Table 1 Relationship between binary region number and characteristic function
From: The Vese-Chan model without redundant parameter estimation for multiphase image segmentation
Ωi | \({b_{1}^{i - 1}}\) | \({b_{2}^{i - 1}}\) | \({b_{3}^{i - 1}}\) | Characteristic function \({{\chi _{i}} = \prod \limits _{j = 1}^{m} \left ({b_{j}^{i - 1} + {{\left ({ - 1} \right)}^{b_{j}^{i - 1}}}{\phi _{j}}} \right)}\) |
|---|---|---|---|---|
Ω1 | 0 | 0 | 0 | χ1=ϕ1ϕ2ϕ3 |
Ω2 | 0 | 0 | 1 | χ2=ϕ1ϕ2(1−ϕ3) |
Ω3 | 0 | 1 | 0 | χ3=ϕ1(1−ϕ2)ϕ3 |
Ω4 | 0 | 1 | 1 | χ4=ϕ1(1−ϕ2)(1−ϕ3) |
Ω5 | 1 | 0 | 0 | χ5=(1−ϕ1)ϕ2ϕ3 |
Ω6 | 1 | 0 | 1 | χ6=(1−ϕ1)ϕ2(1−ϕ3) |
Ω7 | 1 | 1 | 0 | χ7=(1−ϕ1)(1−ϕ2)ϕ3 |
Ω8 | 1 | 1 | 1 | χ8=(1−ϕ1)(1−ϕ2)(1−ϕ3) |