Split, Merge, and Refine: Fitting Tight Bounding Boxes via Over-Segmentation and Iterative Search
Bibliographic record
Abstract
Achieving tight bounding boxes of a shape while guaranteeing complete boundness is an essential task for efficient geometric operations and unsupervised semantic part detection. But previous methods fail to achieve both full coverage and tightness. Neural-network-based methods are not suitable for these goals due to the non-differentiability of the objective, while classic iterative search methods suffer from their sensitivity to the initialization. We propose a novel framework for finding a set of tight bounding boxes of a 3D shape via over-segmentation and iterative merging and refinement. Our result shows that utilizing effective search methods with appropriate objectives is the key to producing bounding boxes with both properties. We employ an existing pre-segmentation to split the shape and obtain over-segmentation. Then, we apply hierarchical merging with our novel tightness-aware merging and stopping criteria. To overcome the sensitivity to the initialization, we also define actions to refine the bounding box parameters in an Markov Decision Process (MDP) setup with a soft reward function promoting a wider exploration. Lastly, we further improve the refinement step with Monte Carlo Tree Search (MCTS) based multi-action space exploration. By thoughtful evaluation on diverse 3D shapes, we demonstrate full coverage, tightness, and an adequate number of bounding boxes of our method without requiring any training data or supervision. It thus can be applied to various downstream tasks in computer vision and graphics.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".