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# Color Difference Calculations
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Color difference calculations provide perceptual measures of how different two colors appear to human vision. Colormath implements multiple industry-standard Delta E algorithms, each optimized for different applications and levels of accuracy.
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## Capabilities
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### CIE 1976 Delta E
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The original CIE Delta E formula, simple but less perceptually uniform than newer methods.
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```python { .api }
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def delta_e_cie1976(color1, color2):
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    """
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    Calculate CIE 1976 Delta E difference.
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    Parameters:
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    - color1: First color object (Lab, Luv, or other color space)
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    - color2: Second color object (same type as color1)
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    Returns:
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    float: Delta E difference value (typically 0-100+)
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    Notes:
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    - Simple Euclidean distance in Lab space
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    - Values < 1: Not perceptible by human eye
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    - Values 1-2: Perceptible through close observation
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    - Values 2-10: Perceptible at a glance
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    - Values > 10: Colors appear as different colors
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    """
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```
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### CIE 1994 Delta E
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Improved formula with weighting factors for different viewing conditions.
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```python { .api }
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def delta_e_cie1994(color1, color2, K_L=1, K_C=1, K_H=1, K_1=0.045, K_2=0.015):
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    """
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    Calculate CIE 1994 Delta E difference.
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    Parameters:
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    - color1: First color object (Lab color recommended)
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    - color2: Second color object (same type as color1)
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    - K_L: Lightness weighting factor (default: 1)
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    - K_C: Chroma weighting factor (default: 1)
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    - K_H: Hue weighting factor (default: 1)
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    - K_1: First parametric factor (default: 0.045)
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    - K_2: Second parametric factor (default: 0.015)
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    Returns:
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    float: Delta E difference value
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    Notes:
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    - Better perceptual uniformity than CIE 1976
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    - Separate weighting for lightness, chroma, and hue
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    - Standard conditions: K_L=K_C=K_H=1
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    - Textiles: K_L=2, K_C=K_H=1
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    """
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```
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### CIE 2000 Delta E
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Most advanced and perceptually accurate Delta E formula currently available.
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```python { .api }
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def delta_e_cie2000(color1, color2, Kl=1, Kc=1, Kh=1):
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    """
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    Calculate CIE 2000 Delta E difference.
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    Parameters:
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    - color1: First color object (Lab color recommended)
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    - color2: Second color object (same type as color1)
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    - Kl: Lightness weighting factor (default: 1)
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    - Kc: Chroma weighting factor (default: 1)
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    - Kh: Hue weighting factor (default: 1)
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    Returns:
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    float: Delta E difference value
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    Notes:
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    - Most perceptually uniform Delta E formula
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    - Addresses issues with CIE 1994 in blue region
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    - Industry standard for color quality control
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    - Recommended for most applications
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    - Values < 1: Not perceptible
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    - Values 1-2: Just perceptible
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    - Values 2-5: Perceptible
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    - Values > 5: Well perceptible
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    """
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```
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### CMC Delta E
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Color Measurement Committee formula with adjustable tolerances for different industries.
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```python { .api }
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def delta_e_cmc(color1, color2, pl=2, pc=1):
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    """
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    Calculate CMC Delta E difference.
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    Parameters:
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    - color1: First color object (Lab color recommended)
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    - color2: Second color object (same type as color1)
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    - pl: Lightness tolerance factor (default: 2)
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    - pc: Chroma tolerance factor (default: 1)
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    Returns:
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    float: Delta E difference value
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    Notes:
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    - Designed for textile industry applications
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    - Standard acceptability: pl=2, pc=1 (CMC 2:1)
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    - Perceptibility threshold: pl=1, pc=1 (CMC 1:1)
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    - Good performance in neutral colors
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    """
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```
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## Usage Examples
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### Basic Color Difference
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```python
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from colormath.color_objects import LabColor
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from colormath.color_diff import delta_e_cie2000
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# Create two Lab colors
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color1 = LabColor(lab_l=50.0, lab_a=20.0, lab_b=-30.0)
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color2 = LabColor(lab_l=52.0, lab_a=18.0, lab_b=-28.0)
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# Calculate Delta E 2000 (recommended)
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diff = delta_e_cie2000(color1, color2)
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print(f"Delta E 2000: {diff:.2f}")
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```
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### Comparing Different Delta E Methods
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```python
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from colormath.color_objects import LabColor
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from colormath.color_diff import (
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    delta_e_cie1976, delta_e_cie1994, 
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    delta_e_cie2000, delta_e_cmc
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)
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color1 = LabColor(lab_l=50, lab_a=0, lab_b=0)
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color2 = LabColor(lab_l=52, lab_a=2, lab_b=-1)
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# Compare all methods
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diff_1976 = delta_e_cie1976(color1, color2)
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diff_1994 = delta_e_cie1994(color1, color2)
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diff_2000 = delta_e_cie2000(color1, color2)
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diff_cmc = delta_e_cmc(color1, color2)
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print(f"CIE 1976: {diff_1976:.2f}")
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print(f"CIE 1994: {diff_1994:.2f}")
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print(f"CIE 2000: {diff_2000:.2f}")
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print(f"CMC:      {diff_cmc:.2f}")
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```
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### Working with Different Color Spaces
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```python
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from colormath.color_objects import sRGBColor, LabColor
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from colormath.color_conversions import convert_color
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from colormath.color_diff import delta_e_cie2000
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# Create RGB colors
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rgb1 = sRGBColor(rgb_r=0.8, rgb_g=0.2, rgb_b=0.1)
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rgb2 = sRGBColor(rgb_r=0.85, rgb_g=0.15, rgb_b=0.12)
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# Convert to Lab for Delta E calculation
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lab1 = convert_color(rgb1, LabColor)
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lab2 = convert_color(rgb2, LabColor)
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# Calculate difference
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diff = delta_e_cie2000(lab1, lab2)
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print(f"RGB color difference: {diff:.2f}")
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```
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### Industry-Specific Tolerances
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```python
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from colormath.color_objects import LabColor
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from colormath.color_diff import delta_e_cie1994, delta_e_cmc
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color_standard = LabColor(lab_l=50, lab_a=10, lab_b=-5)
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color_sample = LabColor(lab_l=51, lab_a=12, lab_b=-3)
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# Graphic arts (standard conditions)
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diff_graphics = delta_e_cie1994(color_standard, color_sample)
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# Textiles (K_L=2 for textile industry)
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diff_textiles = delta_e_cie1994(color_standard, color_sample, K_L=2)
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# CMC for acceptability (2:1 ratio)
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diff_cmc_accept = delta_e_cmc(color_standard, color_sample, pl=2, pc=1)
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# CMC for perceptibility (1:1 ratio)
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diff_cmc_percept = delta_e_cmc(color_standard, color_sample, pl=1, pc=1)
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print(f"Graphics:      {diff_graphics:.2f}")
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print(f"Textiles:      {diff_textiles:.2f}")
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print(f"CMC Accept:    {diff_cmc_accept:.2f}")
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print(f"CMC Percept:   {diff_cmc_percept:.2f}")
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```
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### Batch Color Difference Analysis
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```python
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from colormath.color_objects import LabColor
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from colormath.color_diff import delta_e_cie2000
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# Reference color
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reference = LabColor(lab_l=50, lab_a=0, lab_b=0)
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# Sample colors to compare
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samples = [
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    LabColor(lab_l=52, lab_a=2, lab_b=-1),
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    LabColor(lab_l=48, lab_a=-1, lab_b=3),
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    LabColor(lab_l=50, lab_a=5, lab_b=-2),
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    LabColor(lab_l=53, lab_a=-3, lab_b=4)
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]
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# Calculate differences
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differences = [delta_e_cie2000(reference, sample) for sample in samples]
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# Analyze results
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for i, diff in enumerate(differences):
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    status = "PASS" if diff < 2.0 else "FAIL"
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    print(f"Sample {i+1}: ΔE = {diff:.2f} [{status}]")
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```
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### Quality Control Workflow
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```python
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from colormath.color_objects import LabColor
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from colormath.color_diff import delta_e_cie2000
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def assess_color_quality(standard_color, test_color, tolerance=2.0):
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    """
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    Assess color quality against standard.
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    Parameters:
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    - standard_color: Reference color
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    - test_color: Color to test
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    - tolerance: Maximum acceptable Delta E
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    Returns:
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    dict: Quality assessment results
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    """
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    diff = delta_e_cie2000(standard_color, test_color)
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    if diff <= tolerance * 0.5:
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        grade = "Excellent"
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    elif diff <= tolerance:
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        grade = "Acceptable"
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    else:
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        grade = "Reject"
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    return {
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        'delta_e': diff,
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        'grade': grade,
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        'pass': diff <= tolerance,
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        'tolerance': tolerance
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    }
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# Example usage
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standard = LabColor(lab_l=50, lab_a=10, lab_b=-10)
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test_sample = LabColor(lab_l=51, lab_a=11, lab_b=-9)
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result = assess_color_quality(standard, test_sample)
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print(f"Grade: {result['grade']}")
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print(f"Delta E: {result['delta_e']:.2f}")
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print(f"Pass: {result['pass']}")
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```
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## Delta E Interpretation Guidelines
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### General Perception Thresholds
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| Delta E Range | Perception Level | Description |
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|---------------|------------------|-------------|
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| 0-1           | Not perceptible  | Colors appear identical |
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| 1-2           | Just perceptible | Very close observation needed |
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| 2-5           | Perceptible      | Colors appear similar but different |
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| 5-10          | Well perceptible | Clear color difference |
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| 10+           | Very different   | Colors appear as different colors |
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### Industry-Specific Tolerances
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| Industry | Application | Typical Tolerance | Method |
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|----------|-------------|-------------------|---------|
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| Printing | Commercial printing | ΔE < 3-5 | CIE 2000 |
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| Textiles | Color matching | ΔE < 1-2 | CMC 2:1 |
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| Paints | Automotive coatings | ΔE < 1 | CIE 2000 |
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| Displays | Monitor calibration | ΔE < 2 | CIE 2000 |
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| Photography | Color reproduction | ΔE < 2-3 | CIE 2000 |
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## Method Selection Guidelines
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### When to Use Each Method
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- **CIE 1976**: Simple applications, historical compatibility
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- **CIE 1994**: Better than 1976, still widely used in industry
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- **CIE 2000**: Most accurate, recommended for new applications
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- **CMC**: Textile industry, neutral color evaluation
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### Computational Performance
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| Method | Speed | Accuracy | Use Case |
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|--------|-------|----------|----------|
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| CIE 1976 | Fastest | Low | Quick screening |
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| CIE 1994 | Fast | Medium | General purpose |
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| CIE 2000 | Slower | High | Quality control |
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| CMC | Fast | Medium | Textiles |