Erosion

Resources:

• page=641 Ch. 9.2

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Given that $A$ and $B$ are sets in $Z^2$, the erosion of $A$ by $B$ is defined as

$$A\ominus B=\{z|(B{)}_z\subseteq A\}$$

Where

• $A$ is a set of foreground pixels
• $B$ is a structuring element
• $\mathbf{z}$ are the foreground values ($1$’s).

Conceptually it can be though of a morphological operation that “shrinks” objects in an image by removing pixels around the edges. Think of it as a way to thin or reduce the boundaries of shapes. It’s often used to remove small noise, separate objects that are close together, or make shapes smaller.