2000 character limit reached
Sulcal Pattern Matching with the Wasserstein Distance (2307.00385v1)
Published 1 Jul 2023 in q-bio.NC and eess.IV
Abstract: We present the unified computational framework for modeling the sulcal patterns of human brain obtained from the magnetic resonance images. The Wasserstein distance is used to align the sulcal patterns nonlinearly. These patterns are topologically different across subjects making the pattern matching a challenge. We work out the mathematical details and develop the gradient descent algorithms for estimating the deformation field. We further quantify the image registration performance. This method is applied in identifying the differences between male and female sulcal patterns.
- “A primal sketch of the cortex mean curvature: A morphogenesis based approach to study the variability of the folding patterns,” IEEE Trans. Med. Imag., vol. 22, no. 6, pp. 754–765, 2003.
- K. Im and P.E. Grant, “Sulcal pits and patterns in developing human brains,” NeuroImage, vol. 185, pp. 881–890, 2019.
- “Fast polynomial approximation of heat kernel convolution on manifolds and its application to brain sulcal and gyral graph pattern analysis,” IEEE Transactions on Medical Imaging, vol. 39, pp. 2201–2212, 2020.
- “Shape analysis with hyperbolic wasserstein distance,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016, pp. 5051–5061.
- “Sliced wasserstein distance for learning gaussian mixture models,” in 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2018, pp. 3427–3436.
- “Unpaired deep learning for accelerated mri using optimal transport driven cyclegan,” IEEE Transactions on Computational Imaging, vol. 6, pp. 1285–1296, 2020.
- “A gradient descent solution to the monge-kantorovich problem,” Applied Mathematical Sciences, vol. 3, pp. 1071–1080, 01 2009.
- “The human connectome project: a data acquisition perspective,” NeuroImage, vol. 62, pp. 2222–2231, 2012.
- “The minimal preprocessing pipelines for the Human Connectome Project,” NeuroImage, vol. 80, pp. 105–124, 2013.
- “Resting-state fMRI in the Human Connectome Project,” NeuroImage, vol. 80, pp. 144–168, 2013.
- “Improved optimization for the robust and accurate linear registration and motion correction of brain images,” NeuroImage, vol. 17, no. 2, pp. 825–841, 2002.
- “Cortical folding patterns and predicting cytoarchitecture,” Cerebral Cortex, vol. 18, no. 8, pp. 1973–1980, 2007.
- “TRACE: A topological graph representation for automatic sulcal curve extraction,” IEEE Trans. Med. Imag., vol. 37, no. 7, pp. 1653–1663, 2018.
- “Weighted fourier series representation and its application to quantifying the amount of gray matter,” IEEE Transactions on Medical Imaging, vol. 26, no. 4, pp. 566–581, 2007.
- G. Peyré and M. Cuturi, “Computational optimal transport,” Foundations and Trends in Machine Learning, vol. 11, no. 5-6, pp. 355–607, 2019.
- “A class of wasserstein metrics for probability distributions.,” Michigan Mathematical Journal, vol. 31, no. 2, pp. 231–240, 1984.
- M. Knott and C. S. Smith, “On the optimal mapping of distributions,” Journal of Optimization Theory and Applications, vol. 43, no. 1, pp. 39–49, 1984.
- “Optimal mass transport: Signal processing and machine-learning applications,” IEEE Signal Processing Magazine, vol. 34, no. 4, pp. 43–59, 2017.
- J. Munkres, “Algorithms for the assignment and transportation problems,” Journal of the Society for Industrial and Applied Mathematics, vol. 5, no. 1, pp. 32–38, 1957.
- J. Benamou and Y. Brenier, “A computational fluid mechanics solution to the monge-kantorovich mass transfer problem,” Numerische Mathematik, vol. 84, no. 3, pp. 375–393, 2000.
- “Rapid acceleration of the permutation test via transpositions,” International Workshop on Connectomics in Neuroimaging, vol. 11848, pp. 42–53, 2019.
- “Why sex matters: brain size independent differences in gray matter distributions between men and women,” Journal of Neuroscience, vol. 29, pp. 14265–14270, 2009.
- “Gender difference analysis of cortical thickness in healthy young adults with surface-based methods,” NeuroImage, vol. 31, pp. 31–38, 2006.