Sparse-data based 3D surface reconstruction with vector matching

TL;DR

This paper introduces a novel method for 3D surface reconstruction from sparse 2D level lines, combining vector matching with total variation regularizers, and demonstrates its effectiveness on synthetic and real data.

Contribution

The paper proposes a new model and fast algorithm for 3D surface reconstruction from sparse data using normal vector matching and total variation regularization.

Findings

Effective reconstruction of detailed 3D surfaces from sparse level lines

The algorithm performs well on both synthetic and real-world data

The model captures complex structures with high accuracy

Abstract

Three dimensional surface reconstruction based on two dimensional sparse information in the form of only a small number of level lines of the surface with moderately complex structures, containing both structured and unstructured geometries, is considered in this paper. A new model has been proposed which is based on the idea of using normal vector matching combined with a first order and a second order total variation regularizers. A fast algorithm based on the augmented Lagrangian is also proposed. Numerical experiments are provided showing the effectiveness of the model and the algorithm in reconstructing surfaces with detailed features and complex structures for both synthetic and real world digital maps.