How to average every single pixel with its surroundings points so each pixel got the same value.

Hello everyone,

I got a grid that contain two numbers of information for every pixel.

But, what I need to do is to average every pixel in grid number one, so they equal the number 10 or almost 10 if not possible. When the pixel reach the number by combining the pixel values from it's surroundings, the pixel also include information from grid number two, which is the number I seek for.

Shortly again:

I want to find the value in grid number 2 for every time grid number 1 reach a value around 10. What is troublesome is that the size of the combining grid vary from pixel to pixel.

Does anyone have a clue to handle this problem? Do I need to use a filter that runs though every pixel or some kind of integration over an area of 10?? The original data is in 3D and I don’t know if it best do this averaging over a volume (like a cubic) or like a square in 2D slice or something third....

Thank you for your time! :)

Answer 1

[Image Analyst]

OK, I did it for you. See attached m-file. For a full size image, it would take a huge amount of time to check every possible permutation for the one for the sum that is closest to 10. Why do you think you need to do this? What is the use case? Also note that there will be edge effects because the corners have only 4 elements and the edges have only 6 elements so their sums will tend to be lower.

[Nick Yin Larsen]

Thank you for your time Image Analyst !

My use case is: that I got 3D map of a head, which basically is many 2D slices stack on each other.

I am applying some power toward the head and the result shows the amount of power for every single pixel/voxel have absorbed.

The human head contain information of the weight for every single pixel/voxel, which is the suppose to be the top left image information. The amount of power absorbed to every pixel/voxel is the information on the top right image.

What I have to find out is the amount of power is applied for every 10 gram of tissue(not for every pixel as I already know), so I have to combine the weight of the surrounding pixels/voxels so it will sum up to 10 gram.

Then I have to see if the highest maximum power for every 10 gram exceed the limit of a giving person can absorb.

I can see with the answer suggestion you gave the sliding block is a 3x3, but what should I do if 3x3 does not sum up to 10 gram of tissue?

Thank you again! :)

[Image Analyst]

In general it will not. Why should it? I'm not sure you have the correct approach. In general, if you look at the 27 neighbors in a volume or 9 neighbors in a slice, their weights will add up to whatever they add up to. Let's say they add up to 15 but by picking and choosing some strange arrangement of only 17 of the 27 neighbors, you can get a sum of 9.9 grams instead of 27 like for the whole volume. Now let's say you zap the head with some power. I don't think it's appropriate to get the power per 10 grams by just summing up the power in that odd arrangement of pixels and ignoring the power that went to the other pixels. It just doesn't make sense.

I think it would be better to just somehow get the power in each voxel and divide by the mass of that voxel to get the power per 1 gram, then multiply by 10. Now you'll have a map of the power per 10 grams everywhere in the image. This approach makes intuitive logical sense to me.

[Nick Yin Larsen]

Okay, actually the si unit from power map is already W/kg so you are suggesting that I should multiply it with 1/10^8 to get the value per 10 gram right?

But what if that pixel got a weight of let's see 0.02 gram, then it is not over 10 gram of tissue? :)

It is called local average SAR(Specific aborption rate) and it is used in MRI to determine the amount of power is applied in and small area, that is why I need to combine the mass so it is around 10 gram.

[Image Analyst]

The rate is the rate. It doesn't matter if it's 1 milligram or 10 grams or a kilogram.

If you have the rate (Watts per kg) and you have the mass (in kg), then you can find the power (Watts) in that voxel by multiplying the rate in W/kg by the actual mass in kg of that voxel. Just look at the units: (W/kg)*kg -- the kg cancel out and you get Watts.

[Nick Yin Larsen]

Maybe it is because I am not at explaining stuff that I am not that clear in my language, sorry... Well I am not suppose to cancel the kg out from the W/kg, since my result should be like does an average area of 10 gram of tissue exceed 3.2W/kg as the law requires.

That is why in the mass map, every pixel need to combine the weight until it each the value of 10, which your example shows very clearly. Beside that, the W/kg map have to average over the same pixels as the 10 gram map did.

I have not done anything alike this before and I am very grateful for your time and guidance! :)

Does it help if I also got the information of the grid size like x, y and z and each voxel is 1mm^3?

Answer 2

[Image Analyst]

You'll probably have to use nlfilter() because you'll need to apply some special filter that applies special algorithm to each window location. The brute force way (which may be the only way) is to use perms() to check every possible combination of elements in the window. Then check all the sums against 10 to see which cam closest. It's really not that hard so give it a try.