  Specularity prediction is essential to many computer vision applications,
giving important visual cues usable in Augmented Reality (AR), Simultaneous
Localisation and Mapping (SLAM), 3D reconstruction and material modeling.
However, it is a challenging task requiring numerous information from the scene
including the camera pose, the geometry of the scene, the light sources and the
material properties. Our previous work addressed this task by creating an
explicit model using an ellipsoid whose projection fits the specularity image
contours for a given camera pose. These ellipsoid-based approaches belong to a
family of models called JOint-LIght MAterial Specularity (JOLIMAS), which we
have gradually improved by removing assumptions on the scene geometry. However,
our most recent approach is still limited to uniformly curved surfaces. This
paper generalises JOLIMAS to any surface geometry while improving the quality
of specularity prediction, without sacrificing computation performances. The
proposed method establishes a link between surface curvature and specularity
shape in order to lift the geometric assumptions made in previous work.
Contrary to previous work, our new model is built from a physics-based local
illumination model namely Torrance-Sparrow, providing an improved
reconstruction. Specularity prediction using our new model is tested against
the most recent JOLIMAS version on both synthetic and real sequences with
objects of various general shapes. Our method outperforms previous approaches
in specularity prediction, including the real-time setup, as shown in the
supplementary videos.
