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XYSeparable ScaleSpace Filtering by Polynomial Representations and Its Applications
Gou KOUTAKI Keiichi UCHIMURA
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E100D
No.4
pp.645654 Publication Date: 2017/04/01
Online ISSN: 17451361 Type of Manuscript: INVITED PAPER (Special Section on Awardwinning Papers) Category: Keyword: scalespace, spectral decomposition, SIFT,
Full Text: FreePDF(3MB)
Summary:
In this paper, we propose the application of principal component analysis (PCA) to scalespaces. PCA is a standard method used in computer vision. Because the translation of an input image into scalespace is a continuous operation, it requires the extension of conventional finite matrixbased PCA to an infinite number of dimensions. Here, we use spectral theory to resolve this infinite eigenvalue problem 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 scalespace and scalenormalized Laplacian of Gaussian (sLoG) space. As an application of this proposed method, we introduce a method for generating Gaussian blur images and sLoG images, demonstrating that the accuracy of such an image can be made very high by using an arbitrary scale calculated through simple linear combination. Furthermore, to make the scalespace filtering efficient, we approximate the basis filter set using Gaussian lobes approximation and we can obtain XYSeparable filters. As a more practical example, we propose a new Scale Invariant Feature Transform (SIFT) detector.

