Topology-Preserving Smoothing of Retinotopic Maps
Short Title: Topological Smoothing of Retinotopic Maps
Yanshuai Tu, Duyan Ta, Zhong-Lin Lu, Yalin Wang
Retinotopic mapping, i.e., the mapping between visual inputs on the retina and neuronal activations in cortical visual areas, is one of the central topics in visual neuroscience. For human observers, the mapping is obtained by analyzing functional magnetic resonance imaging (fMRI) signals of cortical responses to slowly moving visual stimuli on the retina. Although it is well known from neurophysiology that the mapping is topological (i.e., the topology of neighborhood connectivity is preserved) within each visual area, retinotopic maps derived from the state-of-the-art methods are often not topological because of the low signal-to-noise ratio and spatial resolution of fMRI. The violation of topological condition is most severe in cortical regions corresponding to the neighborhood of the fovea (e.g., < 1 degree eccentricity in the Human Connectome Project (HCP) dataset), significantly impeding accurate analysis of retinotopic maps. This study aims to directly model the topological condition and generate topology-preserving and smooth retinotopic maps. Specifically, we adopted the Beltrami coefficient, a metric of quasiconformal mapping, to define the topological condition, developed a mathematical model to quantify topological smoothing as a constrained optimization problem, and elaborated an efficient numerical method to solve the problem. The method was then applied to V1, V2, and V3 simultaneously in the HCP dataset. Experiments with both simulated and real retinotopy data demonstrated that the proposed method could generate topological and smooth retinotopic maps.
Figures (click on each for a larger version):
- Yanshuai Tu, Duyan Ta, Zhong-Lin Lu, Yalin Wang, Diffeomorphic smoothing for retinotopic mapping , In IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI), Apr. 2020
- Yanshuai Tu, Duyan Ta, Zhong-Lin Lu, Yalin Wang, Topology-Preserving Smoothing of Retinotopic Maps , PLOS Computational Biology, 2021, In Press.