Scikit Image - Finding Local Minima

Quiz

In image processing, the term "minima" or "minimum" refers to points or regions within a digital image where the pixel values reach their lowest level within a specific neighbourhood. In contrast, finding maxima in an image involves identifying points or regions where the values are at their lowest within a local neighbourhood. Local minima denote notable troughs or regions of low intensity within the data. Finding minima plays a significant role in various image analysis tasks, including feature identification, object segmentation, and image enhancement.

Scikit-image libraries offer functions like local_minima() and h_minima() to detect the local minima within an image.

Using the skimage.morphology.local_minima() function

The local_minima() function is used to identify and locate local minima within an n-dimensional array(image). Local minima are points or regions where the pixel values are at their lowest compared to their neighbouring pixels within a specified neighbourhood.

Syntax

Following is the syntax of this function −

skimage.morphology.local_minima(image, footprint=None, connectivity=None, indices=False, allow_borders=True)

Parameters

image (ndarray): This is the n-dimensional array on which local minima will find.
footprint (ndarray, optional): The footprint, also known as the structuring element, is used to determine the neighborhood of each evaluated pixel. It must be a boolean array and have the same number of dimensions as the image. If neither footprint nor connectivity are given, all adjacent pixels are considered part of the neighborhood.
connectivity (int, optional): This parameter is used to determine the neighborhood of each evaluated pixel. It specifies which adjacent pixels are considered neighbors based on their squared distance from the center. Pixels whose squared distance is less than or equal to connectivity are considered neighbors. This parameter is ignored if the footprint is not None.
indices (bool, optional): If True, the output will be a tuple of one-dimensional arrays representing the indices (coordinates) of local minima in each dimension. If False, the output will be a boolean array with the same shape as the image, where True indicates the position of local minima, and False indicates other positions.
allow_borders (bool, optional): If True, it allows plateaus that touch the image border to be considered as valid minima. If set to False, minima that are on the image borders are not considered.

Return Value

It returns minima, which can be either an ndarray or a tuple of ndarrays, depending on the value of the indices parameter.

Example

The following example demonstrates how to find and visualize local minima in an image using the local_minima() function.

import numpy as np
from skimage.morphology import local_minima
from skimage.measure import label
import matplotlib.pyplot as plt
from skimage import io, color, exposure 

# Load the input image
image = io.imread('Images/Tajmahal.jpg')

# For illustration purposes, we focus on a specific region of the image.
x_0 = 170
y_0 = 100
width = 250
height = 150

# Crop the image to the specified region
image = color.rgb2gray(image)[y_0:(y_0 + height), x_0:(x_0 + width)]

# Rescale the image intensity for visualization purposes.
image = exposure.rescale_intensity(image)

# Find local minima by comparing to all neighboring pixels
minima = local_minima(image)

# Label the local minima to distinguish them
label_minima = label(minima)

# Overlay the labeled local minima on the original image
overlay = color.label2rgb(label_minima, image, alpha=0.7, bg_label=0, bg_color=None, colors=[(1, 0, 0)])

# Plot the original and the resultant images
fig, axes = plt.subplots(1, 2, figsize=(10, 5))
ax = axes.ravel()

# Display the original image
ax[0].imshow(image, cmap=plt.cm.gray)
ax[0].axis('off')
ax[0].set_title('Original Image)

# Display the local minima
ax[1].imshow(overlay, cmap=plt.cm.gray)
ax[1].axis('off')
ax[1].set_title('Local Minima (Miximal Connectivity)')

plt.tight_layout()
plt.show()

Output

On executing the above program, you will get the following output −

Using the skimage.morphology.h_minima() function

The h_minima() function is used to find all minima in an image with a minimum depth condition. These local minima are defined as connected sets of pixels with equal gray levels that are strictly smaller than the gray levels of all neighboring pixels.

A local minimum with a depth of 'h' is a point where there exists a path connecting it to another local minimum with the same or lower value. Along this path, the highest value does not exceed 'f(M) + h' compared to the starting minimum's value. Additionally, there should be no path to any other local minimum with an equal or lower value where the highest value is smaller than 'f(M) + h.' This function also identifies the global minima within the image.