On computing shape: a study of the neural processes concerning naturalistic boundary conformation within the ventral visual pathway
Oleskiw, Tim D
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The perception of shape is a remarkable computation, solved rapidly by the brain to extract boundary features within natural scenes while being robust against many visual obstacles. Interestingly, while observers typically have an intuitive understanding of what shape is, it is in fact exceedingly difficult to mathematically describe shape in a natural context. In this dissertation I use computational modeling, primate electrophysiology, and mathematical analysis to study the neural processes underlying computations of shape within the ventral visual pathway. I first present results from an investigation of the spectral receptive field (SRF) model, a Fourier-based method proposed to explain selectivity for boundary conformation of neurons in cortical area V4. Noting that spectral power coefficients are phase-invariant, I analyze the statistical properties of responses evoked by synthetic shape stimuli to demonstrate SRFs as incapable of capturing shape tuning seen in single-unit V4 responses. Computational studies have shown that naturalistic images may be reconstructed from features common to physical scenes, namely contrast boundaries and blur, i.e. the spatial gradient of contrast across each boundary. I next present results from an electrophysiology study of primate V4 using stimuli in which object shape and boundary blur are systematically varied, reporting a population of V4 neurons that are tuned for intermediate blur magnitudes. Importantly, I propose simple joint model in which blur multiplicatively scales shape-selective responses, capturing a range of observed behaviors and revealing distinct neural dynamics. As we progress in understanding the computations of shape in neural networks, it is widely believed that the divisive inhibition of a neuron's firing rate is a fundamental operation, critical to computations of gain control and response invariance within the ventral pathway. However, the precise mechanisms underlying divisive inhibition are not completely understood, making it difficult to predict when this phenomenon will occur in spiking neural networks. Research has shown that balanced excitatory and inhibitory activity can divisively scale a neuron's spiking output, both in vitro and in conductance-based leaky-integrate-and-fire (LIF) model simulations. Interestingly, a review of these simulations suggests that gain modulation depends on another factor: the autocorrelation structure (timescale) of driving input. With numeric simulation and stochastic analysis I then show divisive inhibition to arise from an interaction between the neuron's input and membrane dynamics, developing an analytic approximation for the firing rate of a nonlinear stochastic LIF model wherein input timescale is explicitly parameterized. Furthermore, I demonstrate that by increasing synaptic timescales across a biophysically-plausible range of parameters, a neuron's response is divided by a novel circuit-level mechanism. Background material for this interdisciplinary work is provided to clarify its relevance to neuroscience and mathematics communities.
- Applied mathematics