How to soften the boundaries within a matrix

Hi

I have a matrix M, size N1xN1, which only has positive integers, and is delimited by zones, as seen in the following picture created using image(M) (I changed the colormap and the axes, but that is not relevant for this question)

What I would like to know if there is a way to soften the boundaries between each area, i.e., that the curves do not seem discretized, but interpolated.

Thanks in advnace for any help

Answer 1

[Image Analyst]

You can blur the matrix and rediscretize it.

windowWidth = 9;
kernel = ones(windowWidth) / windowWidth^2;
blurredImage = conv2(M, kernel, 'same');
% Now call discretize to quantize into the levels you had.

[Bjorn Gustavsson]

That will most likely make a completely different boundaries somewhere between the white, light-blue and blue regions. It might be challenging to avoid a tounge of the intermediate level of the three to expand in along the boundary between the higher and lower level regions. Perhaps this could be reduced to a small region around the 3-corner-point if one were to do this with binarizing the levels and determine separate boundaries.

[Image Analyst]

Of course the boundaries will be different - they will be smoother, as requested.

Attach your M in a .mat file if you need more help.

[Bjorn Gustavsson]

Since we don't know the mapping between colours and integers, do you have some particular preference for what I should use for the white, cyan and blue regions in an illustration?

[Andres Salomon Fielbaum Schnitzler]

Thanks. The colormap for those 4 colors is:

White = 7

Cyan = 3

Blue = 2

Red = 5

The idea would be to keep 4 clear regions, but that the boundaries between them are more curved.

[Bjorn Gustavsson]

This should illustrate the problem with Image Analyst's suggestion:

The problem is that the convolution-operation will make the intermediate of the 3 levels with the common corner will "bleed into" a region along the edge between the highest and the lowest levels. This problem you might be able to reduce by going for a couple smoothings of binary edges, that is by dividing the image into

a white-not-white binary image and smoothing that boundary as I.A. suggests, then a cyan-not-cyan and smooth its boundary, then blue-not-blue etc. By doing that your problem-area will be reduced to a region about the size of the convolution-kernel around the "three-region-corner".

[Image Analyst]

Again, attach M in a .mat file with the paperclip icon.

save('answers.mat', 'M');

Make it easy for me to help you. I'll check back in a couple hours.

In the meantime I'm attaching a demo where you can get the boundaries with bwboundary() and then smooth the boundary with a Savitzky-Golay filter.

[Andres Salomon Fielbaum Schnitzler]

Thanks Image Analyst. It was late in my time zone, so I did not connect back yesterday. I am now attaching the 'answers.mat' file, and also the code to create the figure just in case it helps.

Where did you attach the mentioned demo?