Fast Computation of Characteristic Scale Using a Half-Octave Pyramid

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 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. In this paper, we describe a fast method for computing the characteristic scale by interpolating values from a scale-invariant Laplacian pyramid. We present an experimental evaluation of the scale invariance of the impulse response for pyramids computed with three forms of Gaussian filters. We show that interpolation between pixels across scales can be used to provide an accurate estimate of the characteristic scale at each image point.