with $\mathcal{H}_{i+1}$, etc. With the exception of the middle slice, all histopathology images will have a corresponding rigid transform following the registration with the adjacent slice $\mathcal{T}^H_{Rig}$.

3.  **2D Registration:** We registered $\mathcal{M}_i$ with $\mathcal{H}_i$, for $\forall i \in [1, D]$, by optimizing rigid $\mathcal{T}^M_{Rig}$, affine $\mathcal{T}^M_{Aff}$ and deformable $\mathcal{T}^M_{Def}$ transforms using gradient-based approaches. The rigid and affine registrations only use the prostate masks during the optimization and applied Sum of Square Differences as scoring function. The deformable registration used Free-Form Deformations [@rueckert_nonrigid_1999] to optimize the Mattes Mutual Information computed based on the image intensities. [We used a multi-resolution pyramid with three layers (with shrinking factors 16, 8, and 4 respectively, and a smoothing sigma of 4, 2, and 1 respectively). The affine transform optimization was done using a gradient descent optimizer with a learning rate of 0.01 and 250-500 iterations per resolution layer, while, the deformable registration employed a LBFGSB optimizer with 10-50 iterations per resolution layer.]{}

4.  **Mapping Cancer onto MRI:** A composite transform of $\mathcal{T}^H_{Rig}$, $\mathcal{T}^M_{Rig}$, $\mathcal{T}^M_{Aff}$ and $\mathcal{T}^M_{Def}$ is applied to deform the histopathology image as well as the cancer label and anatomic landmarks into the coordinates of the T2w MRI.

Our approach was developed using 