Connected component labeling in SciPy - Step-by-Step Execution

Concept Flow - Connected component labeling

Input: Binary Image

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Scan Image Pixels

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Check Neighbors for Connectivity

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Assign/Update Labels

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Merge Equivalent Labels

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Output: Labeled Image with Components

The process scans a binary image, checks pixel neighbors to find connected regions, assigns labels to these regions, merges equivalent labels, and outputs the labeled image.

Execution Sample

SciPy

import numpy as np
from scipy.ndimage import label

binary_image = np.array([[1,0,0,1],
                         [1,1,0,0],
                         [0,0,1,1],
                         [0,0,1,1]])

labeled_array, num_features = label(binary_image)

This code labels connected components in a binary image and counts how many distinct components exist.

Execution Table

Step	Pixel Position	Pixel Value	Neighbors Checked	Label Assigned	Current Label Map Snapshot
1	(0,0)	1	None (first pixel)	1	[[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]
2	(0,1)	0	N/A (background)	0	[[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]
3	(0,2)	0	N/A (background)	0	[[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]
4	(0,3)	1	Neighbors: (0,2)=0, (1,3)=0	2	[[1,0,0,2],[0,0,0,0],[0,0,0,0],[0,0,0,0]]
5	(1,0)	1	Neighbors: (0,0)=1	1	[[1,0,0,2],[1,0,0,0],[0,0,0,0],[0,0,0,0]]
6	(1,1)	1	Neighbors: (1,0)=1, (0,1)=0	1	[[1,0,0,2],[1,1,0,0],[0,0,0,0],[0,0,0,0]]
7	(1,2)	0	N/A (background)	0	[[1,0,0,2],[1,1,0,0],[0,0,0,0],[0,0,0,0]]
8	(1,3)	0	N/A (background)	0	[[1,0,0,2],[1,1,0,0],[0,0,0,0],[0,0,0,0]]
9	(2,0)	0	N/A (background)	0	[[1,0,0,2],[1,1,0,0],[0,0,0,0],[0,0,0,0]]
10	(2,1)	0	N/A (background)	0	[[1,0,0,2],[1,1,0,0],[0,0,0,0],[0,0,0,0]]
11	(2,2)	1	Neighbors: (1,2)=0, (2,1)=0	3	[[1,0,0,2],[1,1,0,0],[0,0,3,0],[0,0,0,0]]
12	(2,3)	1	Neighbors: (2,2)=3, (1,3)=0	3	[[1,0,0,2],[1,1,0,0],[0,0,3,3],[0,0,0,0]]
13	(3,0)	0	N/A (background)	0	[[1,0,0,2],[1,1,0,0],[0,0,3,3],[0,0,0,0]]
14	(3,1)	0	N/A (background)	0	[[1,0,0,2],[1,1,0,0],[0,0,3,3],[0,0,0,0]]
15	(3,2)	1	Neighbors: (2,2)=3, (3,1)=0	3	[[1,0,0,2],[1,1,0,0],[0,0,3,3],[0,0,3,0]]
16	(3,3)	1	Neighbors: (3,2)=3, (2,3)=3	3	[[1,0,0,2],[1,1,0,0],[0,0,3,3],[0,0,3,3]]
17	End	N/A	N/A	N/A	Final labeled array with 3 components

💡 All pixels scanned; connected components labeled and counted.

Variable Tracker

Variable	Start	After 1	After 4	After 6	After 11	After 16	Final
labeled_array	[all zeros]	[[1,0,0,0],[0,0,0,0],[0,0,0,0],[0,0,0,0]]	[[1,0,0,2],[0,0,0,0],[0,0,0,0],[0,0,0,0]]	[[1,0,0,2],[1,1,0,0],[0,0,0,0],[0,0,0,0]]	[[1,0,0,2],[1,1,0,0],[0,0,3,0],[0,0,0,0]]	[[1,0,0,2],[1,1,0,0],[0,0,3,3],[0,0,3,3]]	[[1,0,0,2],[1,1,0,0],[0,0,3,3],[0,0,3,3]]
num_features	0	1	2	2	3	3	3

Key Moments - 3 Insights

Why does the pixel at (0,3) get a different label than the pixel at (0,0) even though both are 1?

Because they are not connected through neighboring pixels. The execution_table rows 1 and 4 show that (0,0) is labeled 1 first, then (0,3) is labeled 2 since its neighbors are background (0).

How does the algorithm decide to merge labels if two connected regions are found separately?

The scipy label function merges equivalent labels during scanning when neighbors with different labels are connected. In this example, no merges occur because connected regions are distinct, as seen in the labeled_array snapshots.

Why are some pixels assigned label 0?

Label 0 means background pixels (value 0 in the binary image). They are not part of any connected component, as shown in multiple execution_table rows where pixel value is 0 and label assigned is 0.

Visual Quiz - 3 Questions

Look at the execution table at step 6. What label is assigned to pixel (1,1)?

A 2

B 3

C 1

D 0

💡 Hint

Check the 'Label Assigned' column at step 6 in the execution_table.

At which step does the algorithm assign label 3 for the first time?

A Step 11

B Step 4

C Step 16

D Step 1

💡 Hint

Look at the 'Label Assigned' column and find when label 3 appears first in the execution_table.

If the pixel at (0,3) was connected to (0,0), how would the number of features change?

A It would increase to 4

B It would decrease to 2

C It would remain 3

D It would become 1

💡 Hint

Refer to the variable_tracker for num_features and consider merging connected components.

Concept Snapshot

Connected component labeling:
- Input: binary image (0=background, 1=foreground)
- Scan pixels, check neighbors for connectivity
- Assign labels to connected pixels
- Merge equivalent labels
- Output: labeled image and count of components

Full Transcript

Connected component labeling scans a binary image pixel by pixel. For each foreground pixel (value 1), it checks neighbors to see if they belong to an existing component. If yes, it assigns the same label; if no, it assigns a new label. Background pixels (value 0) get label 0. The algorithm merges labels if connected regions are found separately. The output is a labeled image where each connected component has a unique label and the total number of components is counted.