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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Spatial normalization</span></span>
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<p>In <a href="Neuroimaging" title="Neuroimaging">neuroimaging</a>, <b>spatial normalization</b> is an <a href="Image_processing" class="mw-redirect" title="Image processing">image processing</a> step, more specifically an <a href="Image_registration" title="Image registration">image registration</a> method. Human brains differ in size and shape, and one goal of spatial normalization is to deform human brain scans so one location in one subject's brain scan corresponds to the same location in another subject's brain scan.
</p><p>It is often performed in research-based <a href="Functional_neuroimaging" title="Functional neuroimaging">functional neuroimaging</a> where one wants to find common brain activation across multiple human subjects.
The brain scan can be obtained from <a href="Magnetic_resonance_imaging" title="Magnetic resonance imaging">magnetic resonance imaging</a> (MRI) or <a href="Positron_emission_tomography" title="Positron emission tomography">positron emission tomography</a> (PET) scanners.
</p><p>There are two steps in the spatial normalization process:
</p>
<ul><li>Specification/estimation of warp-field</li>
<li>Application of warp-field with resampling</li></ul>
<p>The estimation of the warp-field can be performed in one modality, e.g., MRI, and be applied in another modality, e.g., PET, if MRI and PET scans exist for the same subject and they are <a href="Image_registration" title="Image registration">coregistered</a>.
</p><p>Spatial normalization typically employs a 3-dimensional nonrigid transformation model (a "warp-field") for warping a brain scan to a template.
The warp-field might be parametrized by <a href="Basis_function" title="Basis function">basis functions</a> such as <a href="Cosine" class="mw-redirect" title="Cosine">cosine</a> and <a href="Polynomial" title="Polynomial">polynomia</a>.
</p>
<div class="mw-heading mw-heading2"><h2 id="Diffeomorphisms_as_compositional_transformations_of_coordinates">Diffeomorphisms as compositional transformations of coordinates</h2></div>
<p>Alternatively, many advanced methods for spatial normalization are building on structure preserving transformations <a href="Homeomorphism" title="Homeomorphism">homeomorphisms</a> and <a href="Diffeomorphism" title="Diffeomorphism">diffeomorphisms</a> since they carry smooth submanifolds smoothly during transformation. Diffeomorphisms are generated in the modern field of <a href="Computational_anatomy" title="Computational anatomy">Computational Anatomy</a> based on diffeomorphic flows, also called <a href="Diffeomorphic_Mapping_in_Computational_Anatomy" class="mw-redirect" title="Diffeomorphic Mapping in Computational Anatomy">diffeomorphic mapping</a>. However, such transformations via diffeomorphisms are not additive, although they form a <a href="Computational_anatomy#Groups_and_group_actions" title="Computational anatomy">group with function composition</a> and acting non-linearly on the images via <a href="Group_actions_in_computational_anatomy" title="Group actions in computational anatomy">group action</a>. For this reason, flows which generalize the ideas of additive groups allow for generating large deformations that preserve topology, providing 1-1 and onto transformations. Computational methods for generating such transformation are often called <a href="Large_deformation_diffeomorphic_metric_mapping" title="Large deformation diffeomorphic metric mapping">LDDMM</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> which provide flows of diffeomorphisms as the main computational tool for connecting coordinate systems corresponding to <a href="Computational_anatomy#The_metric_on_geodesic_flows_of_landmarks,_surfaces,_and_volumes_within_the_orbit" title="Computational anatomy">the geodesic flows of Computational Anatomy</a>.
</p><p>There is a number of programs that implement both estimation and application of a warp-field. It is a part of the <a href="Statistical_parametric_mapping" title="Statistical parametric mapping">SPM</a> and <a href="AIR_(program)" title="AIR (program)">AIR</a> programs as well as MRI Studio and MRI Cloud.org.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>
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<div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div>
<ul><li><a href="Voxel-based_morphometry" title="Voxel-based morphometry">Voxel-based morphometry</a></li>
<li><a href="Computational_Anatomy" class="mw-redirect" title="Computational Anatomy">Computational Anatomy</a></li>
<li><a href="LDDMM" class="mw-redirect" title="LDDMM">LDDMM</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>
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<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">
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</style><cite id="CITEREFToga1998" class="citation book cs1">Toga, Arthur W. (November 17, 1998). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=8WdlWJepgWMC"><i>Brain Warping</i></a>. Academic Press. <a href="ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <bdi>9780080525549</bdi>.</cite></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://utah.pure.elsevier.com/en/publications/landmark-matching-on-brain-surfaces-via-large-deformation-diffeom-2">"Landmark matching on brain surfaces via large deformation diffeomorphisms on the sphere — University of Utah"</a>. <i>utah.pure.elsevier.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">March 21,</span> 2016</span>.</cite></span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite id="CITEREFBegMillerTrouvéYounes2005" class="citation journal cs1">Beg, M. Faisal; Miller, Michael I.; Trouvé, Alain; Younes, Laurent (2005). <a rel="nofollow" class="external text" href="https://www.researchgate.net/publication/220660081">"Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms"</a>. <i>International Journal of Computer Vision</i>. <b>61</b> (2): <span class="nowrap">139–</span>157. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1023%2FB%3AVISI.0000043755.93987.aa">10.1023/B:VISI.0000043755.93987.aa</a>. <a href="S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:17772076">17772076</a><span class="reference-accessdate">. Retrieved <span class="nowrap">March 21,</span> 2016</span>.</cite></span>
</li>
<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><cite id="CITEREFJoshiMiller2000" class="citation journal cs1">Joshi, S. C.; Miller, M. I. (January 1, 2000). "Landmark matching via large deformation diffeomorphisms". <i>IEEE Transactions on Image Processing</i>. <b>9</b> (8): <span class="nowrap">1357–</span>1370. <a href="Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000ITIP....9.1357J">2000ITIP....9.1357J</a>. <a href="Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2F83.855431">10.1109/83.855431</a>. <a href="ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1057-7149">1057-7149</a>. <a href="PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/18262973">18262973</a>.</cite></span>
</li>
<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://mricloud.org/">"MRI Cloud"</a>. <i>mricloud.org</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20230602003328/https://mricloud.org/">Archived</a> from the original on June 2, 2023<span class="reference-accessdate">. Retrieved <span class="nowrap">July 6,</span> 2023</span>.</cite></span>
</li>
<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20160401010232/https://www.mristudio.org/wiki/">"MRI Studio Wiki Documentation"</a>. <i>www.mristudio.org</i>. Archived from <a rel="nofollow" class="external text" href="https://www.mristudio.org/wiki/">the original</a> on April 1, 2016<span class="reference-accessdate">. Retrieved <span class="nowrap">July 6,</span> 2023</span>.</cite></span>
</li>
</ol></div></div>
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