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Is there some established Object Detection algorithm that is able to detect the four corners of an arbitrary quadrilateral (x0,y0,x1,y1,x2,y2,x3,y3) as opposed to the more typical perpendicular rectangular (x,y,w,h) ?

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You can use OpenCV's cv2.minAreaRect() to detect oriented/rotated rectangular bounding boxes. Below's an example result from OpenCV-Python-tutorials:

Using cv2.minAreaRect()

Alternatively, you could train a supervised object detection model to output 8 co-ordinate values (x0,y0,x1,y1,x2,y2,x3,y3) of the quadrilateral by training with a labeled oriented-bounding-box dataset. You could also create the bounding box labels yourself for the same by using tools such as VGG Annotator Tool among others.

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