How to Compute Image Moments in OpenCV Python?

Image moments are statistical measures that describe the shape and size characteristics of objects in an image. They are essential for computing features like center of mass, area, and orientation of objects. In OpenCV, image moments are calculated using contours of detected objects.

Syntax

The basic syntax for computing image moments is ?

cv2.moments(contour)

Where contour is a NumPy array containing the contour points of an object.

Understanding Image Moments

Image moments provide valuable information about objects ?

• m00 ? Area of the object
• m10, m01 ? First-order moments used to find centroid
• m20, m11, m02 ? Second-order moments for orientation
• mu20, mu11, mu02 ? Central moments (translation invariant)
• nu20, nu11, nu02 ? Normalized central moments (scale invariant)

Step-by-Step Process

Follow these steps to compute image moments ?

1. Load and convert the image to grayscale
2. Apply thresholding to create a binary image
3. Find contours using cv2.findContours()
4. Compute moments using cv2.moments()
5. Extract required features from the moments

Example 1: Computing Moments for Single Contour

This example demonstrates how to find moments for the first detected contour ?

import cv2
import numpy as np

# Create a sample image with geometric shapes
img = np.zeros((400, 400, 3), dtype=np.uint8)
cv2.rectangle(img, (50, 50), (150, 150), (255, 255, 255), -1)
cv2.circle(img, (300, 100), 50, (255, 255, 255), -1)
cv2.polygon(img, [np.array([(200, 200), (300, 200), (250, 300)])], (255, 255, 255))

# Convert to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

# Apply thresholding
ret, thresh = cv2.threshold(gray, 127, 255, cv2.THRESH_BINARY)

# Find contours
contours, _ = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
print(f"Number of contours detected: {len(contours)}")

# Get moments of the first contour
if contours:
    cnt = contours[0]
    M = cv2.moments(cnt)
    
    # Calculate centroid
    if M["m00"] != 0:
        cx = int(M["m10"] / M["m00"])
        cy = int(M["m01"] / M["m00"])
        print(f"Centroid: ({cx}, {cy})")
    
    # Draw contour and centroid
    cv2.drawContours(img, [cnt], -1, (0, 255, 0), 2)
    cv2.circle(img, (cx, cy), 5, (0, 0, 255), -1)
    
    print("Key moments:")
    print(f"Area (m00): {M['m00']}")
    print(f"Centroid X (m10/m00): {cx}")
    print(f"Centroid Y (m01/m00): {cy}")

Example 2: Computing Moments for All Contours

This example processes all detected contours and computes their moments ?

import cv2
import numpy as np

# Create a sample image with multiple shapes
img = np.zeros((400, 400, 3), dtype=np.uint8)
cv2.rectangle(img, (50, 50), (150, 150), (255, 255, 255), -1)
cv2.circle(img, (300, 100), 50, (255, 255, 255), -1)
cv2.polygon(img, [np.array([(200, 250), (300, 250), (250, 350)])], (255, 255, 255))

# Convert to grayscale and threshold
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, thresh = cv2.threshold(gray, 127, 255, cv2.THRESH_BINARY)

# Find all contours
contours, _ = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
print(f"Total contours found: {len(contours)}")

# Process each contour
for i, cnt in enumerate(contours):
    # Calculate moments
    M = cv2.moments(cnt)
    
    # Skip if contour has zero area
    if M["m00"] == 0:
        continue
        
    # Calculate centroid
    cx = int(M["m10"] / M["m00"])
    cy = int(M["m01"] / M["m00"])
    
    # Draw contour and label
    cv2.drawContours(img, [cnt], -1, (0, 255, 255), 2)
    cv2.circle(img, (cx, cy), 3, (0, 0, 255), -1)
    cv2.putText(img, f'Shape {i+1}', (cx-20, cy-10), 
                cv2.FONT_HERSHEY_SIMPLEX, 0.5, (255, 0, 0), 1)
    
    print(f"\nShape {i+1} moments:")
    print(f"  Area: {M['m00']:.2f}")
    print(f"  Centroid: ({cx}, {cy})")
    print(f"  Central moments - mu20: {M['mu20']:.2f}, mu02: {M['mu02']:.2f}")

print("\nProcessing complete!")

Computing Object Features from Moments

You can derive useful geometric properties from moments ?

import cv2
import numpy as np
import math

# Function to calculate object features from moments
def calculate_features(moments):
    features = {}
    
    if moments["m00"] != 0:
        # Centroid
        features["cx"] = int(moments["m10"] / moments["m00"])
        features["cy"] = int(moments["m01"] / moments["m00"])
        
        # Area
        features["area"] = moments["m00"]
        
        # Orientation (angle of major axis)
        mu20 = moments["mu20"]
        mu02 = moments["mu02"] 
        mu11 = moments["mu11"]
        
        if mu20 != mu02:
            theta = 0.5 * math.atan2(2 * mu11, mu20 - mu02)
            features["orientation"] = math.degrees(theta)
        else:
            features["orientation"] = 0
            
        # Eccentricity
        denominator = (mu20 + mu02)**2
        if denominator != 0:
            numerator = (mu20 - mu02)**2 + 4 * mu11**2
            features["eccentricity"] = math.sqrt(numerator) / (mu20 + mu02)
        else:
            features["eccentricity"] = 0
    
    return features

# Create sample image and process
img = np.zeros((300, 300, 3), dtype=np.uint8)
cv2.ellipse(img, (150, 150), (80, 40), 30, 0, 360, (255, 255, 255), -1)

gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
ret, thresh = cv2.threshold(gray, 127, 255, cv2.THRESH_BINARY)
contours, _ = cv2.findContours(thresh, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)

if contours:
    M = cv2.moments(contours[0])
    features = calculate_features(M)
    
    print("Object Features:")
    print(f"Area: {features['area']:.2f}")
    print(f"Centroid: ({features['cx']}, {features['cy']})")
    print(f"Orientation: {features['orientation']:.2f} degrees")
    print(f"Eccentricity: {features['eccentricity']:.3f}")

Conclusion

Image moments in OpenCV provide powerful tools for shape analysis and object characterization. Use cv2.moments() to extract geometric features like area, centroid, and orientation from object contours for computer vision applications.