Gaussian derivatives

Abstract

We will encounter the Gaussian derivative function at many places throughout this book. The Gaussian derivative function has many interesting properties. We will discuss them in one dimension first. We study its shape and algebraic structure, its Fourier transform, and its close relation to other functions like the Hermite functions, the Gabor functions and the generalized functions. In two and more dimensions additional properties are involved like orientation (directional derivatives) and anisotropy.