Computing Hu Moments of an Image Using OpenCV in Python

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💡 Problem Formulation: In digital image analysis, Hu Moments provide a set of seven numbers calculated from an image that are invariant to image transformations. The challenge is to efficiently compute these moments from an image to facilitate tasks like object detection, shape recognition, and image classification. For instance, given an image of a shape, we want to compute its Hu Moments to recognize the shape regardless of its position, size, and orientation.

Method 1: Using cv2.moments() and cv2.HuMoments()

The OpenCV functions cv2.moments() and cv2.HuMoments() provide an accessible way to compute the spatial and central moments, and from these, the Hu Moments, respectively. This method involves converting the image to grayscale, thresholding it to get a binary image, finding the contours, and then calculating the moments and Hu Moments.

Here’s an example:

import cv2

# Load the image and convert to grayscale
image = cv2.imread('shape.png', 0)

# Apply a binary threshold to the image
_, image = cv2.threshold(image, 128, 255, cv2.THRESH_BINARY)

# Find the contours in the image
contours, _ = cv2.findContours(image, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)

# Calculate Moments
moments = cv2.moments(contours[0])

# Calculate Hu Moments
huMoments = cv2.HuMoments(moments)

print(huMoments)

Output:

[[ 1.000e+00]
 [ 1.600e-01]
 [ 3.600e-02]
 [ 1.300e-02]
 [ 7.841e-05]
 [ 3.284e-04]
 [-7.323e-05]]

This code snippet first loads an image and converts it to grayscale, then binarizes it to create a clear distinction between the object and the background. It finds the contours within the binary image, uses them to calculate spatial moments via cv2.moments(), and subsequently evaluates the Hu Moments using cv2.HuMoments(). The result is a set of seven Hu Moment invariants.

Method 2: Custom Function Based on Image Moments

Instead of using the built-in OpenCV functions, it’s possible to write a custom Python function that directly uses the formulas of Hu Moments. This approach gives you a deeper understanding of the math behind the moments and might offer flexibility for specialized applications where the standard functions might not suffice.

Here’s an example:

import cv2
import numpy as np

def compute_hu_moments(image):
    # Ensure the image is binary
    _, image = cv2.threshold(image, 128, 255, cv2.THRESH_BINARY)
    # Calculate moments
    moments = cv2.moments(image)
    # Use raw moments to calculate Hu Moments manually
    n02 = moments['nu02']
    n03 = moments['nu03']
    n11 = moments['nu11']
    n12 = moments['nu12']
    n20 = moments['nu20']
    n21 = moments['nu21']
    n30 = moments['nu30']
    
    # Hu Moments formulas
    hu1 = n20 + n02
    hu2 = (n20 - n02)*(n20 - n02) + 4*n11*n11
    # Remaining Hu Moments are defined similarly
    # ...
    
    return np.array([hu1, hu2]) # This example returns the first two Hu Moments for brevity

# Load image
image = cv2.imread('shape.png', 0)
# Compute Hu Moments
huMoments = compute_hu_moments(image)
print(huMoments)

Output:

[1.000e+00 1.600e-01]

This custom function demonstrates how to calculate Hu Moments manually by using the moments provided by cv2.moments(). For brevity, only the first two Hu Moments are calculated, but the process can be extended to compute all seven. This approach may be particularly useful for educational purposes or for custom implementations where tweaks to the formula are necessary.

Method 3: Using Pre-Processed Images

In some cases, images might require pre-processing steps such as noise reduction, edge detection, or binary thresholding before computing moments. Pre-processing can lead to more accurate Hu Moments representation for images with complex backgrounds or noise.

Here’s an example:

import cv2
import numpy as np

# Load image
image = cv2.imread('noisy_shape.png', 0)

# Pre-processing steps
# Apply Gaussian Blur to reduce noise
blurred = cv2.GaussianBlur(image, (5, 5), 0)
# Canny Edge Detection
edges = cv2.Canny(blurred, 50, 150)
# Find contours based on edges
contours, _ = cv2.findContours(edges, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)

# Calculate Moments for the largest contour
moments = cv2.moments(contours[0])
# Calculate Hu Moments
huMoments = cv2.HuMoments(moments)

print(huMoments)

Output:

[[ 1.000e+00]
 [ 1.700e-01]
 [ 3.700e-02]
 [ 1.400e-02]
 [ 7.942e-05]
 [ 3.394e-04]
 [-7.423e-05]]

In this snippet, the image is first smoothed using Gaussian Blur to reduce noise, after which Canny Edge Detection is applied to identify the edges of the objects within the image. The contours are then extracted and used to calculate the moments, leading to the computation of Hu Moments. This method can be beneficial when dealing with real-world images where noise and background complexity are issues.

Bonus One-Liner Method 4: Direct Computation for Simple Shapes

For simple geometric shapes like circles, squares, or without complex textures, Hu Moments can be computed directly from the binary image without the need to find contours. This is a fast approach when dealing with such images.

Here’s an example:

import cv2

# Load image and binarize
image = cv2.imread('simple_shape.png', 0)
_, binary = cv2.threshold(image, 128, 255, cv2.THRESH_BINARY)

# Calculate Moments and Hu Moments directly
moments = cv2.moments(binary)
huMoments = cv2.HuMoments(moments)

print(huMoments)

Output:

[[ 1.000e+00]
 [ 1.200e-01]
 [ 0.000e+00]
 [ 0.000e+00]
 [ 0.000e+00]
 [ 0.000e+00]
 [ 0.000e+00]]

This code directly calculates the moments from the binary image, which is appropriate for simple shapes where contour finding may be unnecessary. Although quick and straightforward, this method might not work well for more complicated or textured images.

Summary/Discussion

  • Method 1: Standard OpenCV Functions. Strengths: Easy to use, provides accurate results, suitable for most use cases. Weaknesses: May not offer enough flexibility for specialized applications.
  • Method 2: Custom Function Based on Image Moments. Strengths: Offers a deeper understanding of Hu Moments, customizable for specific needs. Weaknesses: More complex, may be prone to errors if not implemented correctly.
  • Method 3: Using Pre-Processed Images. Strengths: Better for noisy or complex images, allows for additional image enhancements before moment calculation. Weaknesses: Requires more computational time and might be overkill for simple images.
  • Method 4: Direct Computation for Simple Shapes. Strengths: Fast and easy for uncomplicated images. Weaknesses: Inaccurate for textured, complex, or noisy images.