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Data-driven quasi-interpolant spline surfaces for point cloud approximation

Andrea Raffo, Silvia Biasotti

TL;DR

This paper investigates a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds, and introduces a novel data-driven implementation that combines prediction capability and complexity efficiency.

Abstract

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data.

Data-driven quasi-interpolant spline surfaces for point cloud approximation

TL;DR

This paper investigates a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds, and introduces a novel data-driven implementation that combines prediction capability and complexity efficiency.

Abstract

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data.

Paper Structure

This paper contains 26 sections, 15 equations, 10 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Previous Work
  3. Weighted Quasi Interpolant Spline Approximations
  4. Preliminary concepts
  5. Properties
  6. Data-driven implementation
  7. Data pre-processing
  8. wQISA formulation
  9. Parameter settings
  10. Termination criterion
  11. Model assessment
  12. Computational complexity
  13. Experimental settings
  14. Approximation methods
  15. Implicit approximation with radial basis functions
  16. ...and 11 more sections

Figures (10)

  • Figure 1: Noise and outliers robustness. The input point cloud is represented in blue, the output approximation is displayed in red. The noise increases from the left to the right. The outliers increase from top to bottom.
  • Figure 2: Flowchart of the data-driven wQISA algorithm.
  • Figure 3: Point cloud partitioning. (a) The original point cloud $\mathcal{P}$; (b) the training set $\mathcal{T}$; (c) the validation set $\mathcal{V}$; (d) the test set $\mathcal{U}$.
  • Figure 4: CPU times. Log-log plot of the CPU times when increasing the point cloud cardinality and the number of coefficients.
  • Figure 5: Left sides: the original models (from STARC repository STARC). Right sides: outcomes of the wQISA method via Gaussian weights for the areas highlighted in red.
  • ...and 5 more figures

Theorems & Definitions (4)

  • Definition 3.1
  • Remark 3.2
  • Remark 3.3
  • Remark 3.4