Figure 1
From: 3D brain tumor segmentation using a two-stage optimal mass transport algorithm
(a) A diagram illustrating the construction of the TSOMT map \(f^*_{\rho ,\delta }\) between \((\mathcal {M}, \rho )\) and \((\mathcal {N}, \delta \equiv 1)\), where \(\mathcal {M}\), \(\mathcal {N}\), and \(\mathbb {B}^3\) are a 3D brain image, a 3D solid cube, and a 3D unit solid ball, respectively. (b) The bijective and linear simplicial map \(f_{\rho }^*:\tau \in \mathcal {T}(\mathcal {M})\rightarrow f_{\rho }^*(\tau )\in \mathcal {T}(\mathcal {B}^3)\), \(f_{\delta }^*:\tau '\in \mathcal {T}'(\mathcal {N}) \rightarrow f_\delta ^*(\tau ') \in \mathcal {T}'(\mathbb {B}^3)\), and \(f_{\rho ,\delta }^*:\tau \in \mathcal {T}(\mathcal {M})\rightarrow f_{\rho ,\delta }^*(\tau )\in \mathcal {T}(\mathcal {N})\).
