Face-morphing operations allow for the generation of digital faces that simultaneously carry the characteristics of two different subjects. It has been demonstrated that morphed faces strongly challenge face-verification systems, as they typically match two different identities. This poses serious security issues in machine-assisted border control applications and calls for techniques to automatically detect whether morphing operations have been previously applied on passport photos. While many proposed approaches analyze the suspect passport photo only, our work operates in a differential scenario, i.e., when the passport photo is analyzed in conjunction with the probe image of the subject acquired at border control to verify that they correspond to the same identity. To this purpose, in this study, we analyze the locations of biologically meaningful facial landmarks identified in the two images, with the goal of capturing inconsistencies in the facial geometry introduced by the morphing process. We report the results of extensive experiments performed on images of various sources and under different experimental settings showing that landmark locations detected through automated algorithms contain discriminative information for identifying pairs with morphed passport photos. Sensitivity of supervised classifiers to different compositions on the training and testing sets are also explored, together with the performance of different derived feature transformations.

Logical reasoning as performed by human mathematicians involves an intuitive under- standing of terms and formulas. This includes properties of formulas themselves as well as relations between multiple formulas. Although vital, this intuition is missing when supplying atomically encoded formulae to (neural) down-stream models.In this paper we construct continuous dense vector representations of first-order logic which preserve syntactic and semantic logical properties. The resulting neural formula embeddings encode six characteristics of logical expressions present in the training-set and further generalise to properties they have not explicitly been trained on. To facilitate training, evaluation, and comparing of embedding models we extracted and generated data sets based on TPTP’s first-order logic library. Furthermore we examine the expressiveness of our encodings by conducting toy-task as well as more practical deployment tests.