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# elasticdeform: Elastic deformations for N-dimensional images

Gijs van Tulder

### Citation Style Language JSON Export

{
"publisher": "Zenodo",
"DOI": "10.5281/zenodo.4569691",
"title": "elasticdeform: Elastic deformations for N-dimensional images",
"issued": {
"date-parts": [
[
2021,
3,
1
]
]
},
"abstract": "<p>This library implements elastic grid-based deformations for N-dimensional images.</p>\n\n<p>The elastic deformation approach is described in</p>\n\n<ul>\n\t<li>Ronneberger, Fischer, and Brox, &quot;U-Net: Convolutional Networks for Biomedical Image Segmentation&quot; (<a href=\"https://arxiv.org/abs/1505.04597\">https://arxiv.org/abs/1505.04597</a>)</li>\n\t<li>&Ccedil;i&ccedil;ek et al., &quot;3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation&quot; (<a href=\"https://arxiv.org/abs/1606.06650\">https://arxiv.org/abs/1606.06650</a>)</li>\n</ul>\n\n<p>The procedure generates a coarse displacement grid with a random displacement for each grid point. This grid is then interpolated to compute a displacement for each pixel in the input image. The input image is then deformed using the displacement vectors and a spline interpolation.</p>\n\n<p>In addition to the normal, forward deformation, this package also provides a function that can backpropagate the gradient through the deformation. This makes it possible to use the deformation as a layer in a convolutional neural network. For convenience, a TensorFlow wrapper is provided in&nbsp;<code>elasticdeform.tf</code>.</p>\n\n<p>See <a href=\"https://github.com/gvtulder/elasticdeform\">https://github.com/gvtulder/elasticdeform</a></p>",
"author": [
{
"family": "Gijs van Tulder"
}
],
"version": "v0.4.9",
"type": "article",
"id": "4569691"
}
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