A novel method for generating scale space kernels based on wavelet theory

Abstract

The linear scale-space kernel is a Gaussian or Poisson function. These functions were chosen based on several axioms. This representation creates a good base for visualization when there is no information (in advanced) about which scales are more important. These kernels have some deficiencies, as an example, its support region goes from minus to plus infinite. In order to solve these issues several others scale-space kernels have been proposed. In this paper we present a novel method to create scale-space kernels from one-dimensional wavelet functions. In order to do so, we show the scale-space and wavelet fundamental equations and then the relationship between them. We also describe three different methods to generate two-dimensional functions from one-dimensional functions. Then we show results got from scale-space blob detector using the original and two new scale-space bases (Haar and Bi-ortogonal 4.4), and a comparison between the edges detected using the Gaussian kernel and Haar kernel for a noisy image. Finally we show a comparison between the scale space Haar edge detector and the Canny edge detector for an image with one known square in it, for that case we show the Mean Square Error (MSE) of the edges detected with both algorithms.