Q21Digital Image Processing

Edge detection attempts to segment an image by finding the violent borders between objects. Region-based segmentation takes the exact opposite mathematical approach. It attempts to find massive groups of pixels that share identical physical properties (intensity, texture) and groups them into solid, contiguous geometric regions.

This algorithm builds regions mathematically from the inside out, similar to a virus spreading.

• The Seed Point: The algorithm must be initialized with a starting pixel (Seed) inside the target object (e.g., clicking on a cancer tumor).
• The Homogeneity Criterion: A strict mathematical rule is defined. For example: "A pixel belongs to the region IF its intensity is within $\pm 10$ of the Seed pixel's intensity."
• The Execution (Growing): The algorithm violently inspects all 8 neighboring pixels surrounding the Seed. If a neighbor mathematically passes the Homogeneity test, it is annexed into the region. The algorithm recursively repeats this for the new boundaries. It stops growing when it hits a sharp physical edge where the criterion violently fails.

This is a catastrophic recursive algorithm that operates on the entire image simultaneously, without needing a human-defined seed point.

• The Split Phase: The algorithm assumes the entire image is one single region. It applies a mathematical Homogeneity test (e.g., "Is the variance of all pixels $<5$?"). Because the whole image contains a car and a sky, the variance is massive; the test fails. The algorithm violently chops the image perfectly into four equal quadrants (a Quadtree). It recursively tests each quadrant. If a quadrant fails, it chops it into 4 smaller sub-quadrants. It continues this violent fragmentation until every single tiny block mathematically passes the homogeneity test.
• The Merge Phase: The split phase results in a horrific checkerboard of thousands of tiny square blocks. The algorithm now executes the Merge phase. It scans adjacent blocks. If Block A and Block B share a physical border AND mathematically pass the homogeneity test together, they are violently fused back into a single larger, non-square region.
• The Result: The image is perfectly segmented into organic, contiguous shapes without any human intervention.