A mixture model for population codes of Gabor filters

Population coding is a coding scheme which is ubiquitous in neural systems, and is also of more general use in coding stimuli, for example in vision problems. A population of responses to a stimulus can be used to represent not only the value of some variable in the environment, but a full probability distribution for that variable. The information is held in a distributed and encoded form, which may in some situations be more robust to noise and failures than conventional representations. Gabor filters are a popular choice for detecting edges in the visual field for several reasons. They are easily tuned for a variety of edge widths and orientations, and are considered a close model of the edge filters in the human visual system. In this paper, we consider population codes of Gabor filters with different orientations. A probabilistic model of Gabor filter responses is presented. Based on the analytically derived orientation tuning function and a parametric mixture model of the filter responses in the presence of local edge structure with single or multiple orientations a probability density function (pdf) of the local orientation in any point (x, y) can be extracted through a parameter estimation procedure. The resulting pdf of the local contour orientation captures not only angular information at edges, corners or T-junctions but also describes the certainty of the measurement which can be characterized in terms of the entropy of the individual mixture components.