$I$, see Figure \[fig:LBP\_ring\](b-c). The descriptor of the LBP multi-ring is the concatenation of the histograms of the LBP values of each single ring, e.g., an array or a matrix.

Definition and implementation of the edgeLBP operator {#ss:edgeLBP_def}
-----------------------------------------------------

We extend the multi-ring LBP operator to deal with surface tessellations through a sphere-mesh intersection technique, called the *edge Local Binary Pattern (edgeLBP)*. By a surface tessellation, we mean a polygonal mesh $T=(V,E,F)$, which is a collection of vertices $V$, edges $E$ and faces $F$ defining the surface of an object. In our settings, we assume that the faces of the tessellation are convex polygons; examples of admissible surface representations are triangle and quad meshes, [@BLPPSTZ13a].

We assume that the surface property can be stored as a scalar function $h$ defined on the vertices of the tessellations, formally, $h:V\rightarrow\mathbb{R}$. In our settings, we consider two choices for the function $h$: (i) the *L-channel* from the CIELab color space [@CIELAB_1; @CIELAB_2]; (ii) the gray-scale value defined as $0.21R+0.72G+0.07B$ ($R$, $G$ and $B$ are the channels of the RGB color space).

The concept of ring is crucial for the LBP operator: while a pixel grid has the same connectivity everywhere, surface tessellations can 