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Next Best View For Point-Cloud Model Acquisition: Bayesian Approximation and Uncertainty Analysis

Madalena Caldeira, Plinio Moreno

TL;DR

This work adapts the point-net-based neural network for Next-Best-View (PC-NBV) and incorporates dropout layers into the model's architecture, thus allowing the computation of the uncertainty estimate associated with its predictions.

Abstract

The Next Best View problem is a computer vision problem widely studied in robotics. To solve it, several methodologies have been proposed over the years. Some, more recently, propose the use of deep learning models. Predictions obtained with the help of deep learning models naturally have some uncertainty associated with them. Despite this, the standard models do not allow for their quantification. However, Bayesian estimation theory contributed to the demonstration that dropout layers allow to estimate prediction uncertainty in neural networks. This work adapts the point-net-based neural network for Next-Best-View (PC-NBV). It incorporates dropout layers into the model's architecture, thus allowing the computation of the uncertainty estimate associated with its predictions. The aim of the work is to improve the network's accuracy in correctly predicting the next best viewpoint, proposing a way to make the 3D reconstruction process more efficient. Two uncertainty measurements capable of reflecting the prediction's error and accuracy, respectively, were obtained. These enabled the reduction of the model's error and the increase in its accuracy from 30\% to 80\% by identifying and disregarding predictions with high values of uncertainty. Another method that directly uses these uncertainty metrics to improve the final prediction was also proposed. However, it showed very residual improvements.

Next Best View For Point-Cloud Model Acquisition: Bayesian Approximation and Uncertainty Analysis

TL;DR

This work adapts the point-net-based neural network for Next-Best-View (PC-NBV) and incorporates dropout layers into the model's architecture, thus allowing the computation of the uncertainty estimate associated with its predictions.

Abstract

The Next Best View problem is a computer vision problem widely studied in robotics. To solve it, several methodologies have been proposed over the years. Some, more recently, propose the use of deep learning models. Predictions obtained with the help of deep learning models naturally have some uncertainty associated with them. Despite this, the standard models do not allow for their quantification. However, Bayesian estimation theory contributed to the demonstration that dropout layers allow to estimate prediction uncertainty in neural networks. This work adapts the point-net-based neural network for Next-Best-View (PC-NBV). It incorporates dropout layers into the model's architecture, thus allowing the computation of the uncertainty estimate associated with its predictions. The aim of the work is to improve the network's accuracy in correctly predicting the next best viewpoint, proposing a way to make the 3D reconstruction process more efficient. Two uncertainty measurements capable of reflecting the prediction's error and accuracy, respectively, were obtained. These enabled the reduction of the model's error and the increase in its accuracy from 30\% to 80\% by identifying and disregarding predictions with high values of uncertainty. Another method that directly uses these uncertainty metrics to improve the final prediction was also proposed. However, it showed very residual improvements.

Paper Structure

This paper contains 20 sections, 18 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. State of the Art
  3. Deep Learning for the NBV Problem Resolution
  4. Uncertainty in Deep Learning
  5. Methodology
  6. Dataset
  7. Training and Model Architecture
  8. Baseline
  9. Architectural Changes
  10. Performance evaluation metrics
  11. Bayesian PC-NBV Inference and Uncertainty
  12. Inference
  13. Uncertainty Measurements
  14. Results Analysis
  15. Training and Testing Results
  16. ...and 5 more sections

Figures (8)

  • Figure 1: PC-NBV Units Architecture. Convolutional Layers: Orange; Activation Layers: Green; Inputs: Gray; Features: Pink
  • Figure 2: Bayesian PC-NBV architecture. Input and Output: Gray; Larger Units: Purple; Pooling Layers: Yellow; Fully Connected Layers: Blue; Features: Pink; Convolutional Layers: Orange; Activation Layers: Light Green; Dropout Layers: Dark Green.
  • Figure 3: PC-NBV Learning Curve. Loss given by Equation \ref{['eq:loss']}
  • Figure 4: Distribution of the sample's error in function of uncertainty - different combinations. From top to bottom - uncertainty: $\sigma_{NBV}$, \ref{['eq:std_nbv']}; $\overline{\sigma}$, \ref{['eq:std_mean']}; $\sigma_{whole}$, \ref{['eq:std_whole']}. From left to right - error: Euclidean Distance, \ref{['eq:dist_error']}; Squared Differences, \ref{['eq:mse_error']}.
  • Figure 5: Distribution of the sample's Euclidean Distance error in function of the $\sigma_{whole}$ uncertainty and its approximated fit line (in red) with $R^2=0.695$.
  • ...and 3 more figures