The Perspective Face Shape Ambiguity

When a face is viewed under perspective projection, its shape (i.e. the 2D position of features) changes dramatically as the distance between face and camera varies. This causes substantial variation in appearance which is significant enough to disrupt human recognition of unfamiliar faces. However, a face viewed at any distance is still perceived as natural and humans are bad at interpreting the subject-camera distance given only a face image. We show that perspective viewing of faces leads to an ambiguity. Namely, that observed configurational information (position of projected vertices) and shading can be explained by a continuous class of possible faces. To demonstrate the ambiguity, we propose a novel method for efficiently fitting a 3D morphable model to 2D vertex positions when the subject-camera distance is known. By varying this distance, we obtain a subspace of faces, all of which are consistent with the observed data. We additionally show that faces within this subspace can all produce approximately the same shading pattern via a spherical harmonic lighting model.

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