Principles of Shape from Specular Reflection

The reconstruction of (partially) specular object by means of deflectometric methods is a challenging task. It has a long and fairly branched history within the metrology and machine vision communities. We are not aware of any scientific publication surveying the state of the art in a unifying manner and thus stimulating further research. This contribution is intended to close this gap, bringing together prominent ideas from both fields. In avoidance of unnecessary technicality, we lay out the basic theory, including all known forward models of the reflection process. The corresponding inverse problem is ill-posed, so that special emphasis is put on the question of regularization. We embed some novel results on the uniqueness problem and the effectiveness of regularization approaches. Also an overview of numerical methods related to Shape from Specular Reflection is given. For the sake of completeness, we share some thoughts on the construction of an actual measurement system and discuss a practical example.