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.pytest_cache/*
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testing/__pycache__/*
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.DS_Store
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/images/rigid_bunny/rigid_bunny_3D_00*.tiff
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/images/rigid_bunny/*.pptx

‎JOSS_Submission/paper.bib

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@ARTICLE{121791,
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author={Besl, P.J. and McKay, Neil D.},
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journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
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title={A method for registration of 3-D shapes},
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year={1992},
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volume={14},
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number={2},
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pages={239-256},
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doi={10.1109/34.121791}
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}
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@article{CHEN1992145,
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title = {Object modelling by registration of multiple range images},
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journal = {Image and Vision Computing},
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volume = {10},
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number = {3},
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pages = {145-155},
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year = {1992},
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note = {Range Image Understanding},
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issn = {0262-8856},
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doi = {https://doi.org/10.1016/0262-8856(92)90066-C},
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url = {https://www.sciencedirect.com/science/article/pii/026288569290066C},
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author = {Yang Chen and Gérard Medioni},
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keywords = {object modelling, 3D surface registration, range image registration},
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abstract = {We study the problem of creating a complete model of a physical object. Although this may be possible using intensity images, we here use images which directly provide access to three dimensional information. The first problem that we need to solve is to find the transformation between the different views. Previous approaches either assume this transformation to be known (which is extremely difficult for a complete model), or compute it with feature matching (which is not accurate enough for integration). In this paper, we propose a new approach which works on range data directly and registers successive views with enough overlapping area to get an accurate transformation between views. This is performed by minimizing a functional which does not require point-to-point matches. We give the details of the registration method and modelling procedure and illustrate them on real range images of complex objects.}
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}
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@ARTICLE{5432191,
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author={Myronenko, Andriy and Song, Xubo},
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journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
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title={Point Set Registration: Coherent Point Drift},
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year={2010},
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volume={32},
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number={12},
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pages={2262-2275},
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doi={10.1109/TPAMI.2010.46}
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}
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@Article{ harris2020array,
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title = {Array programming with {NumPy}},
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author = {Charles R. Harris and K. Jarrod Millman and St{\'{e}}fan J.
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van der Walt and Ralf Gommers and Pauli Virtanen and David
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Cournapeau and Eric Wieser and Julian Taylor and Sebastian
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Berg and Nathaniel J. Smith and Robert Kern and Matti Picus
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and Stephan Hoyer and Marten H. van Kerkwijk and Matthew
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Brett and Allan Haldane and Jaime Fern{\'{a}}ndez del
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R{\'{i}}o and Mark Wiebe and Pearu Peterson and Pierre
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G{\'{e}}rard-Marchant and Kevin Sheppard and Tyler Reddy and
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Warren Weckesser and Hameer Abbasi and Christoph Gohlke and
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Travis E. Oliphant},
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year = {2020},
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month = sep,
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journal = {Nature},
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volume = {585},
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number = {7825},
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pages = {357--362},
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doi = {10.1038/s41586-020-2649-2},
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publisher = {Springer Science and Business Media {LLC}},
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url = {https://doi.org/10.1038/s41586-020-2649-2}
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}
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@misc{khallaghi_2017,
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title={PyCPD: Tutorial on the Coherent Point Drift Algorithm},
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url={http://siavashk.github.io/2017/05/14/coherent-point-drift/},
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author={Khallaghi , Siavash},
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year={2017},
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month={May}
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}

‎JOSS_Submission/paper.jats

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<?xml version="1.0" encoding="utf-8" ?>
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<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.2 20190208//EN"
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"JATS-publishing1.dtd">
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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="1.2" article-type="other">
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<front>
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<journal-meta>
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<journal-id></journal-id>
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<journal-title-group>
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<journal-title>Journal of Open Source Software</journal-title>
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<abbrev-journal-title>JOSS</abbrev-journal-title>
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</journal-title-group>
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<issn publication-format="electronic">2475-9066</issn>
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<publisher>
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<publisher-name>Open Journals</publisher-name>
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</publisher>
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</journal-meta>
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<article-meta>
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<article-id pub-id-type="publisher-id">0</article-id>
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<article-id pub-id-type="doi">N/A</article-id>
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<title-group>
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<article-title>PyCPD: Pure NumPy Implementation of the Coherent Point
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Drift Algorithm</article-title>
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</title-group>
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<contrib-group>
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<contrib contrib-type="author">
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<contrib-id contrib-id-type="orcid">0000-0001-6717-8979</contrib-id>
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<name>
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<surname>Gatti</surname>
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<given-names>Anthony A.</given-names>
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</name>
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<xref ref-type="aff" rid="aff-1"/>
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<xref ref-type="aff" rid="aff-2"/>
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</contrib>
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<contrib contrib-type="author">
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<name>
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<surname>Khallaghi</surname>
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<given-names>Siavash</given-names>
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</name>
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<xref ref-type="aff" rid="aff-3"/>
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<xref ref-type="corresp" rid="cor-1"><sup>*</sup></xref>
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</contrib>
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<aff id="aff-1">
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<institution-wrap>
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<institution>Stanford University, USA</institution>
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</institution-wrap>
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</aff>
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<aff id="aff-2">
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<institution-wrap>
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<institution>NeuralSeg Ltd., Canada</institution>
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</institution-wrap>
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</aff>
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<aff id="aff-3">
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<institution-wrap>
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<institution>Independent Researcher, Canada</institution>
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</institution-wrap>
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</aff>
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</contrib-group>
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<author-notes>
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<corresp id="cor-1">* E-mail: <email></email></corresp>
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</author-notes>
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<volume>¿VOL?</volume>
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<issue>¿ISSUE?</issue>
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<fpage>¿PAGE?</fpage>
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<permissions>
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<copyright-statement>Authors of papers retain copyright and release the
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work under a Creative Commons Attribution 4.0 International License (CC
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BY 4.0)</copyright-statement>
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<copyright-year>2022</copyright-year>
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<copyright-holder>The article authors</copyright-holder>
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<license license-type="open-access" xlink:href="https://creativecommons.org/licenses/by/4.0/">
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<license-p>Authors of papers retain copyright and release the work under
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a Creative Commons Attribution 4.0 International License (CC BY
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4.0)</license-p>
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</license>
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</permissions>
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<kwd-group kwd-group-type="author">
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<kwd>Python</kwd>
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<kwd>Point-cloud</kwd>
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<kwd>Registration</kwd>
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<kwd>Expectation-Maximization</kwd>
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</kwd-group>
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</article-meta>
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</front>
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<body>
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<sec id="background">
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<title>Background</title>
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<p>Point cloud registration is a common problem in many areas of
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computer science, particularly computer vision. Point clouds come from
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many types of data such as LIDAR commonly used for self-driving
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vehicles, and other sorts of 3D scanners (e.g., structured light) are
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commonly used to map the surface of physical objects. Point clouds are
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also used to represent the surface of an anatomical structure
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extracted from a medical image. Point cloud registration finds a
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transformaton from one point cloud to another. Point cloud
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registration has use cases in many fields from self-driving vehicles
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to medical imaging and virtual reality. Typically, point cloud
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registraton is classified into rigid (only rotations or translations),
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affine (rigid + shearing and scaling) and non-rigid also called
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deformable registration (non-linear deformation).</p>
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<p>Point cloud registration typically requires 2 point clouds. The
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first point cloud is the “fixed” or “target” point cloud and the
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second is the “moving” or “source” point cloud. We try to find the
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transformation that will best align the moving (or source) point cloud
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with the fixed point cloud. One of the most well known rigid point
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cloud registration algorithms is the Iterative Closest Point (ICP)
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algorithm
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(<xref alt="Besl &amp; McKay, 1992" rid="ref-121791" ref-type="bibr">Besl
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&amp; McKay, 1992</xref>;
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<xref alt="Chen &amp; Medioni, 1992" rid="ref-CHEN1992145" ref-type="bibr">Chen
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&amp; Medioni, 1992</xref>). ICP is an iterative algorithm where the
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following steps are iterated: i) for every point on the moving point
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cloud find the closes point on the fixed point cloud ii) use a least
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squares approach to find the optimal transformation matrix (rotation,
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tranlsation, scaling, shear) to align the point correspondences found
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in i) iii) apply the transformation from ii) to the moving point cloud
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These steps are repeated until the root mean squared point-to-point
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distances from i) converges.</p>
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<p>The coherent point drift (CPD) algorithm was created by Myronenko
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and Song
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(<xref alt="Myronenko &amp; Song, 2010" rid="ref-5432191" ref-type="bibr">Myronenko
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&amp; Song, 2010</xref>) to overcome many of the limitaitons of ICP
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and other previous registration methods. Namely, these other methods
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didnt necessarily generalize to greater than 3 dimensions and they
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were prone to errors such as noise, outliers, or missing points. The
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CPD alogirthm is a probabilistic multidimensional algorithm that is
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robust and works for both rigid and non-rigid registration. In CPD the
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moving point cloud is modelled as a Gaussian Mixture Model (GMM) and
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the fixed point cloud is treated as observations from the GMM. The
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optimal transformation parameters maximze the Maximum Likelihood /
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Maximum A Posteriori (MAP) estimation that the observed point cloud is
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drawn from the GMM. A key point of the CPD algorithm is that it forces
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the points to move coherently by preserving topological structure. The
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CPD algorithm is also an iterative algorithm that iterates between an
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expectation (E) step and a maximization (M) step until convergence is
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achieved. The E-step estimates the posterior probability distributions
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of the GMM centroids (moving points) given the data (fixed points)
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then the M-step updates the transfomration to maximize the posterior
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probability that the data belong to the GMM distributions. The E- and
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M-steps are iterated until convergence.</p>
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</sec>
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<sec id="statement-of-need">
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<title>Statement of need</title>
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<p>Due to the robustness and the broad array of uses for the CPD
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algorithm the original CPD paper has currently (March 2022) been
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referenced &gt;2000 times. The CPD algorithm is available in Matlab.
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However, no open-source python version previously existed. In this
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paper we present a pure
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NumPy(<xref alt="Harris et al., 2020" rid="ref-harris2020array" ref-type="bibr">Harris
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et al., 2020</xref>) version of the CPD algorithm to enable general
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use of CPD for the Python community. Furthermore, the full
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implementation in Numpy makes the algorithm accesible for others to
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learn from. To help in learning, a blog post that coincides with this
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library has previously been
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<ext-link ext-link-type="uri" xlink:href="http://siavashk.github.io/2017/05/14/coherent-point-drift/">published</ext-link>
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(<xref alt="Khallaghi, 2017" rid="ref-khallaghi_2017" ref-type="bibr">Khallaghi,
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2017</xref>).</p>
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</sec>
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<sec id="summary">
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<title>Summary</title>
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<p>The PyCPD package implements the CPD algorithm in NumPy. The
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library itself includes a module to implement the Expectation
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Maximization (EM) algorithm. Sub-modules inherent the EM functionality
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and implement rigid, affine, and deformable registration using EM. CPD
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registration using affine, rigid, and deformable methods all allow for
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the transformation learned from CPD to be applied to any point cloud.
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Thus, it is possible to learn the transformation on a subset of the
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points and then apply it to the whole point cloud to reduce
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computation time. Finally, the low-rank approximation for deformable
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registration that was described by Myronenko and Song
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(<xref alt="Myronenko &amp; Song, 2010" rid="ref-5432191" ref-type="bibr">Myronenko
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&amp; Song, 2010</xref>) was implemented. A low rank approximation of
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the Gaussian kernal is used to reduce computation time and has the
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added benefit of regularizing the non-rigid deformation.</p>
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<fig>
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<caption><p>Visualization of the 3D rigid registration from the
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examples. Each panel represents a different iteration in the
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registraiton process.
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<styled-content id="figU003A1"></styled-content></p></caption>
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<graphic mimetype="image" mime-subtype="tiff" xlink:href="../images/rigid_bunny/rigid_bunny_3d_registration.tiff" xlink:title="" />
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</fig>
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<p>Examples of the PyCPD algorithm are included
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<xref alt="Figure 1" rid="figU003A1">Figure 1</xref>. Examples are
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available for 2D and 3D versions of all registration methods (rigid,
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affine, deformable). Examples of how to use the low-rank approximation
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as well as how to use a sub-set of the points for registraton are also
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included in the examples.</p>
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</sec>
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<sec id="acknowledgements">
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<title>Acknowledgements</title>
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<p>We acknowledge contributions from: - Alvin Wan for testing on
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Python 3.x. - Talley Lambert for pointing out that the moving point
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cloud should be immutable during registration, - Matthew DiFranco for
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fixing the check for target point clouds. - normanius for pointing out
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that the contribution of uniform distribution was not being added in
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the E-step. - Kai Zhang for finding a bug when transforming a point
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cloud using rigid registration parameters. - sandyhsia for finding a
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bug when updating the variance during deformable registration.</p>
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</sec>
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</body>
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<back>
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<ref-list>
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<ref-list>
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<ref id="ref-121791">
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<element-citation publication-type="article-journal">
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<person-group person-group-type="author">
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<name><surname>Besl</surname><given-names>P. J.</given-names></name>
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<name><surname>McKay</surname><given-names>Neil D.</given-names></name>
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</person-group>
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<article-title>A method for registration of 3-d shapes</article-title>
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<source>IEEE Transactions on Pattern Analysis and Machine Intelligence</source>
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<year iso-8601-date="1992">1992</year>
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<volume>14</volume>
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<issue>2</issue>
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<pub-id pub-id-type="doi">10.1109/34.121791</pub-id>
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</element-citation>
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</ref>
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<ref id="ref-CHEN1992145">
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<element-citation publication-type="article-journal">
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<person-group person-group-type="author">
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<name><surname>Chen</surname><given-names>Yang</given-names></name>
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<name><surname>Medioni</surname><given-names>Gérard</given-names></name>
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</person-group>
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<article-title>Object modelling by registration of multiple range images</article-title>
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<source>Image and Vision Computing</source>
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<year iso-8601-date="1992">1992</year>
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<volume>10</volume>
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<issue>3</issue>
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<issn>0262-8856</issn>
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<uri>https://www.sciencedirect.com/science/article/pii/026288569290066C</uri>
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<pub-id pub-id-type="doi">https://doi.org/10.1016/0262-8856(92)90066-C</pub-id>
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</element-citation>
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</ref>
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<ref id="ref-5432191">
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<element-citation publication-type="article-journal">
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<person-group person-group-type="author">
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<name><surname>Myronenko</surname><given-names>Andriy</given-names></name>
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<name><surname>Song</surname><given-names>Xubo</given-names></name>
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</person-group>
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<article-title>Point set registration: Coherent point drift</article-title>
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<source>IEEE Transactions on Pattern Analysis and Machine Intelligence</source>
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<year iso-8601-date="2010">2010</year>
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<volume>32</volume>
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<issue>12</issue>
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<pub-id pub-id-type="doi">10.1109/TPAMI.2010.46</pub-id>
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</element-citation>
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</ref>
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<ref id="ref-harris2020array">
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<element-citation publication-type="article-journal">
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<person-group person-group-type="author">
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<name><surname>Harris</surname><given-names>Charles R.</given-names></name>
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<name><surname>Millman</surname><given-names>K. Jarrod</given-names></name>
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<name><surname>Walt</surname><given-names>Stéfan J. van der</given-names></name>
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<name><surname>Gommers</surname><given-names>Ralf</given-names></name>
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<name><surname>Virtanen</surname><given-names>Pauli</given-names></name>
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<name><surname>Cournapeau</surname><given-names>David</given-names></name>
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<name><surname>Wieser</surname><given-names>Eric</given-names></name>
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<name><surname>Taylor</surname><given-names>Julian</given-names></name>
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<name><surname>Berg</surname><given-names>Sebastian</given-names></name>
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<name><surname>Smith</surname><given-names>Nathaniel J.</given-names></name>
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<name><surname>Kern</surname><given-names>Robert</given-names></name>
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<name><surname>Picus</surname><given-names>Matti</given-names></name>
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<name><surname>Hoyer</surname><given-names>Stephan</given-names></name>
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<name><surname>Kerkwijk</surname><given-names>Marten H. van</given-names></name>
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<name><surname>Brett</surname><given-names>Matthew</given-names></name>
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<name><surname>Haldane</surname><given-names>Allan</given-names></name>
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<name><surname>Río</surname><given-names>Jaime Fernández del</given-names></name>
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<name><surname>Wiebe</surname><given-names>Mark</given-names></name>
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<name><surname>Peterson</surname><given-names>Pearu</given-names></name>
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<name><surname>Gérard-Marchant</surname><given-names>Pierre</given-names></name>
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<name><surname>Sheppard</surname><given-names>Kevin</given-names></name>
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<name><surname>Reddy</surname><given-names>Tyler</given-names></name>
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<name><surname>Weckesser</surname><given-names>Warren</given-names></name>
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<name><surname>Abbasi</surname><given-names>Hameer</given-names></name>
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<name><surname>Gohlke</surname><given-names>Christoph</given-names></name>
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<name><surname>Oliphant</surname><given-names>Travis E.</given-names></name>
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</person-group>
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<article-title>Array programming with NumPy</article-title>
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<source>Nature</source>
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<publisher-name>Springer Science; Business Media LLC</publisher-name>
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<year iso-8601-date="2020-09">2020</year><month>09</month>
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<volume>585</volume>
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<issue>7825</issue>
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<uri>https://doi.org/10.1038/s41586-020-2649-2</uri>
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<pub-id pub-id-type="doi">10.1038/s41586-020-2649-2</pub-id>
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</element-citation>
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</ref>
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<ref id="ref-khallaghi_2017">
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<element-citation>
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<person-group person-group-type="author">
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<name><surname>Khallaghi</surname><given-names>Siavash</given-names></name>
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</person-group>
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<article-title>PyCPD: Tutorial on the coherent point drift algorithm</article-title>
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<year iso-8601-date="2017-05">2017</year><month>05</month>
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<uri>http://siavashk.github.io/2017/05/14/coherent-point-drift/</uri>
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</element-citation>
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</ref>
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</ref-list>
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</ref-list>
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</back>
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</article>

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