We are working in collaboration with geographers to study a set of pebbles digital images. Among the features geographers want to get automatically, pebble sides number is intuitively defined as shown in Fig 1. It is merely computed after a thick polygonalisation of pebble contour. We propose an incremental and linear algorithm, free of restrictive hypothesis, which relies on previous works of Debled et al. [DRFRD05, DRFRD06, DRRRD05]. We give some results on synthetical and real images.