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Utilizing Reinforcement Learning for Bottom-Up part-wise Reconstruction of 2D Wire-Frame Projections

Julian Ziegler, Patrick Frenzel, Mirco Fuchs

TL;DR

This work presents a reinforcement learning framework for bottom-up reconstruction of 2D wire-frame projections by an agent that iteratively transforms a reconstruction line to align with target edges in a 60×60 state space. It introduces two action-space variants (SAT and FAT), multiple reward schemes including a combined $G_t = R_t + E_t$ formulation, and curriculum learning strategies (action-based and difficulty-based) to improve training stability. Empirical results show that the combined reward with difficulty curriculum yields the strongest and most stable performance, achieving mean IoU values approaching $0.97$ in simplified settings and up to $0.85$ in harder multi-detection tasks with extended training. The approach demonstrates the potential of iterative, image-based RL for wire-frame reconstruction and provides a framework for applying curricula and tailored rewards to similar segmentation-like tasks.

Abstract

This work concerns itself with the task of reconstructing all edges of an arbitrary 3D wire-frame model projected to an image plane. We explore a bottom-up part-wise procedure undertaken by an RL agent to segment and reconstruct these 2D multipart objects. The environment's state is represented as a four-colour image, where different colours correspond to background, a target edge, a reconstruction line, and the overlap of both. At each step, the agent can transform the reconstruction line within a four-dimensional action space or terminate the episode using a specific termination action. To investigate the impact of reward function formulations, we tested episodic and incremental rewards, as well as combined approaches. Empirical results demonstrated that the latter yielded the most effective training performance. To further enhance efficiency and stability, we introduce curriculum learning strategies. First, an action-based curriculum was implemented, where the agent was initially restricted to a reduced action space, being able to only perform three of the five possible actions, before progressing to the full action space. Second, we test a task-based curriculum, where the agent first solves a simplified version of the problem before being presented with the full, more complex task. This second approach produced promising results, as the agent not only successfully transitioned from learning the simplified task to mastering the full task, but in doing so gained significant performance. This study demonstrates the potential of an iterative RL wire-frame reconstruction in two dimensions. By combining optimized reward function formulations with curriculum learning strategies, we achieved significant improvements in training success. The proposed methodology provides an effective framework for solving similar tasks and represents a promising direction for future research in the field.

Utilizing Reinforcement Learning for Bottom-Up part-wise Reconstruction of 2D Wire-Frame Projections

TL;DR

This work presents a reinforcement learning framework for bottom-up reconstruction of 2D wire-frame projections by an agent that iteratively transforms a reconstruction line to align with target edges in a 60×60 state space. It introduces two action-space variants (SAT and FAT), multiple reward schemes including a combined formulation, and curriculum learning strategies (action-based and difficulty-based) to improve training stability. Empirical results show that the combined reward with difficulty curriculum yields the strongest and most stable performance, achieving mean IoU values approaching in simplified settings and up to in harder multi-detection tasks with extended training. The approach demonstrates the potential of iterative, image-based RL for wire-frame reconstruction and provides a framework for applying curricula and tailored rewards to similar segmentation-like tasks.

Abstract

This work concerns itself with the task of reconstructing all edges of an arbitrary 3D wire-frame model projected to an image plane. We explore a bottom-up part-wise procedure undertaken by an RL agent to segment and reconstruct these 2D multipart objects. The environment's state is represented as a four-colour image, where different colours correspond to background, a target edge, a reconstruction line, and the overlap of both. At each step, the agent can transform the reconstruction line within a four-dimensional action space or terminate the episode using a specific termination action. To investigate the impact of reward function formulations, we tested episodic and incremental rewards, as well as combined approaches. Empirical results demonstrated that the latter yielded the most effective training performance. To further enhance efficiency and stability, we introduce curriculum learning strategies. First, an action-based curriculum was implemented, where the agent was initially restricted to a reduced action space, being able to only perform three of the five possible actions, before progressing to the full action space. Second, we test a task-based curriculum, where the agent first solves a simplified version of the problem before being presented with the full, more complex task. This second approach produced promising results, as the agent not only successfully transitioned from learning the simplified task to mastering the full task, but in doing so gained significant performance. This study demonstrates the potential of an iterative RL wire-frame reconstruction in two dimensions. By combining optimized reward function formulations with curriculum learning strategies, we achieved significant improvements in training success. The proposed methodology provides an effective framework for solving similar tasks and represents a promising direction for future research in the field.

Paper Structure

This paper contains 15 sections, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Setting
  4. Methodology
  5. Environment and Action Space Configurations:
  6. Reward Functions:
  7. Learning Curricula:
  8. Experiments:
  9. Experimental Setup:
  10. Results
  11. Reward Functions:
  12. Curriculum Learning Experiments:
  13. Discussion
  14. Reward Functions:
  15. Curriculum Learning Experiments:

Figures (2)

  • Figure 1: Example Episode with wire-frame translations (blue) and reconstruction line transformations (green) highlighted. For more in-depth visualizations, please visit our https://github.com/juliantziegler/RL_Wire-Frame_Reconstruction.
  • Figure 2: Mean IoU of the conducted Experiments. Best viewed in colour.