Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Curvy: A Parametric Cross-section based Surface Reconstruction

Aradhya N. Mathur, Apoorv Khattar, Ojaswa Sharma

TL;DR

This work uses a compact parametric polyline representation using adaptive splitting to represent the cross-sections and performs learning using a Graph Neural Network to reconstruct the underlying shape in an adaptive manner reducing the dependence on the number of cross-sections provided.

Abstract

In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in this problem setting. Most methods in the classical literature lack the ability to generalize based on object class and employ complex mathematical machinery to reconstruct reliable surfaces. We present a simple learnable approach to generate a large number of points from a small number of input cross-sections over a large dataset. We use a compact parametric polyline representation using adaptive splitting to represent the cross-sections and perform learning using a Graph Neural Network to reconstruct the underlying shape in an adaptive manner reducing the dependence on the number of cross-sections provided.

Curvy: A Parametric Cross-section based Surface Reconstruction

TL;DR

This work uses a compact parametric polyline representation using adaptive splitting to represent the cross-sections and performs learning using a Graph Neural Network to reconstruct the underlying shape in an adaptive manner reducing the dependence on the number of cross-sections provided.

Abstract

In this work, we present a novel approach for reconstructing shape point clouds using planar sparse cross-sections with the help of generative modeling. We present unique challenges pertaining to the representation and reconstruction in this problem setting. Most methods in the classical literature lack the ability to generalize based on object class and employ complex mathematical machinery to reconstruct reliable surfaces. We present a simple learnable approach to generate a large number of points from a small number of input cross-sections over a large dataset. We use a compact parametric polyline representation using adaptive splitting to represent the cross-sections and perform learning using a Graph Neural Network to reconstruct the underlying shape in an adaptive manner reducing the dependence on the number of cross-sections provided.
Paper Structure (18 sections, 3 equations, 6 figures, 1 table)

This paper contains 18 sections, 3 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related work
  3. Pointcloud generation
  4. Surface reconstruction
  5. Approach
  6. Adaptive Splitting
  7. Training on parametric space
  8. Permutation Invariance and Neighborhoods
  9. Learning Point Cloud Representation
  10. Cross-Section Attention
  11. Adapting for Variable Cross-sections
  12. Training Details
  13. Training details
  14. Results and Discussion
  15. Cross-section dependence
  16. ...and 3 more sections

Figures (6)

  • Figure 1: Overview of our reconstruction approach. Starting from a parametric representation of the given cross-sections, we train a network to generate a surface point cloud.
  • Figure 2: Converting a piecewise parametric representation of a cross-section (left) to a graph (right). The nodes in the graph are matrices of coefficients of the parametric functions.
  • Figure 3: During training, the graph embedding decoder tries to generate an embedding that is similar to the point cloud embedding generated from the pre-trained encoder. This representation is then used by the decoder to generate the point cloud of a relevant shape.
  • Figure 4: (Left) Comparison of reconstruction quality with an increasing number of cross-sections. Input to the network is the set of cross-sections (red) belonging to the ground truth mesh(blue).
  • Figure 5: Failure cases resulting in incorrect shapes. Input to the network are the cross-sections (red) belonging to the ground truth mesh(white).
  • ...and 1 more figures