Population Modeling in Neuroscience Using Computer Vision and Machine Learning to learn from Brain Images Overview 1. Part 1: Theory 1. 2. Learning 2. Part 2: Applications ernst.schwartz@meduniwien.ac.at www.cir.meduniwien.ac.at? Source Target Source Target S T S T
S T S T arg min E( )=M(S, T )+R( ) arg min E( )=M(S, T )+R() sx 0 0 tx 0 sy 0 ty 0 0 sz tz 0 0 0 1 Rigid: rotation + scaling sx.. tx. sy. ty.. sz tz... 1 Affine: rotation + scaling + shearing Non-rigid non-diffeomorphic!
topological space that resembles Euclidean space near each point S T arg min E( )=M(S, T )+R( R ) topological space that resembles Euclidean space near each point Type A Mathematical Type A Mathematical Type A Mathematical of Diffeomorphisms of Diffeomorphisms
Type A Mathematical Type A Mathematical of Diffeomorphisms stay in group during optimization by picking an appropriate regularizer R of Diffeomorphisms Yields a distance between images Type A Mathematical Type B but only defined with respect to a template of Diffeomorphisms Yields a distance between images Type B Data-driven knn
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ISOMAP [Tennenbaum 2000] Embedding ISOMAP [Tennenbaum 2000] Embedding Embedding representation in Euclidean space representation in Euclidean space allows for easier application of standard methods
Embedding Embedding representation in Euclidean space density estimation representation in Euclidean space regression Distance is only one possible property to maintain during mapping Many others have been used; local neighborhoods, curvature, tangent spaces,... Two schools: Graph people and Kernel people Questions? Applications a small, subjective selection of recent papers [Ying et al. 2014]
[Ying et al. 2014] [Ying et al. 2014] [Ying et al. 2014] [Gerber et al. 2009] [Gerber et al. 2009] [Gerber et al. 2010]
[Hamm et al. 2010] [Hamm et al. 2010] [Hamm et al. 2010] [olz et al. 2010] [olz et al. 2010] [olz et al. 2012]
[olz et al. 2012] [Yang et al. 2011] [Yang et al. 2011] [Yang et al. 2011] [Aljabar et al. 2011] [Aljabar et al. 2011]
[Aljabar et al. 2011] [Aljabar et al. 2011] Small excursion: Alignment [Bhatia et al. 2014] [Langs et al. 2010] Take-home messages Infinity +1 ways of comparing images First question to ask: is it useful? For data-driven methods, you need data (and lots of it) There is no free lunch: analytical methods are complex and computationally demanding [Bhatia et al. 2014]
References ernst.schwartz@meduniwien.ac.at More questions? www.cir.meduniwien.ac.at J. B. Tenenbaum, V. de Silva, J. C. Langford, A Global Geometric Framework for Nonlinear Dimensionality Reduction, Science 290, (2000), 2319 2323 A. Sotiras, C. Davatzikos, N. Paragios, Deformable Medical : A Survey, IEEE Trans. on Med. Imag. 32 (7), (2013), 1153-1190 S. Gerber, T. Tasdizen, S. Joshi, R. hitaker, On the Structure of the Space of Brain Images, Proc. of MICCAI 2009 (1), 305-312 J. Hamm, D.H. Ye, R. Verma, C. Davatzikos, GRAM: A framework for geodesic registration on anatomical manifolds, Medial Image Analysis 14, (2010), 633-642 R. olz, P. Aljabar, J.B. Hajnal, A. Hammers, D. Rueckert & ADNI, LEAP: Learning embeddings for atlas propagation, NeuroImage 49, (2010), 1316-1325 R. olz, P. Aljabar, J.V. Hajnal, J. Lötjönen, D. Rueckert & ADNI, Nonlinear dimensionality reduction combining MR imaging with non-imaging information, Medical Image Analysis 16, (2012), 819-830 References X. Yang, A. Goh, A. Qiu, Locally Linear Diffeomorphic Metric Embedding (LLDME) for surface-based anatomical shape modeling, NeuroImage 56, (2011), 149-161 S. Ying, G. QU, Q. ang, Hierarchical unbiased graph shrinkage (HUGS): A novel groupwise registration for large data set, NeuroImage 84, (2014), 626-638 P. Aljabar, R. olz, L. Srinivasan, S.J. Counsell, M.A. Rutherford, A.D. Edwards, J.V. Hajnal and D. Rueckert, A combined manifold learning analysis of shape and appearance to characterize neonatal brain development, IEEE Trans. on Med. Imag. 30 (12), (2011), 2072-2086 K.K. Bhatia, A. Rao, A.N. Price, R. olz, J. V. Hajnal, D. Rueckert & ADNI, Hierarchical Learning for Regional Image Analysis, IEEE Trans. on Med. Imag. 33 (2), (2014), 444-461 G. Langs, Y. Tie, L. Rigolo, A. Golby, and P. Golland, Functional Geometry Alignment and Localization of Brain Areas, Advances in Neural Information Processing Systems NIPS 23, (2010), pp. 1225 1233