Scale-space filtering using a piecewise polynomial representation

Scale-space image processing is a basic technique used for object recognition and low-level feature extraction in computer vision. Many Gaussian filtering techniques have been proposed. Recently, the spectral decomposition method was proposed, which is an infinite version of principal components analysis. Using this method, Gaussian blurred images can be represented as polynomials with a scale parameter and a Gaussian blurred image with an arbitrary scale can be obtained from simple linear combinations of the convolved eigenimages. However, the scale is limited to a small range in this method. In this study, we propose an improvement to the spectral decomposition of a Gaussian kernel by widening the scale using a piecewise polynomial representation. We present an analysis of the continuous spectral decompositions of a Gaussian kernel and their eigensolutions. Experimental results show that the proposed method can generate accurate Gaussian blurred images with an arbitrary scale and a wide scale range.