the problem of reconstructing missing parts of curves by using the global statistics of natural curves to find the mean physical curve for given inducer configurations, resulting in more physically plausible reconstructions and insights into why some configurations yield consistent perceptual completions.
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.