- Green Line: Manhattan Distance
- Red Line: Euclidean Distance

University of Michigan - Ann Arbor

The Manhattan distance between two points is the sum of the absolute differences of their corresponding Cartesian coordinates. For two points $$x$$ and $$y$$ in a $$k$$-dimensional space, the distance is calculated as: $$d(x, y) = \sum_{i=1}^k |x_i - y_i|$$

Manhattan Distance

Euclidean distance is the straight-line distance between two points in a Euclidean space. For two points $$x$$ and $$y$$ in a $$k$$-dimensional space, the distance is calculated as the square root of the sum of the squared differences between their coordinates:

$$d(x, y) = \\sqrt{ \\sum_{i=1}^k (x_i - y_i)^2 }$$

Euclidean Distance

Two-dimensional Euclidean distance is the straight-line distance between two points in a 2D Cartesian coordinate system. For two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$, it is calculated using the distance formula derived from the Pythagorean theorem:

$$d = \\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

In computer vision and image processing, this metric is commonly used to determine the proximity of feature points, such as preventing a corner detection algorithm from returning multiple nearby coordinates for the same physical corner.

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