Conditions of Similarity between Hermite and Gabor Filters as Models of the Human Visual System

Among the suggested mathematical models for receptive field profiles, the Gabor model is well known and widely used. Another less used model that agrees with the Gaussian derivative model for human vision is the Hermite model which is based on analysis filters of the Hermite transform. It has the advantage of an orthogonal basis and a better fit to cortical data. In this paper we present an analytical comparison based on minimization of the energy error between the two models, and so the optimal parameters letting the two models be close to each other are found. The results show that both models are equivalent and extract about the same frequency information. Actually, we can implement a Hermite filter with an equivalent Gabor filter and vice versa, provided that conditions leading to error minimization are held.