An uniform grid, where each pixel/voxel got is own value. I want to create a new grid where each pixel/voxel got the same value even tho the grid becomes non-uniform.

Hello everyone,

I am not the professinal with Matlab and I have a problem to solve.

I have to divide a "special stone" to small pieces of 100 gram. In my case we are talking about a 3D-problem but I will illustrate it in 2D so people get the idea. So in my case I got a stone, which got many different weights randomly distributed, which is illustrated in the picture below (left side).

Each number contain a specific weight so in this case there are 9 densities (1-9), both the position and the resolution for each pixel/voxel is known and we can say it is 5 mm in this case and uniform distributed.

I have to create new grid where each pixel/voxel in this stone contains 100 gram like on the right side.

I really don't know how to execute this well but got an idea, which I have illustrated in the 2nd figur, where I could use some kind of of filter where the mass can 95-105 gram or something... I like have showed here:

But I have no clue how to begin I hope you people can help me out! :)

Thank you very much for your time.

[Walter Roberson]

Nick, we do not delete posts just because no complete answer was received. The discussions are deliberately public, so that everyone can see, including other people who might come along later with similar questions.

Answer 1

[Walter Roberson]

If the task is to move the pixels on the left around so that they can be organized into blocks with each block totaling 95 to 105, and each of the blocks is to have a mixture of densities: then that would be what is known as a "Knapsack Problem", possibly even one of the Bin Packing Problems. Such problems cannot be solved with filters; such problems are computationally difficult.

[Nick Yin Larsen]

That is not the task but an idea :) I don't know how to execute the problem solving, do you have any technique in your mind? I am totally clueless.

[Image Analyst]

Well I thought of exactly the same thing as Walter so I think it is the task, though maybe you don't realize it. Search for knapsack and MATLAB and I'm sure you find example pages and uploaded code.

[Nick Yin Larsen]

Hello image analyst, I have been looking at the Knapsack problem and I don't think it is totally the same. In the Knapsack problem you need the weight and total weight which I got, but I don't grade the weight and say which one is more important.

I have made a new post here where the description is hopefully more clear: http://se.mathworks.com/matlabcentral/answers/283012-an-uniform-grid-where-each-pixel-voxel-got-is-own-value-i-want-to-create-a-new-grid-where-each-pix

Thank you for your time :)

[Walter Roberson]

Your new question is nearly an exact repetition of this one. It should not have been made as a new question; now the discussion is divided :(

[Nick Yin Larsen]

Hello Walter! :) Thank you very much for your attention, I will delete this post soon since I have modified my question in this page:

http://se.mathworks.com/matlabcentral/answers/283012-an-uniform-grid-where-each-pixel-voxel-got-is-own-value-i-want-to-create-a-new-grid-where-each-pix.

I hope it can help you guys to help me if possible, and thank you for your time I really appreciate that! :)

[Walter Roberson]

You cannot delete posts.

[Nick Yin Larsen]

I have changed my description in the other post so it is not exactly the same... Did you look at it after I have made some adjustment? :) I think it is more clear and specific what I am trying to do :)

[Walter Roberson]

Yes, I saw. The correspondence between numbers and "weight" is clearer now, but nothing else is clear yet.

[Nick Yin Larsen]

okay, well the point is that I have to devide the stone into sub areas where it only contain a specific weight and it should be around 300 gram in this case it could be with many different weights. I just don't know what kind of techniques can help me to solve my problem.

So short: I got a stone with different densities randomly distributed (I have converted it to kg) and then I have to split the stone in different sub areas with an equal or almost weight.

I made this analog because I got a humanhead where I know all the density values of the tissue and then I have to know the weight for each pixels, so I subdivide the head to areas with 100 gram so I know how much energy I can apply to it....

[Walter Roberson]

Then you certainly cannot rearrange the pixels as would have been valid for your original question.

[Walter Roberson]

It seems implausible to me that the outer boundaries of a segmented image of a human head would be cuboid: surely you have ragged boundaries with an roi mask which lives within a cuboid scan? It matters because fitting the ragged edges is going to affect how the areas are chosen. But then you run into difficulty with not knowing the density of the areas beside the edges that stick out.

[Nick Yin Larsen]

True, it is not that correct to use cuboid but I am working with resolutions of 1 mm for each pixel value of the density.

But do you have any suggestion how I can execute it in a smart way? I "just" to divide the head in smaller sub volumen where each of those volumens contain a weight of 100 gram :)

[Walter Roberson]

I am falling asleep now so my reply will be later

[Walter Roberson]

Nick, in the irregular-sized cuboid voxels, is there a resolution limit on those? Your source information is 1 mm, but how fine-grained is your beam width for delivering the radiation dose? And how much beam spread is there? Would it be correct that what you have is a two or three beam system, any one beam of which is sub-clinical (to pass through the non-targeted regions without change) but with multiple beams focused together in a region to reach a total dosage that is clinical?