In the context of image analysis, an image can be segmented into regions of interest. These regions are often labeled with unique identifiers or labels. The weight of a labeled region provides an aggregated value that represents the combined contribution of all the pixels within that region.

In other words, the weight of a labeled region in an image refers to the sum of pixel intensities within that region.

To calculate the weight, we sum up the pixel intensities within the labeled region. The pixel intensity refers to the value associated with each pixel in the image, which could represent properties such as brightness or color.

By summing the pixel intensities, we obtain a single value that represents the overall “mass” or “quantity” within the labeled region.

Weight of Labeled Region in Mahotas

In Mahotas, the weight of a labeled region can be calculated using the mahotas.labeled_sum() function.

A labeled region in mahotas is represented by a labeled image, where each pixel is assigned a unique label that corresponds to the region it belongs to.

To understand it in a clear way, let us consider a grayscale image where each pixel represents a scalar intensity value. The labeled image is obtained by segmenting this grayscale image into different regions and assigning a unique label to each region.

The mahotas.labeled_sum() function

The mahotas.labeled_sum() function takes the labeled_sum function takes an input array and a labeled array. It calculates the sum of pixel values for each labeled region in the input array based on the corresponding labels in the labeled array.

The resulting array contains the sum of pixel values for each labeled region, with each element of the array corresponding to a unique label.

Syntax

Following is the basic syntax of the labeled_sum() function in mahortas −

mahotas.labeled_sum(array, labeled, minlength=None)

Where,

• array − A NumPy array representing the image or the data.

• labeled − A labeled array with the same shape as array, where each region is assigned a unique integer label.

• minlength (optional) − An integer specifying the minimum length of the resulting array. If provided, the function pads the resulting array with zeros to reach this length.

Example

Following is the basic example to determine the weight of labeled region of an image −

import mahotas as mh
import numpy as np
from pylab import imshow, show
# Generate a grayscale image
image = mh.imread(''tree.tiff'')
# Generate a labeled array
labeled = mh.imread(''sea.bmp'')
# Calculate the sum of pixel values for each labeled region
result = mh.labeled_sum(image, labeled)
print(result)

Output

After executing the above code, we get the following output −

[ 30 115  58 157 226 154 169  24  63  48 124 123 159 146  44 163 202 174
 208  30  39 109 100 221 245 101  16 162  42   0 214  71  46  31 110 197
  91 137 118 192 104 119 139  23 198 176 219 192  60   1 218 143  67 122
 249  14 165  70 159  16  18 204 135 185  74 175 110  39   8  98 208 238
  86 169  42  21  39 129 100 146 162  48 217 228 204  30  54 164 174  80
 144 172 232 115  48 165 136 234  37 147 195 242   2 227  75   6  95 100
  92 230 200  96  93  59  30  28  60 122 213  65 133  53  58  91 191  36
 174 106  95  25 201  70  73 234  59  76   2 207 238  66  87 140 174 222
 122 239  37  79 220  57 126  38 150 236  60  37 196  58 236 241 148 207
 253  56 103  79  72  71  47 242 169   8  88  19 176  16 195  88 134 188
 205  78 248  96 156  86  35  57  69 241 142 203 198 182 165  31 127  36
 227  47 195  47 117 217 134  45  50  95  76  47  34 182  21 140 138 192
  17 232 158 182 162 136 104 145 229 165  33 107  14 117 185 115  73 129
 217 105 244   0  63 124   0   0 109  56   0 107]

Weight of Labeled Regions with a Minimum Length

To calculate the weight of labeled regions with minimum length, we need to pass the ”minlength” parameter to the labeled_sum() function in mahotas.

By setting the minimum length value, only regions with a length equal to or greater than the specified minimum length will be taken into account during the weight calculation process.

This feature allows us to filter out smaller regions and focus on the larger and potentially more significant regions.

If any region doesn’t meet the minimum length requirement, the weight of that region is assigned as ”0”.

Example

Here, we are calculating the weight of labeled regions by specifying a minimum length −

import mahotas as mh
import numpy as np
image = mh.imread(''tree.tiff'')
# Perform labeling to obtain the labeled image
labeled_img, n_labels = mh.label(image)
# Calculate the weight of each labeled region with a minimum length of 2
weights = mh.labeled_sum(image, labeled_img, minlength=2)
# Print the weights of each labeled region
for label, weight in enumerate(weights, start=1):
   print(f"Weight of region {label}: {weight}")

Output

Output of the above code is as follows −

Weight of region 1:  0
Weight of region 2: 40
Weight of region 3: 86
Weight of region 4: 37

Weight of Labeled Regions with Custom Labels

To calculate the weight of labeled regions with custom labels, first, generate a custom labeled image, where each region is assigned a specific label.

The labeled image will have the same dimensions as the original image, with each pixel assigned the corresponding label value based on the region it belongs to. Then, calculate the weight of labeled regions.

Example

Now, we are trying to calculate the weight of labeled regions with custom labels −

import mahotas as mh
import numpy as np
# Generate a binary image
binary_img = np.array([[0, 1, 0, 0],[1, 1, 1, 0],[0, 0, 0, 1]])
# Generate a custom labeled image with specific labels
labeled_img = np.array([[0, 1, 0, 0],[2, 2, 2, 0],[0, 0, 0, 3]])
# Calculate the weight of each labeled region
weights = mh.labeled_sum(binary_img, labeled_img)
# Print the weights of each labeled region
for label, weight in enumerate(weights, start=1):
   print(f"Weight of region {label}: {weight}")

Output

Following is the output of the above code −

Weight of region 1: 0
Weight of region 2: 1
Weight of region 3: 3
Weight of region 4: 1