Fast Computation of Scale Normalised Gaussian Receptive Fields

The characteristic (or intrinsic) scale of a local image pattern is the scale parameter at which the Laplacian provides a local maximum. Nearly every position in an image will exhibit a small number of such characteristic scales. Computing a vector of Gaussian derivatives (a Gaussian jet) at a characteristic scale provides a scale invariant feature vector for tracking, matching, indexing and recognition. However, the computational cost of directly searching the scale axis for the characteristic scale at each image position can be prohibitively expensive. We describe a fast method for computing a vector of Gaussian derivatives that are normalised to the characteristic scale at each pixel. This method is based on a scale equivariant half-octave binomial pyramid. The characteristic scale for each pixel is determined by an interpolated maximum in the Difference of Gaussian as a function of scale. We show that interpolation between pixels across scales can be used to provide an accurate estimate of the intrinsic scale at each image point. We present an experimental evaluation that compares the scale invariance of this method to direct computation using FIR filters, and to an implementation using recursive filters. With this method we obtain a scale normalised Gaussian Jet at video rate for a 1/4 size PAL image on a standard 1.5 Ghz Pentium workstation.