Gradually varied surface

In mathematics, a gradually varied surface is a special type of digital surfaces. It is a function from a 2D digital space (see digital geometry) to an ordered set or a chain.

A gradually varied function is a function from a digital space ${\displaystyle \Sigma }$ to ${\displaystyle \{A_{1},\dots ,A_{m}\}}$ where ${\displaystyle A_{1}<\cdots <A_{m}}$ and ${\displaystyle A_{i}}$ are real numbers. This function possesses the following property: If x and y are two adjacent points in ${\displaystyle \Sigma }$, assume ${\displaystyle f(x)=A_{i}}$, then ${\displaystyle f(y)=A_{i}}$, ${\displaystyle f(x)=A_{i+1}}$, or ${\displaystyle A_{i-1}}$.

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