Minimum bounding box

The minimum bounding box of a point set is the same as the minimum bounding box of its convex hull, a fact which may be used heuristically to speed up computation.

It is the Cartesian product of N intervals each of which is defined by the minimal and maximal value of the corresponding coordinate for the points in S. Axis-aligned minimal bounding boxes are used as an approximate location of an object in question and as a very simple descriptor of its shape.

Minimum bounding box algorithms based on the rotating calipers method can be used to find the minimum-area or minimum-perimeter bounding box of a two-dimensional convex polygon in linear time, and of a three-dimensional point set in the time it takes to construct its convex hull followed by a linear-time computation.

[2] Matlab implementations of the latter as well as the optimal compromise between accuracy and CPU time are available.

In digital image processing, the bounding box is merely the coordinates of the rectangular border that fully encloses a digital image when it is placed over a page, a canvas, a screen or other similar bidimensional background.