How to make PDE geometry from the BW mask?

Hello, I'd like to analyzed my data with temporally changed boundary shape by adapting the FEM.

Here, I already got the BW mask for the boundary, but I still don't how to change it as a geometry structure for the FEM which can put into the "geometryFromEdges" function. My BW mask data have the all the coorrdinate of x and y position as a matrix. In this case, how can I change it to the geometry feature which can fit on the geometryFromEdges ?

Answer 1

[Abhishek Chakram]

Hi Hyuntae Jeong,

To adapt a BW mask representing the boundary of a domain into a geometry structure suitable for FEM analysis in MATLAB, especially for use with the “geometryFromEdges” function, you will need to convert the boundary represented by your BW mask into a set of edges or curves that describe the geometry. This process involves several steps:

1.Extract Boundary Coordinates: You can use the “bwboundaries” function to extract the boundaries from the binary mask.

BW = imread('path_to_your_mask_image.png'); % Load your BW mask
BW = imbinarize(BW); % Ensure it's binary in case it's not
boundaries = bwboundaries(BW, 'noholes');

This will give you a cell array boundaries where each cell contains the (x, y) coordinates of a boundary. If your mask has one main object, you can focus on the first cell.

2. Simplify Boundary: Simplify the extracted boundary to reduce the number of points while maintaining the shape. You can use “reducepoly” function for the same.

boundary = boundaries{1}; % Assuming one main boundary
simplifiedBoundary = reducepoly(boundary, tolerance); % Set 'tolerance' appropriately

3. Create Geometry Definition: Once you have the simplified boundary, you need to create a set of edges that can be used with “geometryFromEdges”. In MATLAB, this often involves defining the boundary using lines, circles, and other shapes programmatically. For a custom shape, you might need to interpolate the boundary points into a spline or a set of line segments that approximate the boundary well. Here is how you might approach it with line segments:

% Example: Creating a custom geometry function for a simple shape
function [sf, name] = customGeometry(simplifiedBoundary)
    % Assuming simplifiedBoundary is an Nx2 matrix of (x,y) points
    % Create line segments between consecutive points
    str = [];
    for i = 1:size(simplifiedBoundary, 1)-1
        str = [str, 'L', '(' num2str(simplifiedBoundary(i,1)), ',', num2str(simplifiedBoundary(i,2)), ')', '-', ...
                   '(' num2str(simplifiedBoundary(i+1,1)), ',', num2str(simplifiedBoundary(i+1,2)), ')'];
        if i < size(simplifiedBoundary, 1)-1
            str = [str, '+'];
        end
    end
    sf = str;
    name = 'customBoundary';
end

Then, use your custom geometry in the PDE model:

model = createpde();
[sf, name] = customGeometry(simplifiedBoundary);
geometryFromEdges(model, @(x) eval(name));

You can refer to the following documentation to know more about functions used:

• bwboundaries: https://www.mathworks.com/help/images/ref/bwboundaries.html
• imread: https://www.mathworks.com/help/matlab/ref/imread.html
• imbinarize: https://www.mathworks.com/help/images/ref/imbinarize.html
• reducepoly: https://www.mathworks.com/help/images/ref/reducepoly.html
• createpde: https://www.mathworks.com/help/pde/ug/createpde.html

Best Regards,

Abhishek Chakram

[Hyuntae Jeong]

Thank you for your answer!! I will try this