This dissertation constructs a new computational processing framework to robustly and precisely quantify retinotopic maps based on their angle distortion properties. More generally, this framework solves the problem of how to robustly and precisely quantify (angle) distortions of noisy or incomplete (boundary enclosed) 2-dimensional surface to surface mappings. This framework builds upon the Beltrami Coefficient (BC) description of quasiconformal mappings that directly quantifies local mapping (circles to ellipses) distortions between diffeomorphisms of boundary enclosed plane domains homeomorphic to the unit disk. A new map called the Beltrami Coefficient Map (BCM) was constructed to describe distortions in retinotopic maps. The BCM can be used to fully reconstruct the original target surface (retinal visual field) of retinotopic maps. This dissertation also compared retinotopic maps in the visual processing cascade, which is a series of connected retinotopic maps responsible for visual data processing of physical images captured by the eyes. By comparing the BCM results from a large Human Connectome project (HCP) retinotopic dataset (N=181), a new computational quasiconformal mapping description of the transformed retinal image as it passes through the cascade is proposed, which is not present in any current literature. The description applied on HCP data provided direct visible and quantifiable geometric properties of the cascade in a way that has not been observed before. Because retinotopic maps are generated from in vivo noisy functional magnetic resonance imaging (fMRI), quantifying them comes with a certain degree of uncertainty. To quantify the uncertainties in the quantification results, it is necessary to generate statistical models of retinotopic maps from their BCMs and raw fMRI signals. Considering that estimating retinotopic maps from real noisy fMRI time series data using the population receptive field (pRF) model is a time consuming process, a convolutional neural network (CNN) was constructed and trained to predict pRF model parameters from real noisy fMRI data