Polygon Measurement Tool

A Python package for measuring polygons in YOLO format annotation files with UI features and reference scale measurement.

Features

• Enhanced UI: Crosshair cursor overlay for precise measurement
• High Accuracy: Three-measurement reference scale averaging
• Real-time Preview: Live measurement display with visual feedback
• Cross-platform: Works on Windows, macOS, and Linux
• GUI Integration: Directory selection dialog for ease of use
• Batch Processing: Process multiple image-label pairs automatically

Installation

From PyPI (recommended)

pip install polygon-measure

From Source

git clone https://github.com/
cd polygon-measure
pip install -e .

Development Installation

pip install -e ".[dev]"

Requirements

• Python 3.7+
• OpenCV 4.5.0+
• NumPy 1.19.0+
• Pandas 1.1.0+
• SciPy 1.5.0+

Usage

Command Line Interface

Using GUI (recommended)

polygon-measure --gui

Using Command Line Arguments

polygon-measure --images ./images --labels ./labels --output ./measurements

Using Short Arguments

polygon-measure -i ./images -l ./labels -o ./measurements

Python API

from polygon_measure import EnhancedPolygonMeasurementTool

# Initialize the tool
tool = EnhancedPolygonMeasurementTool(
    images_dir="./images",
    labels_dir="./labels",
    output_dir="./measurements"
)

# Run the measurement process
tool.run()

Run as Module

python -m polygon_measure --gui

How It Works

1. Scale Setting Process

For each image, you need to set the reference scale:

1. Draw 3 reference lines on the ruler (each representing 1 cm)
2. Press 'S' after drawing each line to save it
3. Tool calculates average scale from the 3 measurements
4. Statistical validation ensures measurement consistency

2. Measurement Process

• Load YOLO format label files automatically
• Calculate polygon dimensions using the reference scale
• Export measurements to CSV format
• Process multiple image-label pairs in batch

3. Controls

During scale setting:

• S - Save current measurement
• R - Reset/redraw current line
• G - Toggle grid overlay
• Q - Quit/skip current image
• ESC - Exit tool

Algorithm & Mathematical Implementation

Measurement Algorithm Flowchart

flowchart TD
    A["Input: Polygon Points<br/>(normalized coordinates)<br/>+ Image Shape"] --> B{"Polygon has<br/>≥ 3 points?"}
    
    B -->|No| C["Return: max_length=0<br/>max_width=0<br/>area=0"]
    
    B -->|Yes| D["Convert Normalized to<br/>Pixel Coordinates<br/><br/>x_pixel = x_norm × width<br/>y_pixel = y_norm × height"]
    
    D --> E["Calculate Max Length<br/>(Max Distance Between Any Two Points)"]
    
    E --> F["Calculate Max Width<br/>(Perpendicular to Longest Dimension)"]
    
    F --> G{"SciPy Available<br/>& Convex Hull<br/>Succeeds?"}
    
    G -->|Yes| H["Advanced Method:<br/>1. Generate Convex Hull<br/>2. For each edge:<br/>   - Find perpendicular vector<br/>   - Project all points<br/>   - Calculate width<br/>3. Return maximum width"]
    
    G -->|No| I["Simple Fallback Method:<br/>Bounding Box Approach<br/><br/>width_x = max_x - min_x<br/>width_y = max_y - min_y<br/>return min(width_x, width_y)"]
    
    H --> J["Calculate Area<br/>(Shoelace Formula)"]
    I --> J
    
    J --> K["Return Dictionary:<br/>{'max_length': float,<br/> 'max_width': float,<br/> 'area': float}"]
    
    style A fill:#e1f5fe
    style C fill:#ffebee
    style K fill:#e8f5e8
    style G fill:#fff3e0

Mathematical Formulas

1. Coordinate Conversion

Convert from normalized YOLO coordinates (0-1 range) to pixel coordinates:

x_pixel = x_normalized × image_width
y_pixel = y_normalized × image_height

2. Maximum Length Calculation

The maximum length is computed as the greatest Euclidean distance between any two vertices of the polygon.

Euclidean Distance Formula:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Maximum Length:

max_length = max{distance(pᵢ, pⱼ) | i,j ∈ {1,2,...,n}, i ≠ j}

where p₁, p₂, ..., pₙ are the polygon vertices.

3. Maximum Width Calculation

Advanced Method (Convex Hull Approach)

For accurate width measurement, the algorithm uses the convex hull and calculates the width perpendicular to each edge:

1. Edge Vector: e⃗ = p₂ - p₁

2. Unit Edge Vector: û = e⃗ / ||e⃗||

3. Perpendicular Unit Vector: n̂ = [-û_y, û_x]

4. Width for each edge:

   width = max{n̂ · pᵢ} - min{n̂ · pᵢ}
   

   where the dot product n̂ · pᵢ projects point pᵢ onto the perpendicular direction.

5. Maximum Width: max_width = max{width_edge₁, width_edge₂, ..., width_edgeₖ}

Simple Fallback Method

When SciPy is unavailable or convex hull computation fails:

width_x = max(x_coordinates) - min(x_coordinates)
width_y = max(y_coordinates) - min(y_coordinates)
max_width = min(width_x, width_y)

4. Area Calculation (Shoelace Formula)

The polygon area is calculated using the Shoelace formula¹:

For a polygon with vertices (x₁,y₁), (x₂,y₂), ..., (xₙ,yₙ):

Area = ½|∑ᵢ₌₁ⁿ (xᵢy_{i+1} - x_{i+1}yᵢ)|

where indices are taken modulo n (i.e., x_{n+1} = x₁, y_{n+1} = y₁).

Implementation Features

• Robust Fallback: Automatically switches to simpler algorithms when advanced libraries are unavailable
• Pixel-Perfect Accuracy: All calculations performed in pixel space for maximum precision
• Convex Hull Optimization: Uses computational geometry for true maximum width measurement
• Statistical Validation: Reference scale measurements include coefficient of variation analysis

References

1. Shoelace Formula (Surveyor's Formula): Braden, Bart (1986). "The Surveyor's Area Formula". The College Mathematics Journal. 17 (4): 326–337.
2. Convex Hull Algorithms: de Berg, Mark; van Kreveld, Marc; Overmars, Mark; Schwarzkopf, Otfried (2000). Computational Geometry: Algorithms and Applications. Springer-Verlag.
3. Euclidean Distance: Derived from the Pythagorean theorem, fundamental to metric geometry.

Output Format

The tool generates CSV files with the following columns:

• image_name - Name of the processed image
• polygon_count - Total number of polygons in the image
• polygon_id - ID of the current polygon
• max_length_cm - Maximum length in centimeters
• max_length_pixels - Maximum length in pixels
• max_width_cm - Maximum width in centimeters
• max_width_pixels - Maximum width in pixels
• area_cm2 - Area in square centimeters
• area_pixels2 - Area in square pixels
• scale_pixels_per_cm - Scale factor used for conversion

Directory Structure

your-project/
├── images/           # Input images
├── labels/           # YOLO format label files (.txt)
└── measurements/     # Output CSV files

YOLO Label Format

The tool expects YOLO segmentation format:

class_id x1 y1 x2 y2 x3 y3 ... xn yn

Where coordinates are normalized (0-1) relative to image dimensions.

Advanced Features

Statistical Analysis

• Measures consistency across the 3 reference measurements
• Warns if coefficient of variation exceeds 10%
• Provides standard deviation and mean calculations

Visual Enhancements

• Large, readable fonts with high contrast
• Smart text positioning to avoid UI overlap
• Grid overlay for precise alignment
• Color-coded measurement panels

Error Handling

• Graceful fallback for missing scipy (uses simple width calculation)
• Validation of input directories and files
• Comprehensive error messages and logging

Troubleshooting

Common Issues

1. No matching files found

   • Ensure image and label files have matching names
   • Check that label files have .txt extension
   • Verify directory paths are correct

2. Scale setting issues

   • Ensure you complete all 3 reference measurements
   • Press 'S' after drawing each line
   • Check that reference lines are drawn on a ruler

3. GUI not working

   • Install tkinter: sudo apt-get install python3-tk (Linux)
   • Use command line arguments as fallback

Development

Project Structure

polygon_measure/
├── __init__.py
├── __main__.py
├── cli.py
├── config.py
├── core/
│   ├── __init__.py
│   ├── measurement.py
│   └── geometry.py
├── ui/
│   ├── __init__.py
│   ├── directory_selector.py
│   └── display.py
└── utils/
    ├── __init__.py
    └── file_utils.py

Contributing

1. Fork the repository
2. Create a feature branch
3. Make your changes
4. Add tests if applicable
5. Submit a pull request

Support

For issues and questions:

• Review the command line help: polygon-measure --help
• Create an issue on GitHub