Scale-space compression and its application using spectral theory

In this paper, we propose the application of principal component analysis (PCA) to scale-spaces. PCA is a standard method used in computer vision tasks such as recognition of eigenfaces. Because the translation of an input image into scale-space is a continuous operation, it requires the extension of conventional finite matrix based PCA to an infinite number of dimensions. Here, we use spectral theory to resolve this infinite eigenproblem through the use of integration, and we propose an approximate solution based on polynomial equations. In order to clarify its eigensolutions, we apply spectral decomposition to gaussian scale-space. As an application of this proposed method we introduce a method for generating gaussian blur images, demonstrating that the accuracy of such an image can be made very high by using an arbitrary scale calculated through simple linear combination.