5 Best Ways to Compute Image Moments in OpenCV Python

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💡 Problem Formulation: In the realm of image processing and computer vision, computing image moments is essential for tasks such as object detection, shape analysis, and image recognition. Image moments capture basic information about the shape and structure of an image. We seek methods for calculating image moments using OpenCV and Python, taking an input image and producing a set of moment values as the output.

Method 1: Using cv2.moments()

OpenCV provides the cv2.moments() function which calculates the moments of a binary image. These moments are a weighted average of the pixel intensities and can be used to calculate the center of mass, area, and other characteristics of an image.

Here’s an example:

import cv2
import numpy as np

# Load image as grayscale
image = cv2.imread('image.jpg', cv2.IMREAD_GRAYSCALE)

# Convert to binary via thresholding
_, binary = cv2.threshold(image, 127, 255, cv2.THRESH_BINARY)

# Calculate moments
moments = cv2.moments(binary)

print(moments)

Output will be a dictionary containing moment values, such as {'m00': 15120.0, 'm10': 6008000.0, ...}.

This code snippet starts by loading an image in grayscale, then applies a threshold to convert it to a binary image. It then computes the moments of the image using the cv2.moments() function, returning a dictionary where each key-value pair represents a moment and its value.

Method 2: Contour Detection and Moment Calculation

Another way to compute moments is by finding contours in the image with cv2.findContours() and then calculating the moments of these contours. This is useful when you need to analyze specific objects within an image.

Here’s an example:

import cv2

# Load image, convert to binary
image = cv2.imread('image.jpg', cv2.IMREAD_GRAYSCALE)
_, binary = cv2.threshold(image, 127, 255, cv2.THRESH_BINARY)

# Find contours
contours, _ = cv2.findContours(binary, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)

# Iterate through contours and compute moments
for contour in contours:
    moments = cv2.moments(contour)
    print(moments)

Each iteration will print moments for a different contour, e.g., {'m00': 5520.0, 'm10': 442342.0, ...} and so on.

The snippet finds contours in the given binary image using the cv2.findContours() function and then calculates the moments of each contour separately. This approach allows you to analyze the moments for individual objects within an image.

Method 3: Central Moments

Central moments are invariant to translation and can be calculated using the central moments from the cv2.moments() dictionary. Central moments provide more robust descriptors for shape analysis.

Here’s an example:

import cv2

# Load and threshold image
image = cv2.imread('image.jpg', cv2.IMREAD_GRAYSCALE)
_, binary = cv2.threshold(image, 127, 255, cv2.THRESH_BINARY)

# Calculate moments
moments = cv2.moments(binary)

# Central moments
cx = moments['m10'] / moments['m00']
cy = moments['m01'] / moments['m00']

print("Central moments: cx = {}, cy = {}".format(cx, cy))

This will display the central moments as coordinates, like Central moments: cx = 456, cy = 389.

After calculating the image moments, the code computes the central moments (centroids) using the m10, m01, and m00 moment values. Central moments are useful in determining the geometric center of an object.

Method 4: Hu Moments

Hu Moments are a set of seven numbers calculated using moments that are invariant to image transformations. They are widely used for image recognition and matching because of their invariance properties.

Here’s an example:

import cv2

# Load and threshold image
image = cv2.imread('image.jpg', cv2.IMREAD_GRAYSCALE)
_, binary = cv2.threshold(image, 127, 255, cv2.THRESH_BINARY)

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

print("Hu Moments:", huMoments.flatten())

It prints the Hu Moments as an array, e.g., Hu Moments: [2.676...e-01 6.458...e-02 8.234...e-04 ...].

Here, after computing moments, the code snippet leverages cv2.HuMoments() to obtain the seven Hu moments, which form a 1D array after being flattened. These can then be used for image comparison tasks.

Bonus One-Liner Method 5: Computing Moments with NumPy Directly

For a direct approach, you can calculate raw image moments using NumPy functions without using OpenCV’s built-in methods.

Here’s an example:

import numpy as np

# Load image as binary
binary_image = ...

# Calculate raw image moments with numpy
m00 = np.sum(binary_image)
m10 = np.sum(binary_image * np.arange(binary_image.shape[1]))
m01 = np.sum(binary_image * np.arange(binary_image.shape[0]).reshape(-1, 1))

print("Raw moments:", m00, m10, m01)

This results in the raw moments being printed out, for example: Raw moments: 15120 6008000 2552000.

This efficient one-liner code sample utilizes NumPy to compute the zeroth and first-order moments. For more complex moments, the calculation would be extended analogously, exploiting NumPy’s powerful array operations.

Summary/Discussion

  • Method 1: cv2.moments(). Straightforward use of OpenCV function. Good for quick and general moment calculations. Not specialized for particular objects or shapes within an image.
  • Method 2: Contour Detection and Moment Calculation. Ideal for computing moments of individual objects. Requires additional steps to find contours, which may be computationally expensive for complex images.
  • Method 3: Central Moments. Best for translation-invariant descriptors of object shape. Requires initial moment calculations and additional computation to find the centroid.
  • Method 4: Hu Moments. Excellent for image recognition and matching with robustness to transformations. More abstract and takes more computation than basic moments.
  • Bonus Method 5: NumPy Direct Moments. Fast and direct using NumPy. May require additional understanding of mathematical underpinnings for implementation. Less intuitive than using built-in OpenCV functions.