**5.4 Shape index**

Koenderink separated the shape index in different regions depending on the type of curvature, which is obtained through the eigenvalues of the Hessian matrix, which is represented by K1 and K2 as given by the following equation (Koenderink &. Van Doorn, 1992).

$$\mathbf{q} = \frac{2}{\pi} \tan^{-1} \frac{\mathbf{k}\_2 + \mathbf{k}\_1}{\mathbf{k}\_2 + \mathbf{k}\_1} \quad ; \quad \mathbf{k}\_2 \ge \mathbf{k}\_1 \tag{8}$$

The result of the shape index φ has values between [-1, 1] which can be classified, according to Koenderink, depending on its local topography, as shown in table 1.


Table 1. Classification of the Shape Index

Figure 5 shows the image from the surface local form depending on the value of the Shape Index, and Figure 6 shows an example of the SFS vector from a rectangular piece used during experiments.

Fig. 5. Representation of local forms in the Shape Index classification.

Fig. 6. SFS Vector Descriptor Example
