Hysteresis Thresholding

You’re implementing the hysteresis thresholding step that typically comes after non-maximum suppression (NMS) in Canny edge detection.

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1. Background Knowledge (concepts & theory)

After you compute the gradient magnitude of an image and perform non-maximum suppression, you get a thin edge magnitude map: large values at likely edge locations, small values elsewhere. However, this map is still noisy: many weak responses may be due to noise, texture, or small fluctuations, not true object boundaries.

A single global threshold (e.g., “keep all pixels with magnitude > T”) is often too crude:

• If T is high → you lose real but weak edges (breaks in contours).
• If T is low → you keep a lot of noise and speckles.

Hysteresis thresholding uses two thresholds to fix this. Pixels with magnitude above a high threshold are considered strong edges (reliable). Pixels between low and high thresholds are weak edges: they are kept only if they are connected (via an 8-connected path) to at least one strong edge. Everything at or below the low threshold is discarded. This preserves continuous edges while suppressing isolated noise.

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2. Algorithm / Approach Pattern

At a high level, the pattern is:

1. Classify pixels into:

• Strong edge
• Weak edge
• Non-edge

2. Graph traversal from strong edges:

• Treat each strong edge pixel as a seed.
• From each seed, perform a search (DFS/BFS) over neighbors.
• Whenever you encounter a weak edge that is connected via 8-connectivity, promote it to a final edge and continue from there.

3. Output binary edge map:

• All visited strong + connected weak pixels → 1
• Everything else → 0

Conceptually, you’re doing connected-component growing starting from strong edges, but you are allowed to grow only through pixels labeled as weak.

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3. Step-by-Step Strategy to Implement

Assume you are given:

• mag – 2D array of edge magnitudes after NMS
• low – low threshold
• high – high threshold

Target: output edges – 2D binary array (0/1 or False/True).

Step 1: Initial classification

Create a label map (same size as mag):

• Strong: mag > high
• Weak: low < mag <= high
• Non-edge: mag <= low

For example:

import numpy as np

strong = mag > high
weak = (mag > low) & (mag <= high)

# Optional: a working label map
# 0 = non-edge, 1 = weak, 2 = strong
labels = np.zeros_like(mag, dtype=np.uint8)
labels[weak] = 1
labels[strong] = 2

Step 2: Initialize output and a queue/stack

• Create edges initialized to 0.
• For each strong pixel:
• Mark it as edge in edges.
• Push its coordinates into a queue (for BFS) or stack (for DFS).

from collections import deque