  The mapping between visual inputs on the retina and neuronal activations in
the visual cortex, i.e., retinotopic map, is an essential topic in vision
science and neuroscience. Human retinotopic maps can be revealed by analyzing
the functional magnetic resonance imaging (fMRI) signal responses to designed
visual stimuli in vivo. Neurophysiology studies summarized that visual areas
are topological (i.e., nearby neurons have receptive fields at nearby locations
in the image). However, conventional fMRI-based analyses frequently generate
non-topological results because they process fMRI signals on a voxel-wise
basis, without considering the neighbor relations on the surface. Here we
propose a topological receptive field (tRF) model which imposes the topological
condition when decoding retinotopic fMRI signals. More specifically, we
parametrized the cortical surface to a unit disk, characterized the topological
condition by tRF, and employed an efficient scheme to solve the tRF model. We
tested our framework on both synthetic and human fMRI data. Experimental
results showed that the tRF model could remove the topological violations,
improve model explaining power, and generate biologically plausible retinotopic
maps. The proposed framework is general and can be applied to other sensory
maps.
