Figure 4. Architecture of Frangi-Net over 8 scales σ .

For each single-scale a Frangi-Net computes spatial derivatives $\frac{{\partial }^{2}g}{\partial x^2},$ $\frac{{\partial }^{2}g}{\partial x\partial y},$ and $\frac{{\partial }^{2}g}{\partial y^2}.$ These are used to form a Hessian matrix of which eigenvalues λ₁ and λ₂ are extracted. Both are used to compute structureness S and blobness R_b which are required to compute the final vesselness at each pixel V_σ.