the MRI from the mid-gland to apex, but lacking between the mid-gland and the prostate base. Slice correspondences between the MRI and histopathology were identified by an expert urologist and a radiology-pathology registration expert and validated by a multi-disciplinary team of radiologists, pathologists and urologists.

Radiology - Pathology Registration {#radiology---pathology-registration .unnumbered}
----------------------------------

Our approach is summarized in  \[fig:flowchart\] and described below:

![Summary of our approach. First, we align the serial histopathology slices relative to each other to reconstruct the 3D histopathology volume. Second, we register the histopathology slices relative to the T2w MRI using rigid, affine and deformable transforms. Finally, we map the extent of cancer from the histopathology images onto the radiology images.[]{data-label="fig:flowchart"}](figures/flowchart.pdf){width="\linewidth"}

1.  **Pre-Processing:** We applied the prostate masks, $\mathcal{M}^{Pr}$ and $\mathcal{H}^{Pr}$ onto $\mathcal{M}$ and $\mathcal{H}$, respectively, to exclude the structures outside the prostate from image registration. The gross rotation angles or left-right flipping was applied as well.

2.  **3D Histopathology Reconstruction:** We registered $\mathcal{H}_i$ relative each other, to ensure their 3D consistency within the 3D reconstruction, $\mathcal{H}$. We selected the middle slice $\mathcal{H}_i, i = \frac{M}{2}$ as the first fixed image and registered $\mathcal{H}_{i-1}$ to $\mathcal{H}_i$, $\mathcal{H}_{i-2}$ with $\mathcal{H}_{i-1}$, etc, as well as $\mathcal{H}_{i+1}$ to $\mathcal{H}_{i}$, $\mathcal{H}_{i+2}$ 