{"title":"Single Encoding Diffusion MRI: A Probe to Brain Anisotropy","authors":"Maëliss Jallais, D. Wassermann","doi":"10.1007/978-3-030-56215-1_8","DOIUrl":"https://doi.org/10.1007/978-3-030-56215-1_8","url":null,"abstract":"","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50967686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Magnus Herberthson, Evren Özarslan, Carl-Fredrik Westin
{"title":"Variance Measures for Symmetric Positive (Semi-) Definite Tensors in Two Dimensions.","authors":"Magnus Herberthson, Evren Özarslan, Carl-Fredrik Westin","doi":"10.1007/978-3-030-56215-1_1","DOIUrl":"https://doi.org/10.1007/978-3-030-56215-1_1","url":null,"abstract":"<p><p>Calculating the variance of a family of tensors, each represented by a symmetric positive semi-definite second order tensor/matrix, involves the formation of a fourth order tensor <i>R</i><sub><i>abcd</i></sub>. To form this tensor, the tensor product of each second order tensor with itself is formed, and these products are then summed, giving the tensor <i>R</i><sub><i>abcd</i></sub> the same symmetry properties as the elasticity tensor in continuum mechanics. This tensor has been studied with respect to many properties: representations, invariants, decomposition, the equivalence problem et cetera. In this paper we focus on the two-dimensional case where we give a set of invariants which ensures equivalence of two such fourth order tensors <i>R</i><sub><i>abcd</i></sub> and <math><mrow><msub><mover><mi>R</mi><mo>~</mo></mover><mrow><mi>a</mi><mi>b</mi><mi>c</mi><mi>d</mi></mrow></msub></mrow></math>. In terms of components, such an equivalence means that components <i>R</i><sub><i>ijkl</i></sub> of the first tensor will transform into the components <math><mrow><msub><mover><mi>R</mi><mo>~</mo></mover><mrow><mi>i</mi><mi>j</mi><mi>k</mi><mi>l</mi></mrow></msub></mrow></math> of the second tensor for some change of the coordinate system.</p>","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"2021 ","pages":"3-22"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10201932/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9887503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Topologically Robust B-spline Reconstruction of Fibers from 3D Images","authors":"Dennis Mosbach, K. Schladitz, B. Hamann, H. Hagen","doi":"10.1007/978-3-030-83500-2_14","DOIUrl":"https://doi.org/10.1007/978-3-030-83500-2_14","url":null,"abstract":"","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"34 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50980907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Florack, Rick Sengers, S. Meesters, L. Smolders, A. Fuster
{"title":"Riemann-DTI Geodesic Tractography Revisited","authors":"L. Florack, Rick Sengers, S. Meesters, L. Smolders, A. Fuster","doi":"10.1007/978-3-030-56215-1_11","DOIUrl":"https://doi.org/10.1007/978-3-030-56215-1_11","url":null,"abstract":"","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"14 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50968017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Slator, A. Ho, S. Bakalis, L. Jackson, L. Chappell, D. Alexander, J. Hajnal, M. Rutherford, J. Hutter
{"title":"Anisotropy in the Human Placenta in Pregnancies Complicated by Fetal Growth Restriction","authors":"P. Slator, A. Ho, S. Bakalis, L. Jackson, L. Chappell, D. Alexander, J. Hajnal, M. Rutherford, J. Hutter","doi":"10.1007/978-3-030-56215-1_13","DOIUrl":"https://doi.org/10.1007/978-3-030-56215-1_13","url":null,"abstract":"","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50968115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Implicit Visualization of 2D Vector Field Topology for Periodic Orbit Detection","authors":"Alexander Straub, G. Karch, F. Sadlo, T. Ertl","doi":"10.1007/978-3-030-83500-2_9","DOIUrl":"https://doi.org/10.1007/978-3-030-83500-2_9","url":null,"abstract":"","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"14 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50981031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Challenges for Tractogram Filtering","authors":"Daniel Jörgens, M. Descoteaux, R. Moreno","doi":"10.1007/978-3-030-56215-1_7","DOIUrl":"https://doi.org/10.1007/978-3-030-56215-1_7","url":null,"abstract":"","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"152 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50967675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introduction to Vector Field Topology","authors":"Tobias Günther, Irene Baeza Rojo","doi":"10.1007/978-3-030-83500-2_15","DOIUrl":"https://doi.org/10.1007/978-3-030-83500-2_15","url":null,"abstract":"","PeriodicalId":74126,"journal":{"name":"Mathematics and visualization","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50980912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}