This is a Python-based software for upsampling 3-dimensional segmented medical images using a mesh-based method. This method may be useful for reducing staircasing artifacts and increasing accuracy in medical image-derived ultrasound simulations, among other applications requiring accurate segmentation upsampling.

*The software is Python-based and MATLAB is used to generate sample shapes and run tests.

The software was developed in following environment:
Python version 3.9
MATLAB R2023b
Please check the compatibility of lateral Python versions using this link: https://www.mathworks.com/support/requirements/python-compatibility.html.

Python package Installation:
pip install numpy scipy vtk numba

MATLAB package:
k-Wave (http://www.k-wave.org/)

The algorithm accepts and returns the following variables:

Input:

originalImage: low resolution input image (binary 3D array - two labels, integer 3D array - more than two labels)
spacing: spacing of the original image (1 x 3 floating point array)
$dx$: scale of upsampling (scalar float for isotropic upsampling, 1 x 3 floating point array for an anisotropic medical image)
$\sigma$: the standard deviation for the Gaussian smoothing kernel (scalar float, recommended range: 0 - 1)
$I$: isovalue for isosurface extraction (scalar float, recommand range: 0.4 - 0.5)

Output:

newImage: high resolution output with defined spacing

example_multilabel_testobject.m upsamples a code-generated complex shape and compares it to a high-resolution code-generated ground truth.

example_vertebra.m resamples a medical image-based segementation of a human spine. Figure 1 depicts slices through the 3D spine volume, demonstrating the upsampling of a multi-label spine segmentation with input parameters $\sigma = 0.7$ and isovalue = 0.4. The input image is sourced from Liebl $et$ $al$. 2021 ¹. This demonstration resamples the original anisotropic voxel spacing of [0.2910, 0.2910, 1.2500] millimetres to an isotropic [0.8, 0.8, 0.8] millimetre voxel spacing. Gap post-processing was not applied.

Figure 1: Mesh-based upsampling demonstration with a segmented spine (subverse003) from the Verse2020 spine segmentation dataset ¹.

example_AustinWoman_Kidney.m upsamples a segmented medical image of a kidney and surrounding organs from the female Visible Human Project dataset ² with input parameters $\sigma = 0.4$ and isovalue = 0.4. This demonstration upsamples the original voxel spacing of [1, 1, 1] millimetres to an isotropic [0.8, 0.8, 0.8] millimetre voxel spacing. Gap post-processing was applied.

Figure 2: Mesh-based upsampling demonstration with a kidney and surrounding organs from the female Visible Human Project dataset ².

SinglelabelGridSearch.m provides a grid-search method to find optimal parameter ($\sigma$, isovalue) settings for upsampling a single-label code-based image. Mis-labelling errors are evaluated using a high-resolution code-based image.

MultilabelGridSearch.m provides a grid-search method to find optimal parameter ($\sigma$, isovalue) settings for upsampling a multi-label code-based image. Errors resulting from gaps between labels and volume differences are evaluated using a high-resolution code-based image.

methodComparsion.m provides a comparsion of the mesh-based upsampling method against naive (nearest-neighbour and trilinear interpolation) upsampling methods.

normalizationComparsion.m compares error metrics for evaluating the accuracy of the upsampled result using a high-resolution ground truth.

IsovalueVSVolume.m provides the variation of volume ratio against isovalue, which can be used by the user to select the isovalue based on the desired volume.