Fig. 7.

Two-dimensional trajectory of the coefficients α_P, α_N, and β² during training mapped in the Tversky coefficients space α_P,tversky = 2 α_P/(1 + β²) and ${\alpha }_{N,\text{tversky}}=2{\beta }^2{\alpha }_P/\left(1+{\beta }^2\right)$. In this representation, using the Dice loss corresponding to operating at a fixed point (1,1), using the Effectiveness loss corresponding to operating at a fixed point on the gray line α_P,tversky + α_N,tversky = 2, and using the Tversky loss corresponding operating at a fixed point anywhere in the plane defined by α_P,tversky ≥ 0 and α_N,tversky ≥ 0. With the adaptive training methodology, the parameters are updated at every iteration step leading to a dynamic trajectory as the optimization is carried out (colormap correspond to iteration number).