Manhattan Distance

Updated 24 Sep 2026

•
What it is
- •
  distance measured as the sum of absolute coordinate differences; also called city-block or $D_4$ distance on a pixel grid
•
Formula
- •
  $d_1(p,q)=|x_1-x_2|+|y_1-y_2|$
•
Interpretation
- •
  the minimum number of unit moves when only horizontal and vertical movement is allowed
•
Example
- •
  from $(0,0)$ to $(3,4)$ : $d_1=7$
•
Related
- •
  Pixel Neighborhood
•

Linked references 3