Comments on: Dilation algorithms—structuring element decomposition

By: Steve

Steve — Mon, 05 Oct 2009 14:48:39 +0000

Anne—That’s a very good point. The performance of implementations of binary dilation and erosion can be data-dependent. When we do performance benchmarking of binary dilation, we usually use a couple of images: one with just a few foreground pixels and one with many foreground pixels. It’s difficult to write a binary dilation routine that performs equally well for all kinds of input images.

For grayscale dilation and erosion, though, the performance is not data dependent and structuring element decomposition is a clear win.

By: Anne

Anne — Wed, 23 Sep 2009 21:21:41 +0000

Hi Steve,

It seems to me that the time savings you get by decomposing the structuring element depend a bit on the initial volume. In the case of a mostly empty volume with only a small percentage of non-zero voxels, I think decomposition could actually cost more time! For the limiting case, say we have a 3D volume with only 1 nonzero voxel which we are dilating with a 5×5x5 structuring element. In the case of no decomposition, 125 comparison are made. However, if you decompose the structuring element into 3 linear elements, you have to do 1*5 (first step) + 5*5 (second step) + 25*5 (third step) = 155 comparisons. Is my logic correct here?

Thanks,
Anne

By: Steve

Steve — Fri, 20 Mar 2009 12:33:24 +0000

Lala—Dilation and erosion are dual operators. There is relatively little difference between them in terms of algorithms and implementation. Everything I’ve written about dilation applies to erosion, so I have no plans to write anything further that’s specific to erosion. Closing is just dilation followed by erosion.

By: lala

lala — Thu, 19 Mar 2009 21:47:11 +0000

Hi Steve,

I’m searching for algorithm concepts behind the implementation of erosion and closing in the Image Processing Toolbox in Matlab. Looks like you haven’t update on this yet. Can you please give me a brief detail on this? Thank you very much.

~Lala