Volume 8 (2012)
Article 19 pp. 415-428

Distance Transforms of Sampled Functions

Received: December 18, 2009

Revised: May 30, 2012

Published: September 2, 2012

Revised: May 30, 2012

Published: September 2, 2012

**Keywords:**distance transform, minimum convolution, image processing

**Categories:**short, algorithms, transform, distance transform, convolution, min-convolution, vision, image processing

**ACM Classification:**F.2.1, I.4

**AMS Classification:**68T45, 68W40

**Abstract:**
[Plain Text Version]

We describe linear-time algorithms for solving a class of problems that involve transforming a cost function on a grid using spatial information. These problems can be viewed as a generalization of classical distance transforms of binary images, where the binary image is replaced by an arbitrary function on a grid. Alternatively they can be viewed in terms of the minimum convolution of two functions, which is an important operation in grayscale morphology. A consequence of our techniques is a simple and fast method for computing the Euclidean distance transform of a binary image. Our algorithms are also applicable to Viterbi decoding, belief propagation, and optimal control.