image package: strel class, non-flat morphology and spatial transformations

strel class

The strel class was something that I wanted to implement a long time ago but had never found the time. The name strel comes from structuring element (SE), the shapes used in morphological operations such as dilation and erosion. I have only seen it as a standard way to create SEs, but is actually much more. Specially, SE decomposition can have a really nice increase in performance.

Roberto Metere submitted his own implementation of the class last month and we have been working on it, slowly adding it to the other functions of the package. It started as a single .m function, no OOP at all, but he managed to implement @strel with the old @class style while keeping matlab compatibility. All the basic methods have been implemented: the object constructor, getnhood, getheight and reflect.

The idea behind SE decomposition is that morphology operations take as much space as the number of pixels in a SE. The bigger the SE, the slower it will be. However, some SE can be replaced by a sequence of smaller ones so it's in our best interest to use them. For an example on performance, see how the use of a square compares to use of 1 row and 1 column of the same size:

octave> im1 = im2 = randp (5, 2000) > 15;
octave> t = cputime ();
octave> im1 = conv2 (im1, true (20), "same") > 0; # dilation by 1 square
octave> cputime () - t
ans =  2.6402
octave> t = cputime ();
octave> im2 = conv2 (im2, true (20, 1), "same") > 0; # dilation by 1 column
octave> im2 = conv2 (im2, true (1, 20), "same") > 0; # dilation by 1 row
octave> cputime () - t
ans =  0.52803
octave> isequal (im1, im2)
ans =  1

At the moment, decomposition is only being done for rectangular, square and cube shapes but other will come with time. Functions that can gain from SE decomposition, are written so that it does not matter if it has been implemented for a specific shape. This means that when it is implemented for another shape, its effect will be immediate across the whole image package. The only file where this is done is inst/@strel/getsequence.m so send us patches.

Going through imdilate() and imerode() to make them use strel, brought up a bunch of other matlab incompatibilities that I hope are now fixed, as well as other improvements. I'm a bit interested in morphology of volumes so one of the changes made was making them work for N-dimensional images (think MRI scans).

On top of the matlab shapes for strel, I implemented the cube as an optional shape. I also wanted to implement ball as a volume but unfortunately, matlab has already done it wrong as a non-flat ellipsoid. Note that non-flat is unrelated to volumes.

Non-flat morphology

This has confused me for a very long time. Because of the name (non-flat), and because 3D images are the norm for me, I have always assumed that a non-flat SE was one used for volumes. The fact that the only non-flat standard shape in matlat is named ball, which immediately brings up the idea of volume, also helped to the confusion.

Actually, non-flat morphology is something that only makes sense for grayscale operations. A non-flat SE is defined by two different matrices, one defining the neighbourhood (same as a flat SE) and another defining the height of each neighbour. These heights are added to the image pixels values before the erosion and dilation, in the same way as the variable S in ordfiltn.

Basically, not useful for volumes at all but the image package can do this now. To create a non-flat SE, use the arbitrary shape of strel.

Spatial transformations

Pantxo Diribarne has also submitted a set of functions for spatial transformations: maketform, cp2tform, tformfwd, and tforminv. These are still not completely implemented and generally restricted to 2D transforms. Adding the missing options should now be much easier.