5 Best Ways to Find Laplacian Pyramids for an Image Using OpenCV in Python

💡 Problem Formulation: When working with image processing tasks, sometimes it’s necessary to transform an image into different scales to analyze it at various resolutions. Laplacian pyramids are a type of image pyramid used to reconstruct an image from its smoothed versions, emphasizing multi-scale edge information. This article explores methods to construct Laplacian pyramids for an image using OpenCV in Python, starting from the base image and progressively downscaling. The desired output is a set of images that represent different layers of the Laplacian pyramid.

Method 1: Using PyrDown and PyrUp

This method involves using the cv2.pyrDown() function to downsample an image, followed by cv2.pyrUp() to upsample the downsampled image to its original size. By subtracting the upsampled image from the original, one obtains a level of the Laplacian pyramid.

Here’s an example:

import cv2

# Load the image
image = cv2.imread('input.jpg')

# Downsample the image
lower_reso = cv2.pyrDown(image)

# Upsample the downsampled image
higher_reso = cv2.pyrUp(lower_reso)

# Calculate the Laplacian
laplacian = cv2.subtract(image, higher_reso)

Output: An image representing one level of the Laplacian pyramid.

The example first reads an image from disk using cv2.imread(). The image is then downsampled with cv2.pyrDown(), upscaled back using cv2.pyrUp(), and finally, the Laplacian is obtained by subtracting the upscaled version from the original image, which emphasizes edges at that resolution scale.

Method 2: Repeated Scaling and Differencing

This method involves iteratively downscaling the original image using cv2.pyrDown(), then computing the Laplacian by taking the difference between the current downscaled image and its upsampled version.

Here’s an example:

import cv2

# Load the image
original_image = cv2.imread('input.jpg')
current_level = original_image

# List to store the Laplacian pyramid
laplacian_pyramid = []

# Build the pyramid
while current_level.shape[0] >= 2:
    lower_reso = cv2.pyrDown(current_level)
    higher_reso = cv2.pyrUp(lower_reso, dstsize=current_level.shape[:2])
    laplacian = cv2.subtract(current_level, higher_reso)
    laplacian_pyramid.append(laplacian)
    current_level = lower_reso

Output: A list of images, each representing a different level of the Laplacian pyramid.

The code performs a while loop, repeatedly downscaling the image until its resolution is too low, and simultaneously computes the Laplacian for every level. The result is a list of images, with each image corresponding to one level of the Laplacian pyramid.

Method 3: Utilizing Custom Kernels for Difference

Rather than using upscaling and downscaling functions, one could define a custom Laplacian filter kernel and apply it directly to the image to find the Laplacian representation.

Here’s an example:

import cv2
import numpy as np

# Load the image
image = cv2.imread('input.jpg', cv2.IMREAD_GRAYSCALE)

# Define the Laplacian kernel
laplacian_kernel = np.array([[0, 1, 0], [1, -4, 1], [0, 1, 0]])

# Apply the Laplacian kernel
laplacian = cv2.filter2D(image, -1, laplacian_kernel)

Output: An image showing the edges of the input image as defined by the Laplacian kernel.

In this approach, a custom kernel representing the Laplacian filter is applied to the image using the cv2.filter2D() function. This method gets edge information directly without needing to scale the image up and down, potentially saving computational resources.

Method 4: Using Gaussian Pyramids as a Base

A Gaussian pyramid is a precursor to the Laplacian pyramid. Here we create the Gaussian pyramid first and then use these layers to construct the Laplacian pyramid.

Here’s an example:

import cv2

# Load the image
image = cv2.imread('input.jpg')

# Create Gaussian Pyramid
gaussian_pyramid = [image]
for i in range(6):
    image = cv2.pyrDown(image)
    gaussian_pyramid.append(image)

# Create Laplacian Pyramid
laplacian_pyramid = [gaussian_pyramid[-1]]
for i in range(5, 0, -1):
    size = (gaussian_pyramid[i-1].shape[1], gaussian_pyramid[i-1].shape[0])
    laplacian = cv2.subtract(gaussian_pyramid[i-1], cv2.pyrUp(gaussian_pyramid[i], dstsize=size))
    laplacian_pyramid.append(laplacian)

Output: A list of images, each representing a layer of the Laplacian pyramid derived from the Gaussian pyramid.

This code snippet uses cv2.pyrDown() iteratively to create each level of the Gaussian pyramid and then to create the Laplacian pyramid by upsampling and subtracting the Gaussian pyramid levels in a reverse order.

Bonus One-Liner Method 5: Direct Function for Pyramid Layers

OpenCV doesn’t have a direct one-liner function to create a Laplacian pyramid. However, using NumPy and list comprehensions, we can create a more concise version of the methods outlined above.

Here’s an example:

import cv2
import numpy as np

# Load the image
image = cv2.imread('input.jpg')

# Generate Gaussian pyramid and derive Laplacian pyramid
laplacian_pyramid = [image - cv2.pyrUp(cv2.pyrDown(image))]
for i in range(5):
    image = cv2.pyrDown(image)
    laplacian_pyramid.append(image - cv2.pyrUp(image))

Output: A list of images; the first element being the top of the Laplacian pyramid followed by layers built from scaled-down images.

This one-liner code effectively combines downsampling and upsampling in a list comprehension to build a Laplacian pyramid, although in reality, it’s still multiple lines of code encapsulated into a loop for brevity.

Summary/Discussion

• Method 1: PyrDown and PyrUp. Efficient for single-level pyramid creation. Limited to constructing one level at a time.
• Method 2: Repeated Scaling and Differencing. Constructs a full pyramid; iterative approach. Could be slower due to loop iterations.
• Method 3: Custom Kernels for Difference. Direct method for edge detection. Does not construct scale space representations.
• Method 4: Using Gaussian Pyramids as a Base. Provides a solid foundation for pyramid construction. More steps required, less direct than other methods.
• Method 5: Direct Function (List Comprehension). Syntactically concise. Complexity hidden within the list comprehension, less readable.