Add some HiP-CT docs

docs/data/hipct.md

@@ -0,0 +1,56 @@
+# HiP-CT data
+
+HiP-CT stands for hierarchical phase-contrast tomography.
+For more information on the modality see the [HiP-CT website](https://mecheng.ucl.ac.uk/hip-ct/).
+Most of the time HiP-CT consists of a single 'low' (but still quite high!) resolution scan of a whole sample, and then one or more 'high' resolution scans of particular volumes of interest within the same sample.
+
+## Data acquisition and naming
+
+There are HiP-CT scans of two donors, S45 and I58.
+The data are part of the [Pilot human brains dataset](https://lincbrain.org/dandiset/000005) on lincbrain.
+
+Datasets have the name `sub-<donor>_sample-<sample name>_chunk<chunk number>_PC.ome.zarr`.
+The chunk number is set to `yyxx`, where yy is the resolution of the scan in micrometers, and xx is a scan number that is unique between datasets.
+For example, a chunk number of `402` is the second 4um scan.
+The lowest resolution dataset (equivalently, highest chunk number) is the overview dataset that contains an image of the whole sample.
+There are then one or more datasets at higher resolution.
+
+## Registration
+
+Each high resolution dataset is registered to the overview dataset using [`hipct-reg`](https://github.com/hipCTProject/hipct-reg).
+Each transform maps the pixel coordinates of the high resolution zoom datasets to the overview full-sample dataset.
+The transform is of the form:
+
+$$
+T(\mathbf{x}) = s \left ( \mathbf{R} \cdot\mathbf{x} \right ) + \mathbf{t}
+$$
+
+Where
+
+- $s$ is a scaling factor
+- $\mathbf{R}$ is a rotation matrix that rotates about the z-axis.
+- $\mathbf{t}$ is a translation vector
+
+The rotation matrix takes the form
+
+$$
+\mathbf{R} = \begin{pmatrix}
+\cos(-\theta) & \sin(-\theta) & 0 \\
+-\sin(-\theta) & \cos(-\theta) & 0 \\
+0 & 0 & 1 \\
+\end{pmatrix}
+$$
+
+The transform has 5 parameters (1 scaling, 1 rotation, 3 translation).
+
+### Registration accuracy
+
+The HiP-CT registration pipeline is designed to be accurate enough to approximately visually align two datasets. **It is not designed for pixel perfect registration.** We recommend anyone doing analysis relying on the registration between two datasets performs a more accurate registration themselves, using our registration as an initial starting point.
+
+### Registration data
+
+
+| Dataset | Overview dataset | $\mathbf{t}$ | $s$ | $\theta$ (degrees) |
+| -------- | -------- | -------- | -------- | -------- |
+| `sub-I58_sample-blockIC2_chunk-101_PC`     | `sub-I58_sample-blockIC2_chunk-401_PC`     |   (3746.4467746089194, 3660.0610535229666, 1127.3616712249263)   | 0.2016106611944697 | -6.496401244495998 |
+| `sub-I58_sample-blockIC2_chunk-201_PC`    | `sub-I58_sample-blockIC2_chunk-401_PC`     |   (2119.695989239648, 2321.6572801771194, 971.0041825720597)   | 0.5181803632402424 | 0.5004912711693281 |

docs/javascripts/mathjax.js

@@ -0,0 +1,19 @@
+window.MathJax = {
+    tex: {
+      inlineMath: [["\\(", "\\)"]],
+      displayMath: [["\\[", "\\]"]],
+      processEscapes: true,
+      processEnvironments: true
+    },
+    options: {
+      ignoreHtmlClass: ".*|",
+      processHtmlClass: "arithmatex"
+    }
+  };
+
+  document$.subscribe(() => {
+    MathJax.startup.output.clearCache()
+    MathJax.typesetClear()
+    MathJax.texReset()
+    MathJax.typesetPromise()
+  })

mkdocs.yml

@@ -23,6 +23,8 @@ nav:
   - Upload data: "upload.md"
   - API:
     - LINC Client: https://lincbrain.readthedocs.io
+  - Data:
+    - HiP-CT: "data/hipct.md"
   - Contribute documentation: "contribute.md"
   - About this doc: "about.md"
 
@@ -34,6 +36,8 @@ markdown_extensions:
   - pymdownx.magiclink
   - toc:
       permalink: True
+  - pymdownx.arithmatex:
+      generic: true
 
 # List of plugins
 plugins:
@@ -61,4 +65,9 @@ extra:
       name: Docker Hub
     - icon: fontawesome/brands/python
       link: https://pypi.org/project/lincbrain-cli
-      name: PyPI
+      name: PyPI
+
+
+extra_javascript:
+  - javascripts/mathjax.js
+  - https://unpkg.com/mathjax@3/es5/tex-mml-chtml.js