What is spatial resolution and how to measure it?

How to measure spatial resolution

Select a test pattern or image: To measure spatial resolution, we need a test pattern or an image that contains known features or structures. These features should have varying spatial frequencies and be positioned close to each other. Test patterns are often designed with alternating black and white lines.
Display the test pattern or image: Use an appropriate software or library to display the test pattern or image on your imaging system.
Peak detection: Analyze the image to find distinct features or edges. In the case of a test pattern, this might involve finding the transitions between black and white lines. In more complex images, it may involve finding edges or changes in contrast.
Calculate spatial resolution: Measure the distance between the detected features, such as the spacing between the alternating lines in the test pattern. Spatial resolution is then calculated in LP/mm or pixels per unit distance.
Output the result: The result of our spatial resolution measurement is typically provided in LP/mm or pixels per unit distance. This value represents the system’s ability to distinguish fine details or high-frequency components in an image.

Code example

This code demonstrates how to measure spatial resolution using a custom image and provides the resulting LP/mm value.

import cv2
import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import find_peaks
# Reading the image using imread() function
custom_image = cv2.imread('../custom.png', cv2.IMREAD_GRAYSCALE)
# Displaying the image using imshow() function
plt.imshow(custom_image, cmap='gray')
cv2.waitKey(0)
# Check if the image is in a valid format
if custom_image is not None and custom_image.ndim == 2:
    # Calculate the spatial resolution
    line_sum = np.sum(custom_image, axis=0)
    # Find peaks by comparing pixel intensity to a threshold (adjust as needed)
    threshold = 0.5  # We can adjust this threshold
    peaks, _ = find_peaks(line_sum, height=threshold)
    # Calculate spatial resolution based on peak distances
    mm_per_image = 10  # Width of the image in millimeters
    pixel_per_mm = custom_image.shape[1] / mm_per_image
    peak_distances = np.diff(peaks)
    spatial_resolution = pixel_per_mm / np.mean(peak_distances)
    print(f"Spatial Resolution: {spatial_resolution:.2f} LP/mm")
else:
    print("Failed to load the custom image or the image is not in a valid format.")

Code explanation

Here’s a detailed explanation of the provided code for measuring spatial resolution using a custom image:

Lines 7–11: In this section, we load a custom image named custom.png using the OpenCV (cv2) library. The cv2.IMREAD_GRAYSCALE flag specifies that the image should be loaded as a grayscale image. The loaded image is then displayed using Matplotlib. The cv2.waitKey(0) function is used to display the image indefinitely until a key is pressed.
Lines 13–30:
1. The code checks whether the image was loaded successfully (custom_image is not None) and if it’s in a valid format for spatial resolution measurement. A valid format, in this case, is a 2-D grayscale image (custom_image.ndim == 2).
2. If the image is in a valid format, it proceeds with calculating the spatial resolution:
  1. The line_sum calculates the sum of pixel intensities along the horizontal axis, effectively creating a line profile of the image.
  2. Peak detection is performed by finding points where the line profile exceeds a specified threshold. The threshold can be adjusted to control the sensitivity of peak detection.
  3. The spatial resolution is then calculated based on the detected peaks and their distances. It uses a scaling factor to convert the pixel-based measurement to LP/mm (line pairs per millimeter).
3. Finally, the code prints the calculated spatial resolution to the console. If the image is not loaded or is in an invalid format, it displays an error message.

This code demonstrates how to load a custom image, validate its format, and measure the spatial resolution based on pixel intensities and peak detection. The spatial resolution is presented as LP/mm, indicating the ability to distinguish line pairs within the image.

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