# Biased Anisotropic Diffusion--A Unified Regularization and Diffusion Approach to Edge Detection

### K. Niklas Nordstrom

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-89-514

May 1989

### http://www.eecs.berkeley.edu/Pubs/TechRpts/1989/CSD-89-514.pdf

We present and analyze a global edge detection algorithm based on variational regularization. The algorithm can also be viewed as an anisotropic diffusion method. We thereby unify these two, from the original outlook, quite different methods. This puts anisotropic diffusion, as a method in early vision, on more solid grounds; it is just as well-founded as the well-accepted standard regularization techniques. The unification also brings the anisotropic diffusion method an appealing sense of optimality, thereby intuitively explaining its extraordinary performance.

The algorithm to be presented moreover has the following attractive properties.

1. It only requires the solution of a single boundary value problem over the entire image domain -- almost always a very simple (rectangular) region.

2. It converges to the solution of interest.

The first of these properties implies very significant advantages over other existing regularization methods; the computation cost is typically cut by an order of magnitude or more. The second property represents considerable advantages over the existing diffusion methods; it removes the problem of deciding when to stop, as well as that of actually stopping the diffusion process.

BibTeX citation:

@techreport{Nordstrom:CSD-89-514, Author = {Nordstrom, K. Niklas}, Title = {Biased Anisotropic Diffusion--A Unified Regularization and Diffusion Approach to Edge Detection}, Institution = {EECS Department, University of California, Berkeley}, Year = {1989}, Month = {May}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1989/5619.html}, Number = {UCB/CSD-89-514}, Abstract = {We present and analyze a global edge detection algorithm based on variational regularization. The algorithm can also be viewed as an anisotropic diffusion method. We thereby unify these two, from the original outlook, quite different methods. This puts anisotropic diffusion, as a method in early vision, on more solid grounds; it is just as well-founded as the well-accepted standard regularization techniques. The unification also brings the anisotropic diffusion method an appealing sense of optimality, thereby intuitively explaining its extraordinary performance. <p>The algorithm to be presented moreover has the following attractive properties. <p>1. It only requires the solution of a single boundary value problem over the entire image domain -- almost always a very simple (rectangular) region. <p>2. It converges to the solution of interest. <p>The first of these properties implies very significant advantages over other existing regularization methods; the computation cost is typically cut by an order of magnitude or more. The second property represents considerable advantages over the existing diffusion methods; it removes the problem of deciding when to stop, as well as that of actually stopping the diffusion process.} }

EndNote citation:

%0 Report %A Nordstrom, K. Niklas %T Biased Anisotropic Diffusion--A Unified Regularization and Diffusion Approach to Edge Detection %I EECS Department, University of California, Berkeley %D 1989 %@ UCB/CSD-89-514 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1989/5619.html %F Nordstrom:CSD-89-514