Curve Reconstruction via the Global Statistics of Natural Curves

TL;DR

This paper introduces a method for reconstructing missing parts of curves by leveraging the global statistics of natural curves, focusing on physically plausible completions and addressing data limitations through scale invariance and extensibility properties.

Contribution

It proposes a simple, physically motivated curve reconstruction model that utilizes statistical geometrical properties to improve robustness and applicability.

Findings

Mean curves are often scale invariant.

Extensibility of mean curves enhances sample efficiency.

Physically plausible reconstructions align with perceptual likelihoods.

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.