Polarized Microscopy Crystal Area Analysis

Automated quantification of birefringent crystal area from polarized light microscopy images using adaptive thresholding and morphological image analysis.

Overview

Under crossed polarizers, amorphous (isotropic) regions appear dark while crystalline domains exhibit birefringence and transmit light as bright regions. This tool segments and quantifies those bright crystalline regions, providing:

• Crystal area fraction (%) for each image
• Connected-component statistics (count, mean/median/max object size)
• Publication-ready figures (composite overlay + summary bar chart)
• Reproducible CSV output with full analysis parameters

Algorithm

 Polarized image (RGB)
        │
        ▼
 Extract signal channel (green / brightness / grayscale)
        │
        ▼
 Estimate background from dark pixels (intensity < 128)
   ├── bg_median
   └── bg_MAD (median absolute deviation)
        │
        ▼
 Adaptive threshold:  T = max(μ_bg + k × MAD_bg, T_min)
        │
        ▼
 Binary mask  →  Morphological opening  →  Small-object removal
        │
        ▼
 Connected-component labelling  →  Area quantification

The adaptive threshold ensures consistent segmentation across images with widely varying crystal densities — from near-zero to near-complete coverage — by anchoring the threshold to the dark (non-crystal) pixel population rather than the global intensity distribution.

Example Output

Composite Segmentation

Top row: original polarized micrographs. Bottom row: detected crystal regions (red overlay).

Crystal Area Chart

CSV Results

Sample	Crystal Area (%)	N Objects	Threshold
Sample 1	9.81	1,072	23.0
Sample 2	77.72	5	10.0
Sample 3	7.73	1,815	21.0

Installation

git clone https://github.com/YOUR_USERNAME/polarized-microscopy-crystal-analysis.git
cd polarized-microscopy-crystal-analysis
pip install -r requirements.txt

Dependencies: NumPy, Pandas, scikit-image, Matplotlib, Pillow

Usage

Basic

python crystal_area_analysis.py --input example_data/

Custom parameters

python crystal_area_analysis.py \
    --input path/to/images/ \
    --output path/to/results/ \
    --channel green \
    --k 3 \
    --min-threshold 15 \
    --format png \
    --dpi 150

All options

usage: crystal_area_analysis.py [-h] -i INPUT [-o OUTPUT]
                                [--channel {green,brightness,grayscale}]
                                [--k K] [--min-threshold MIN_THRESHOLD]
                                [--scale-bar-margin SCALE_BAR_MARGIN]
                                [--min-size MIN_SIZE]
                                [--morph-radius MORPH_RADIUS]
                                [--dpi DPI] [--format {tiff,png,pdf}]

Argument	Default	Description
--input	required	Directory with .tif polarized images
--output	<input>/analysis_output	Output directory
--channel	green	Signal channel (green, brightness, grayscale)
--k	2	MAD multiplier for adaptive threshold
--min-threshold	10	Noise-floor threshold (0-255)
--scale-bar-margin	0.08	Fraction of image to mask (scale bar region)
--min-size	5	Minimum object size in pixels
--morph-radius	1	Morphological opening disk radius
--dpi	300	Figure resolution
--format	tiff	Output figure format

Output Files

analysis_output/
├── crystal_area_results.csv       # Quantitative results per image
├── composite_segmentation.png     # Side-by-side original + overlay
├── crystal_area_chart.png         # Summary bar chart
├── analysis_parameters.txt        # Full parameter log
├── sample_1_mask.tif              # Binary mask per image
├── sample_2_mask.tif
└── sample_3_mask.tif

Image Requirements

• Format: .tif (RGB or RGBA)
• Acquisition: Crossed-polarizer configuration
• Naming: Any convention works — files with polarized in the name are auto-detected; otherwise all .tif files in the directory are processed

How It Works

1. Channel extraction — The green channel typically carries the strongest birefringence signal under standard crossed-polarizer setups. Alternative channels are available for non-standard configurations.

2. Background estimation — Statistics are computed exclusively from pixels with intensity < 128 (the dark sub-population). This prevents the threshold from being inflated in images where crystals dominate the field of view.

3. Adaptive thresholding — T = max(median + k * MAD, floor) provides a noise-robust threshold that adapts to each image's background characteristics while maintaining a minimum sensitivity floor.

4. Morphological cleanup — Opening with a small disk element removes salt noise, followed by connected-component filtering to discard objects below a minimum pixel count.

5. Quantification — Crystal area is the ratio of crystal-positive pixels to total valid pixels (excluding the scale-bar region). Connected-component labelling provides object-level statistics.

Author

Harshvardhan Modh

License

This project is licensed under the MIT License — see LICENSE for details.