Applications to computer vision using spectral theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 25730116
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Perceptual information processing
• Research Institution: Kumamoto University
• Principal Investigator: Gou Koutaki 熊本大学, 大学院先導機構, 助教 (20582935)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: スケールスペース / 主成分分析 / SIFT / 画像認識

Outline of Final Research Achievements

We propose the application of principal components analysis (PCA) to scale-spaces. PCA is a standard method used in computer vision. The translation of an input image into scale-space is a continuous operation, which requires the extension of conventional finite matrix-based PCA to an infinite number of dimensions. In this study, we use spectral decomposition to resolve this infinite eigenproblem by integration and we propose an approximate solution based on polynomial equations. To clarify its eigensolutions, we apply spectral decomposition to the Gaussian scale-space and scale-normalized Laplacian of Gaussian (LoG) space. As an application of this proposed method, we demonstrate that the accuracy of these images can be very high when calculating an arbitrary scale using a simple linear combination. We also propose a new Scale Invariant Feature Transform (SIFT) detector as a more practical example.

Free Research Field

画像処理