Orientation tuning curves: empirical description and estimation of parameters

This paper compares the ability of some simple model functions to describe orientation tuning curves obtained in extracellular single-unit recordings from area 17 of the cat visual cortex. It also investigates the relationships between three methods currently used to estimate preferred orientation from tuning curve data: (a) least-squares curve fitting, (b) the vector sum method and (c) the Fourier transform method (Worgotter and Eysel 1987). The results show that the best fitting model function for single-unit orientation tuning curves is a von Mises circular function with a variable degree of skewness. However, other functions, such as a wrapped Gaussian, fit the data nearly as well. A cosine function provides a poor description of tuning curves in almost all instances. It is demonstrated that the vector sum and Fourier methods of determining preferred orientation are equivalent and identical to calculating a least-square fit of a cosine function to the data. Least-squares fitting of a better model function, such as a von Mises function or a wrapped Gaussian, is therefore likely to be a better method for estimating preferred orientation. Monte-Carlo simulations confirmed this, although for broad orientation tuning curves sampled at 45 degrees intervals, as is typical in optical recording experiments, all the methods gave similarly accurate estimates of preferred orientation. The sampling interval, the estimated error in the response measurements and the probable shape of the underlying response function all need to be taken into account in deciding on the best method of estimating preferred orientation from physiological measurements of orientation tuning data.