Revisiting Marr in Face: The Building of 2D--2.5D--3D Representations in Deep Neural Networks

David Marr's seminal theory of vision proposes that the human visual system operates through a sequence of three stages, known as the 2D sketch, the 2.5D sketch, and the 3D model. In recent years, Deep Neural Networks (DNN) have been widely thought to have reached a level comparable to human vision. However, the mechanisms by which DNNs accomplish this and whether they adhere to Marr's 2D--2.5D--3D construction theory remain unexplored. In this paper, we delve into the perception task to explore these questions and find evidence supporting Marr's theory. We introduce a graphics probe, a sub-network crafted to reconstruct the original image from the network's intermediate layers. The key to the graphics probe is its flexible architecture that supports image in both 2D and 3D formats, as well as in a transitional state between them. By injecting graphics probes into neural networks, and analyzing their behavior in reconstructing images, we find that DNNs initially encode images as 2D representations in low-level layers, and finally construct 3D representations in high-level layers. Intriguingly, in mid-level layers, DNNs exhibit a hybrid state, building a geometric representation that s sur normals within a narrow depth range, akin to the appearance of a low-relief sculpture. This stage resembles the 2.5D representations, providing a view of how DNNs evolve from 2D to 3D in the perception process. The graphics probe therefore serves as a tool for peering into the mechanisms of DNN, providing empirical support for Marr's theory.