If you cut each surface out of wood of certain color and thickness (intarsia) or veneer (marquetry), and then glue them on a flat surface, you will get a picture transformed into a real piece of wood artwork. This is the process of how to create an intarsia pattern (or marquetry pattern) from any photo, and 2D CAD or vector programs will be very helpful. Also, a command Adjust number of colors (in graphics software) can greatly help during the process, reducing the number of colors in the photo, which will make it easier for you to define the surfaces to be outlined.
From the obtained intarsia pattern, we easily made a silhouette that you can download here: Parrot silhouette vector pattern