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Yalin Wang, Yanshuai Tu, Duyan Ta, Zhong-Lin Lu; Diffeomorphic Registration of Retinotopic Maps with Quasiconformal Mapping. Journal of Vision 2021;21(9):2467. doi: https://doi.org/10.1167/jov.21.9.2467.
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© ARVO (1962-2015); The Authors (2016-present)
Human visual cortex consists of multiple functional areas. Identifying these visual areas is an essential topic in vision science. Retinotopic mapping (RM) with functional magnetic resonance imaging (fMRI) provides a non-invasive method to define the visual areas. It is well known from neurophysiology studies that retinotopic mapping is diffeomorphic within each cortical area (i.e., differentiable and invertible). However, because of the low signal-noise ratio of fMRI, retinotopic maps from fMRI are often not diffeomorphic, making it difficult to delineate the visual areas' boundaries. We designed a registration framework with quasiconformal mapping to produce diffeomorphic registration of retinotopic maps: (1) generating a diffeomorphic template based on the retinotopic map of mean fMRI signal in Human Connectome Project (HCP), (2) formulating the registration problem as finding a quasiconformal map that maximizes the alignment of the visual coordinates between each RM and the template, and (3) iteratively improving the registration function by regularizing Beltrami coefficients (a representation of quasiconformal mapping). Because quasiconformal mapping is inherently diffeomorphic, the registration is diffeomorphic. We evaluated registration errors produced by several registration methods on a synthetic retinotopic dataset. The results showed that the proposed method produced the smallest registration errors compared to the state-of-the-art methods, including thin-plate spline registration, Bayesian analysis, diffeomorphic demos, and large deformation diffeomorphic metric mapping. We also applied our method to the retinotopic data from HCP. Compared to the visual coordinates' misalignment based on structural registration, the method reduced the misalignment by ~2.7%, meaning the method generated a better registration. In addition, the method provided better boundary delineation of visual areas. The proposed method improved low-quality RM and can also be used to improve RM templates.
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