How to calculate center of pressure given a 2d array containing pressure data

So as the title says I want to know how to calculate the center of pressure coordinates given that the input will be a 2d matrix with each element representing a "pressure grid".

[Torsten]

a 2d matrix with each element representing a "pressure grid".

??

You want to approximate xc and yc according to xc = integral(x*p)/integral(p) and yc = integral(y*p)/integral(p) ?

[the cyclist]

Do elements with index 1,2,3 ... representing points that are equally spaced in the "real world"? Is the spacing the same along the two dimensions?

[Alex]

I wish to calculate xc and yc based on the discrete version of this formula xc = sum(x*p)/sum(p), yc = sum(y*p)/sum(p). For context each element will represent pressure data from one sensor of a pressure plate, so i guess the question is how do I determine which x and y values to use. The way I understand it is that x&y are distances from a reference point so can I just choose one arbitrarily?

Answer 1

[the cyclist]

If the answers to both of the questions in my comment is "yes", then

% Example input
pressureArray = [1 2 3;
     4 5 6;
     7 8 9]

pressureArray = 3x3

1 2 3 4 5 6 7 8 9

% Get array size
[rows, cols] = size(pressureArray);

% Total pressure
totalPressure = sum(pressureArray,"all");

% Calculate moments about x and y axes
momentX = sum((1:cols)  .* pressureArray,"all");
momentY = sum((1:rows)' .* pressureArray,"all");

% Calculate center of pressure
COP_x = momentX / totalPressure

COP_x = 2.1333

COP_y = momentY / totalPressure

COP_y = 2.4000

The "spatial" coordinates are the indexing of the array (in this case 1:3 along both directions). You may need to apply a multiplier, or translation operation.

[Alex]

Thanks! This works!

Answer 2

[Image Analyst]

If you have the Image Processing Toolbox (I think most people do) then you can do it in one line of code by asking regionprops to compute the weighted centroid.

% Example input from the cyclist
pressureArray = [1 2 3;
    4 5 6;
    7 8 9];
% Using regionprops to compute the weighted centroid.  Requires Image Processing Toolbox.
props = regionprops(true(size(pressureArray)), pressureArray, 'WeightedCentroid')

props = struct with fields:
    WeightedCentroid: [2.1333 2.4000]

[Alex]

Thanks! this method definitely works, it gives the same output as the solution provided by the cyclist.

[Image Analyst]

Yes, and my way is a lot simpler.