Shape reconstruction from gradient data

TL;DR

This paper introduces a new radial basis function-based method for reconstructing object shapes from gradient data obtained by optical sensors, effectively handling irregular, noisy, and incomplete measurements with high accuracy.

Contribution

The paper presents a novel shape reconstruction technique from gradient data using radial basis functions, improving robustness and accuracy over existing methods.

Findings

Effective reconstruction from irregular data

Robust to noise and incompleteness

High accuracy in local and global surface recovery

Abstract

We present a novel method for reconstructing the shape of an object from measured gradient data. A certain class of optical sensors does not measure the shape of an object, but its local slope. These sensors display several advantages, including high information efficiency, sensitivity, and robustness. For many applications, however, it is necessary to acquire the shape, which must be calculated from the slopes by numerical integration. Existing integration techniques show drawbacks that render them unusable in many cases. Our method is based on approximation employing radial basis functions. It can be applied to irregularly sampled, noisy, and incomplete data, and it reconstructs surfaces both locally and globally with high accuracy.