# Spatial Mask Merging
**Marko Mihajlović**, with contributions from **Marina Marjanović**  
*Faculty of Informatics and Computing, Singidunum University, Belgrade, Serbia*

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Official implementation of the Spatial Mask Merging (SMM) algorithm, a post-processing algorithm designed to improve instance segmentation in high-resolution images. It addresses the limitations of traditional tiling methods by merging fragmented masks using graph clustering and spatial metrics.

---

## 📺 Video Tutorial & Podcast

[![Watch: Gigapixel Vision's Fatal Flaw](https://img.youtube.com/vi/qlRl8fOBEMI/maxresdefault.jpg)](https://www.youtube.com/watch?v=qlRl8fOBEMI)

**[▶️ Watch on YouTube: Gigapixel Vision's Fatal Flaw - How SMM & R-Tree Indexing Fix Instance Segmentation](https://www.youtube.com/watch?v=qlRl8fOBEMI)**

**[🎙️ Listen on Spotify Podcasts](https://open.spotify.com/episode/4ftIsGI2tCTQAItR1fgTYL)** - Deep dive into the algorithm, optimization strategies, and real-world applications.

---

## Highlights
- ⚡ **High Performance:** Optimized ILP solver with 50-200% speedup for typical workloads
- 🧩 **Graph-Based Clustering:** Global optimization using correlation clustering with anti-chaining constraints
- 🔍 **Spatial Indexing:** R-tree acceleration for efficient neighbor queries (O(log N) vs O(N))
- 🎯 **Production Ready:** Comprehensive validation, error handling, and enterprise-grade code quality
- 🛡️ **Robust:** Handles edge cases, validates inputs, provides clear error messages
- 📦 **Easy Integration:** Clean API, compatible with SAHI and tiling-based inference pipelines
- 📈 **Scientifically Validated:** Published in Mathematics (MDPI) 2025, tested on iSAID benchmark
- 🔧 **Developer Friendly:** Type hints, comprehensive tests, extensive documentation  

---

## 🗂 Repository Structure

```
spatial-mask-merging/
│
├── docs/                         # Documentation and supporting materials
│   ├── algorithm_overview.md      # Algorithm description and math overview
│   ├── changelog.md               # Version history and updates
│   └── citation.bib               # Reference for academic citation
│
├── examples/                      # Example scripts and notebooks
│
├── smm/                           # Core SMM Python package
│   ├── __init__.py                # Package initialization
│   ├── predictions.py             # SMMPrediction data structure
│   ├── rtree_utils.py             # R-tree spatial indexing utilities
│   └── smm.py                     # Main SMM algorithm (ILP + Greedy)
│
├── tools/                        # Utilities (training, tuning, evaluation)
│   ├── gpu_evaluation.py         # Shared GPU evaluation module (used by all tools)
│   ├── optimize_smm.py           # Optuna-based hyperparameter optimizer for SMM
│   ├── visualization.py          # Visualize predictions or GT masks as PDFs for qualitative inspection
│   └── evaluation.py             # Batch evaluator (GPU-accelerated if PyTorch is available)
│
├── LICENSE                        # MIT License
├── README.md                      # Project readme (this file)
├── requirements.txt               # Python dependencies
└── setup.py                       # Package installation script
```

---

## Algorithm Overview

The **Spatial Mask Merging (SMM)** algorithm performs instance mask refinement by modeling predictions as nodes in a weighted graph, where edge weights express spatial and semantic consistency. The merging process is global, optimizing all candidate relations jointly instead of applying local, greedy rules.

### Main Components

1. **Graph Construction:**  
      Each predicted instance is treated as a vertex in a graph. Edges are established between masks that are spatially close, with edge weights reflecting three factors:  
   - *Spatial proximity* — normalized by distance threshold **τ_d**  
   - *Mask overlap* (IoU) — normalized by **τ_i**  
   - *Confidence consistency* — influenced by detection scores  

   The pairwise edge weight between instances *i* and *j* is computed as:

   ```
   w_ij = β₁ * (1 - D_ij / τ_d)_+ + β₂ * I_ij + β₃ * min(s_i, s_j)
   ```

   where  
   - **D_ij** – boundary distance between masks *M_i* and *M_j*  
   - **I_ij** – intersection-over-union (IoU) between masks  
   - **s_i**, **s_j** – detection confidences of the respective instances  

   The operator *(1 - D_ij / τ_d)_+* denotes the positive part of the normalized distance term (clamped at zero).  

2. **Spatial Pruning via R-tree:**  
   Neighboring masks are efficiently retrieved within a fixed search radius **ρ** using an R-tree spatial index. This ensures the algorithm remains scalable even with dense predictions.

3. **Global Optimization:**  
   Instance grouping is achieved using a correlation clustering objective that balances merging and separation penalties through the parameter **λ**. This provides globally consistent groupings rather than sequential local merges.

4. **Anti-Chaining Constraint:**  
   The anti-chaining threshold **γ** prevents indirect merging of incompatible objects, ensuring that all masks within a merged group are mutually compatible both geometrically and semantically.

---

## Algorithm Parameters

Spatial thresholds, edge weighting factors, and clustering penalties govern the behavior of the **Spatial Mask Merging (SMM)** algorithm. These parameters control the balance between over-merging and under-merging, spatial sensitivity, and candidate mask selection.

The parameters **τ_d**, **τ_i**, and **ρ** primarily regulate *candidate generation*, while the edge-weight coefficients **β₁**, **β₂**, **β₃**, the *correlation clustering penalty* **λ**, and the *anti-chaining threshold* **γ** influence *partitioning resolution*.  

Optimal values are **application-dependent** and vary based on object density, shape complexity, and whether inference is performed using tiling or full-image processing.

### Tunable Hyperparameters

| **Parameter** | **Description** | **Suggested Range** |
|----------------|-----------------|----------------------|
| **τ_d** | Distance scale (in pixels) used to normalize spatial proximity in edge weights *w_ij*. | 5–30 |
| **τ_i** | IoU threshold acting as a normalizing factor for overlap contribution. | 0.1–0.9 |
| **ρ** | R-tree search radius (in pixels) for candidate edge generation. | 10–50 |
| **β₁** | Weight of the distance contribution in *w_ij*. | 0.2–0.4 |
| **β₂** | Weight of the IoU contribution in *w_ij*. | 0.4–0.6 |
| **β₃** | Weight of the confidence contribution in *w_ij*. | 0.1–0.3 |
| **λ** | Correlation clustering penalty controlling over-merging vs. under-merging. Use `lambda_` in code. | 0.1–2.0 |
| **γ** | Pairwise threshold enforcing the anti-chaining constraint. | 0.3–0.7 |

> **Note:** Use `lambda_` (with underscore) in Python code since `lambda` is a reserved keyword.

> **Validation:** All parameters are now validated on initialization. Invalid values (e.g., negative `tau_d`, `tau_i > 1.0`) will raise `ValueError` with clear error messages.

---

## Mask Merging Function Details

The merging function consolidates clustered detections into unified instances, ensuring semantic and spatial consistency across merged groups.

Given a valid merge group  
**A = {o₁, o₂, …, oₖ}**, where each object **oᵢ = (Mᵢ, bᵢ, sᵢ, ℓᵢ)** consists of a binary mask, bounding box, confidence score, and shared label, the merging function **Φ(A)** produces a new object **oₙₑw** as follows:

1. **Mask Fusion:**  
   Combine all masks using a pixel-wise logical OR.  
   This ensures that all covered pixels remain preserved in the merged result.

2. **Bounding Box Update:**  
   Compute the minimal axis-aligned rectangle enclosing all boxes in **A**.

3. **Score Aggregation:**  
   Compute the merged confidence either as an arithmetic mean or as a mask-size-weighted mean.

4. **Class Label Assignment:**  
   Since all members of **A** share the same class label, the merged object inherits this label.

The resulting merged object is  
**oₙₑw = (Mₙₑw, bₙₑw, sₙₑw, ℓₙₑw)**.

### Properties of Φ(A)
- **Idempotence:** Φ({o}) = o  
- **Symmetry:** Invariant to the ordering of elements in A  
- **Mask Preservation:** Ensures no loss of coverage, i.e., ⋃ₜ Mᵢₜ ⊆ Mₙₑw  

This formulation guarantees that merging consolidates spatially and semantically consistent detections into coherent instances, improving robustness of tiled inference without chained or inconsistent groupings.

---

## 📘 Documentation

For a detailed algorithmic explanation, see:  
[**algorithm_overview.md**](docs/algorithm_overview.md)

Changelog:  
[**changelog.md**](docs/changelog.md)

---

## 🧩 Installation

Clone this repository and install dependencies:

```bash
# Clone the repository
git clone https://github.com/mihajlov39547/spatial-mask-merging.git
cd spatial-mask-merging

# (Optional) create a virtual environment
python3 -m venv .venv
source .venv/bin/activate  # bash/linux
.venv\Scripts\activate     # windows

# Install required dependencies
pip install -r requirements.txt

# Verify installation
python check_env.py
```

**Dependencies:**
- **Core:** numpy, scipy, networkx, pulp, rtree, Pillow
- **Tools:** opencv-python-headless, pandas, tqdm, optuna, matplotlib
- **Optional:** torch (for GPU-accelerated evaluation)

**Quick environment check:**
```bash
python check_env.py  # Comprehensive environment validation
pip list             # List installed packages
```

---

## 🚀 Sample Usage

### 1) Core SMM (Python API)

```python
from smm.smm import SpatialMaskMerger
from smm.predictions import SMMPrediction

# Create prediction container for one image
prediction = SMMPrediction(image_name="example.png")

# Add annotations (from your model output)
prediction.add_annotation(
    type="car",
    class_id=0,
    confidence=0.91,
    bbox=[100, 100, 200, 200],
    segmentation=[[[100, 100], [200, 100], [200, 200], [100, 200]]]
)

# Initialize SMM with paper parameters
merger = SpatialMaskMerger(
    tau_d=15.0,      # Distance threshold (pixels)
    tau_i=0.5,       # IoU threshold
    rho=30.0,        # R-tree search radius
    beta1=0.3,       # Distance weight
    beta2=0.5,       # IoU weight
    beta3=0.2,       # Confidence weight
    gamma=0.5,       # Anti-chaining threshold
    lambda_=1.0      # Clustering penalty
)

# Merge masks (returns list of dicts with mask, bbox, score, label)
merged = merger.merge(prediction, image_size_hw=(1024, 1024))
for obj in merged:
    print(f"Label: {obj['label']}, Score: {obj['score']:.2f}")
```

---

### 2) Hyperparameter Optimization (Optuna)

Run Bayesian optimization to tune SMM hyperparameters on your dataset:

```bash
python tools/optimize_smm.py \
  --pred_dir /path/to/preds_json \
  --gt_dir /path/to/gt_json \
  --img_dir /path/to/images \
  --out_dir ./opt_results \
  --trials 30 \
  --seed 42
```

**Optimized Parameters:**
- `tau_d` (5.0-30.0): Distance threshold
- `tau_i` (0.1-0.9): IoU threshold  
- `rho` (10.0-50.0): R-tree search radius
- `beta1` (0.2-0.4): Distance weight
- `beta2` (0.4-0.6): IoU weight
- `beta3` (0.1-0.3): Confidence weight
- `gamma` (0.3-0.7): Anti-chaining threshold
- `lambda_` (0.1-2.0): Clustering penalty

**Outputs:**
- `best_params_ilp.json` — optimized hyperparameters
- `smm_ilp_hparam_importance.json/.pdf` — parameter importance analysis
- `smm_ilp_optuna_trials.csv` — complete trial history

**Performance:**
- Uses shared `gpu_evaluation.py` module for consistent evaluation with `evaluation.py`
- GPU-accelerated evaluation (10-50× faster than CPU)
- ILP solver remains CPU-bound by design

**Note:** SMM uses ILP-based correlation clustering (CPU-bound). GPU acceleration applies only to evaluation metrics.

---

### 3) Batch Evaluation

Evaluate predictions against ground-truth with comprehensive metrics:

```bash
python tools/evaluation.py \
  --pred_dir /path/to/merged_preds_json \
  --gt_dir /path/to/gt_json \
  --img_dir /path/to/images \
  --out_csv ./results.csv \
  --iou_thr 0.5 \
  --downscale 4
```

**Computed Metrics:**
- **Precision/Recall/F1**: Standard classification metrics
- **Dice Coefficient**: Overlap quality measure
- **PQ (Panoptic Quality)**: Combines segmentation and recognition quality
- **Avg Fragments**: Over-segmentation measure (predictions per GT object)
- **Count Error**: Absolute difference in object counts
- **Mean Error**: Average localization error in pixels

**Performance:**
- **GPU mode** (with PyTorch+CUDA): 10-50× faster, 500MB-2GB VRAM
- **CPU mode** (fallback): 1-5 sec/image, 100-500MB RAM
- **Downscaling**: `--downscale 4` reduces memory by 16× with minimal accuracy loss
- **Architecture**: Uses shared `gpu_evaluation.py` module for consistent evaluation logic

**Features:**
- ✅ Automatic GPU→CPU fallback on OOM
- ✅ Robust error handling (skips corrupted files)
- ✅ Progress tracking with tqdm
- ✅ Consistent metrics across CPU/GPU modes
- ✅ Shared evaluation code with optimization tools (DRY architecture)

---

### 4) Visualization

Render predictions or ground-truth polygons as PDFs for qualitative inspection:

```bash
# Visualize predictions
python tools/visualization.py preds \
  --pred-base-dir /path/to/pred_jsons \
  --image-dir /path/to/images

# Visualize ground-truth
python tools/visualization.py gt \
  --folder /path/to/gt_labels_and_images

# Compare GT and predictions
python tools/visualization.py compare \
  --image-path /path/to/image.png \
  --gt-label /path/to/label.txt \
  --pred-json /path/to/pred.json
```

**Output:** Creates `<image_name>_pred_visualization.pdf` or `_gt_visualization.pdf` files with color-coded class overlays.

---

## 🔧 Troubleshooting

### Environment Issues
```bash
# Check all dependencies
python check_env.py

# Verify specific imports
python -c "from smm.smm import SpatialMaskMerger; print('✅ SMM OK')"
python -c "import torch; print('CUDA:', torch.cuda.is_available())"
```

### Common Issues

**ImportError: No module named 'smm'**
- Make sure you're in the project root directory
- Or install in development mode: `pip install -e .`

**GPU Out of Memory**
- Evaluation script auto-falls back to CPU
- Use `--downscale 4` to reduce memory
- Close other GPU processes

**Optimization is slow**
- Expected: 5-30 min/trial (ILP solver is CPU-intensive)
- Use `--subset_per_trial 5` for faster testing
- Reduce `--trials` for initial exploration

**Missing JSON files**
- Ensure prediction and GT files have matching basenames
- Check file extensions are `.json`
- Verify directory paths are correct

---

## 📊 Performance Characteristics

| Component | Method | Time Complexity | Typical Performance | Optimization Status |
|-----------|--------|-----------------|---------------------|--------------------|
| **SMM Core** | ILP | O(E·N) sparse, O(N³) dense* | 0.1-5 sec/image | ✅ Optimized |
| **Optimization** | Optuna | - | 5-30 min/trial | ✅ Robust |
| **Evaluation (GPU)** | PyTorch | O(N²) | 0.1-0.5 sec/image | ✅ Memory-efficient |
| **Evaluation (CPU)** | NumPy | O(N²) | 1-5 sec/image | ✅ Consistent |
| **Shared Module** | gpu_evaluation.py | - | - | ✅ DRY architecture |

*N = number of predicted masks per image, E = number of candidate edges*

### Performance Optimizations Applied

| **Component** | **Optimization** | **Speedup** |
|---------------|------------------|-------------|
| Triangle inequalities | Sparse graph iteration (O(N³) → O(E·N)) | 10-100x |
| IoU computation | Bitwise ops instead of logical ops | 2-3x |
| Boundary pixels | Pre-computation + caching | 30-50% |
| Bbox rasterization | Direct int() for non-negative coords | 10-15% |
| Bbox intersection | Single compound expression | 5-10% |
| **Overall** | **Combined optimizations** | **50-200%** |

### Scalability
- **Small datasets** (<100 objects/image): Near-instantaneous (<0.5s)
- **Medium datasets** (100-500 objects): Fast (0.5-2s)
- **Large datasets** (500+ objects): Efficient with sparse graphs (2-5s)
- **R-tree acceleration:** O(log N) neighbor queries vs O(N) brute force

---

## ✅ Production Status

> **Current Version:** [v1.0.0](https://github.com/mihajlov39547/spatial-mask-merging/releases/tag/v1.0.0) (November 2025)
> 
> **Status:** 🟢 **Production Ready**  
> **Stability:** Extensively tested and optimized  
> **Code Quality:** Enterprise-grade with comprehensive validation  
> **Use Cases:** Research, production deployments, high-resolution image segmentation

### Quality Assurance
- ✅ **Comprehensive Testing:** 35+ unit tests covering all modules
- ✅ **Performance Optimized:** 50-200% faster than initial implementation
- ✅ **Input Validation:** All parameters validated with clear error messages
- ✅ **Error Handling:** Graceful fallbacks for edge cases and failures
- ✅ **Type Safety:** Full type hints throughout codebase
- ✅ **Clean API:** Proper encapsulation, no namespace pollution
- ✅ **Documentation:** Comprehensive docstrings and examples

### Recent Optimizations (November 2025)

**Core Algorithm (`smm.py`):**
- 🚀 Triangle inequality generation: O(N³) → O(E·N) for sparse graphs (10-100x speedup)
- 🚀 IoU computation: 2-3x faster using bitwise operations
- 🚀 Boundary pixel pre-computation: 30-50% runtime reduction
- 🛡️ Comprehensive parameter validation with clear error messages
- 🛡️ ILP solver timeout (300s) with graceful fallback
- 🛡️ Improved empty mask handling for edge cases

**Data Structures (`predictions.py`, `rtree_utils.py`):**
- ✅ Added `validate_all()` method for batch validation
- ✅ Enhanced error messages for invalid inputs
- ✅ Optimized bbox rasterization (10-15% faster)
- ✅ Added `is_optimized()` introspection method
- ✅ Query bbox validation to prevent malformed queries

**Tools (`optimize_smm.py`, `evaluation.py`, `gpu_evaluation.py`, `visualization.py`):**
- ✅ Refactored duplicate GPU code into shared `gpu_evaluation.py` module (~500 lines eliminated)
- ✅ Fixed API usage to match core implementation
- ✅ Added GPU memory management (torch.cuda.empty_cache())
- ✅ Improved error handling and user feedback
- ✅ Better input validation and progress reporting
- ✅ DRY architecture: single source of truth for GPU evaluation logic

**Package (`__init__.py`):**
- ✅ Clean namespace - internal modules not exposed
- ✅ Proper API encapsulation following best practices

---

## Citation
If you use this work, please cite:
```bibtex
@article{mihajlovic2025enhancing,
  title={Enhancing Instance Segmentation in High-Resolution Images Using Slicing-Aided Hyper Inference and Spatial Mask Merging Optimized via R-Tree Indexing},
  author={Mihajlovic, Marko and Marjanovic, Marina},
  journal={Mathematics},
  volume={13},
  number={19},
  pages={3079},
  year={2025},
  publisher={MDPI},
  note={(This article belongs to the Special Issue Mathematics Applications of Artificial Intelligence and Computer Vision)
}
```

## Copyright

Copyright (c) 2025 Marko Mihajlović, with contributions from Marina Marjanović

This repository provides the official implementation of the Spatial Mask Merging (SMM) algorithm.
All source code is distributed under the terms of the MIT License.
Users are permitted to use, modify, and distribute the software freely, provided that proper attribution is given through citation of the above publication.

For any use in academic, scientific, or derivative research, the citation of the original paper is strongly encouraged to acknowledge the theoretical and methodological contribution of this work.

## License

MIT License

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

## Acknowledgments

This research was conducted as part of the development of advanced post-processing techniques for high-resolution aerial imagery segmentation.