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179 lines
7.6 KiB
Markdown
179 lines
7.6 KiB
Markdown
---
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title: Volume Rendering
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layout: post
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excerpt: A had this old CT scan lying around from when I had my wisdom teeth removed so I thought I'd try rendering it.
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assets: /assets/blog/volume_rendering
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draft: true
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thumbnail: /assets/blog/volume_rendering/thumbnail.png
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social_image: /assets/blog/volume_rendering/thumbnail.png
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alt: A volumetric render of a CT scan of my jaw.
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model_viewer: true
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---
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As part of getting my wisdom teeth removed a few years ago, I had a CT scan of my jaw done to see where my wisdom teeth were and at what angle. Spoiler, a hilariously incorrect angle.
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A CT scan works by taking a bunch of 2D x-ray images from many angles. Each of those 2D images encodes information about the density of all the tissues that the beam had to pass through on the way from the source to the detector for that pixel. Using the magic of the [Radon transform][radon], you can take that collection of 2D images and compute a 3D density map of, in this case, my head.
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Being the nerd that I am, I asked if I could have the scan data and they very kindly burned it to a CD for me. At some point in the intervening years I copied the data from the CD to 'my various files I might need at some point place' and forgot about it.
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Since I've been playing around a lot with three.js lately I wondered how hard it would be to finally visualise the scan.
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[radon]: https://en.wikipedia.org/wiki/Radon_transform
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So as not to bury the lede, here's what I ended up with:
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<figure>
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<img class="no-wc invertable" src="{{page.assets}}/billboard.png">
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<volume-viewer model="{{page.assets}}/volume_scan.data.gz" model-metadata="{{page.assets}}/volume_scan_meta.json" camera = '{"type":"perspective","fov":30,"near":0.01,"far":40,"position":[-1.422,1.03,1.964],"rotation":[-0.4831,-0.5702,-0.2759],"zoom":1,"target":[0,0,0]}'>
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</volume-viewer>
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<figcaption class="no-wc">If you have JS enabled this is an interacive volume render.</figcaption>
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</figure>
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Read on if you want to know how I put this together.
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## Step 1: Extracting the data
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The file I got had a `.inv3` format and a quick google sent me to [this page][inv3_file_format] with a nice explanation of the file formt. it turns out it was encoded with an open source tool! Now I could probably have just installed InVesalius and exported the data that way but instead I went with just reading the file which was pretty easy because they chose quite a simple format.
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First step was to extract it:
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```
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tar -xvzf my_scan.inv3
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```
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which gave me these file:
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```
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4.0K main.plist
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130M mask_0.dat
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4.0K mask_0.plist
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258M matrix.dat
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4.0K measurements.plist
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4.0K surface_0.plist
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101M surface_0.vtp
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4.0K surface_1.plist
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3.9M surface_1.vtp
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... more pairs of surface_n.vtp and surface_n.plist
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4.0K surface_8.plist
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4.4M surface_8.vtp
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```
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From my quick skim of the file format page, `main.plist` has the main metadata, `matrix.dat` is the density data. I think `mask_n.dat` and `mask.plist` are basically an array of indices used to categorise each pixel in the raw scan, for example bone, soft tissue etc.I think all the `surface_n.*` pairs and the mask might be from when I was playing around with the tools inside InVesalius sometime in the distant past.
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For the rest of this I will just focus on matrix.dat and the metadata in main.plist.
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[inv3_file_format]: https://github.com/invesalius/invesalius3/wiki/InVesalius-3-Project-file-format
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After a quick `pip install plistlib` we can do:
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```python
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import plistlib
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dir = Path("path/to/scan_files")
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plist = dir / "main.plist"
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with plist.open("rb") as f:
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print(plistlib.load(f))
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{'annotations': {},
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'date': '2021-06-14T18:31:38.718928',
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'format_version': 1,
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'invesalius_version': '3.1.1',
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'masks': {'0': 'mask_0.plist'},
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'matrix': {'dtype': 'int16',
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'filename': 'matrix.dat',
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'shape': [508, 516, 516]},
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'measurements': 'measurements.plist',
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'modality': 'CT',
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'name': 'Hodson^Thomas',
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'orientation': 2,
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'scalar_range': [-1000, 3705],
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'spacing': [0.2, 0.20000000000000284, 0.2],
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'surfaces': {'0': 'surface_0.plist',
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...
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'8': 'surface_8.plist'},
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'window_level': 2132.0,
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'window_width': 6264.0}
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```
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The key data here is that `matrix` is `int16` with shape `[508, 516, 516]`.
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```python
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import numpy as np
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from matplotlib import pyplot as plt
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f = dir / "matrix.dat"
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data = np.memmap(f, dtype = "int16", mode="r", shape = (508, 516, 516))
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plt.imshow(data[data.shape[0]//2], interpolation='nearest')
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```
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<figure>
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<img class="invertable" src="{{page.assets}}/slice.png">
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<figcaption>A slice of the 3D scan data showing a bit of my teeth and jaw bone.</figcaption>
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</figure>
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## Compressing the data
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Next, I resized the data to 300x300x300 voxels to slim it down a bit, rescaled it to fit in 0-255, cast it to `uint8` and finally GZIP compressed it. This took us from 270MB originally down to 14MB. I also wrote out a small JSON file with the scan dimensions and dtype.
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```python
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import json
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from skimage.transform import resize
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print(f"Original data {data.shape = }, {data.dtype = }, {data.nbytes / 10**6:.0f} MB")
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# Resize, rescale to 0-255, coerce to uint8, rotate
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small_data = resize(data, (300, 300, 300), anti_aliasing=True)
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small_data = (small_data - small_data.min()) / (small_data.max() - small_data.min()) * 255
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small_data = small_data.astype(np.uint8)
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small_data = small_data.swapaxes(0,1)
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print(f"Resized data {small_data.shape = }, {small_data.dtype = }, {small_data.nbytes / 10**6:.0f} MB")
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p = Path("/path/to/output")
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import gzip
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with open(p / "volume_scan.data.gz", "wb") as f:
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compressed = gzip.compress(small_data.tobytes(order='C'), compresslevel=9)
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print(f"After GZIP compression, {len(compressed) / 10**6:.0f} MB")
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f.write(compressed)
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with open(p / "volume_scan_meta.json", "w") as f:
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f.write(json.dumps(
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dict(
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dtype = str(small_data.dtype),
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shape = small_data.shape,
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)))
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```
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Looking at the histogram of the raw data and comparing it to the [Hounsfield Scale from here](https://kevalnagda.github.io/ct-windowing):
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```python
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f, ax = plt.subplots(figsize = (9,2))
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values = {"Air":-1000, "": -500, "":500, "Fat":-100, "Water":0, "Soft Tissue":50, "Bone":400, "Metal":1000}
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ax.hist(data.ravel(), bins = 500);
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ax.set(xlim = (-1000, 1000), ylim = (0, 3e6))
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ax.set_xticks(list(values.values()), [f"{k} {v}" for k,v in values.items()], rotation=45, ha='right')
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f.tight_layout()
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f.savefig("hist.svg")
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```
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<figure>
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<img class="invertable" src="{{page.assets}}/hist.svg">
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</figure>
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We could probably get away with clamping all the data from -1000 to -500 to one air value, which would free up a lot of our limited 0-225 for the more interesting stuff happening between -100 and 400. But I didn't really notice an issues with the quantisation so I didn't pursue this.
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EDIT: After I implemented the iso-surface rendering mode and found that I could see interesting regions like my windpipe and inside my sinuses I wondered if having more density precision would help see them. So I using float16 or float32 textures but didn't see much improvement at the expense of doubling or quadrupling the file size, so I switched back to 8 bit values.
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## Viewing the Data
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For the viewer I mostly copied the code from [this excellent tutorial](https://observablehq.com/@mroehlig/3d-volume-rendering-with-webgl-three-js) and integrated it into my existing three.js helper methods.
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The basic idea is we: load the GZIPed file, extract it to raw bytes, load those bytes into a 3D texture according the metadata.
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We create a cube in the three.js scene with a custom material attached to it that just runs our custom shader code.
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Then on the GPU side we have a simple vertex shade that just calculates the raw from the camera to the vertex. This
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