Is it possible to create a geometry for solvepde from a specific image?

MATLAB has a built in Poisson solver (solvepde). In the literature, it explains that there is a way to define the geometry from built in functions. Like the following...

model = createpde();
geometryFromEdges(model,@lshapeg);

I want to do something similar. But I would like to use the image shown below.

I figure I need to use some combination of bwareaopen, edge, bwconncomp, and labelmatrix. But I was not able to understand how to create lines from the edges. I basically want some automated way to create a geometry from the given image above. There is most likely some sort of thresholding that is necessary to find these edges but I am not sure where to begin. Any help is desired.

For testing, I am attaching the JPG that I am using for this experiment.