How can i get the coordinates of corner points of an object inside the image?

I am working on a nonogram solver in matlab for a school project. After separating the largest connected component of the image with the help of the bwareafilt function and chopping down the unwanted parts of the image by reducing its size with the help of regionprops(LCC,'BoundingBox') function, I aim to remove the perspective by finding 4 corners (from which one is not really a corner. It seems like the boundary and the bwboundaries could help, but because of the 'open nature' of the object I am unable to do that. The regionprops function with its 'Extrema' option does not help either. Maybe the attached pictures will make it clear what I want to do (the last picture is where the regionprops(LCC,'Extrema') function "fails"). In addition, the bwconvhull does not help either :/