The specularity prediction task in images, given the camera pose and scene geometry, is challenging and ill-posed. A recent approach called JOint LIght-MAterial Specularity (JOLIMAS) addresses this problem using a geometric model under the assumption that specularities have an elliptical shape. We address the most recent version of the model, Dual JOLIMAS, which is limited to planar and convex surfaces where the local surface's curvature under the specularity is constant. We propose a canonical representation of the JOLIMAS model that is independent of the local surface curvature. To reconstruct our model represented by a 3D quadric, we use at least 3 ellipses fitted to specularities and transform their shape to fit a planar surface and simulate a planar mirror which does not distort the image of the reflected object. After reconstruction, we project the 3D quadric into an ellipse and transform it to fit the current local curvature of the surface on a new viewpoint. We assessed this method on both synthetic and real sequences, and compared it to the previous approach Dual JOLIMAS.