Table 1.

Eigenvalues ${\mathit{\lambda }}_i$ and eigenvectors ${\mathbf{e}}_{\mathbf{i}}$ of $\mathbf{T}$ for each initial orientation initialisation

Initialisation	Eigenvalues ${\mathit{\lambda }}_i$	Eigenvectors ${\mathbf{e}}_{\mathbf{i}}$
No preferred orientation	1: ${\mathit{\lambda }}_1={\mathit{\lambda }}_2={\mathit{\lambda }}_3=K$	${\mathbf{e}}_{\mathbf{i}}=(e_{ij})$, $e_{ij}={\mathit{\delta }}_{ij}$
	2: ${\mathit{\lambda }}_1={\mathit{\lambda }}_2={\mathit{\lambda }}_3=I(\mathbf{p})$
	3: ${\mathit{\lambda }}_1={\mathit{\lambda }}_2={\mathit{\lambda }}_3=\mathit{\nu }(\mathbf{p})$
Hessian matrix	1: $[{\mathit{\lambda }}_1,{\mathit{\lambda }}_2,{\mathit{\lambda }}_3]=[|{\mathit{\kappa }}_1{|}^{-1},|{\mathit{\kappa }}_2{|}^{-1},|{\mathit{\kappa }}_3{|}^{-1}]$	$[{\mathbf{e}}_{\mathbf{1}},{\mathbf{e}}_{\mathbf{2}},{\mathbf{e}}_{\mathbf{3}}]=[{\mathbf{v}}_{\mathbf{1}},{\mathbf{v}}_{\mathbf{2}},{\mathbf{v}}_{\mathbf{3}}]$
	2: $[{\mathit{\lambda }}_1,{\mathit{\lambda }}_2,{\mathit{\lambda }}_3]=[\mathit{\nu }(\mathbf{p}),0,0]$
Structure tensor	$({\mathit{\lambda }}_1-{\mathit{\lambda }}_2)={\Vert ▽I\Vert }^2$, ${\mathit{\lambda }}_3=0$	${\mathbf{e}}_{\mathbf{1}}{{\mathbf{e}}_{\mathbf{1}}}^T=▽I▽I^T$, ${\mathbf{e}}_{\mathbf{2}}={\mathbf{e}}_{\mathbf{3}}=\mathbf{0}$

Note that when no preferred orientation is used, three different saliency measurements can be used. Similarly, two different configurations of the initial eigenvalues are proposed when using Hessian matrix analysis