Bispectrum分析用於訊號與影像之特徵量化

Abstract

本篇論文主要研究Chandran 與 Elgar 提出的Bispectral Invariant演算法對於特徵萃取的效能，並將它應用於一維序列與二維影像的特徵萃取。這個演算法所取得的特徵值是來自於一維序列的Bispectrum，而且對於雜訊有良好的免疫能力。而對二維影像而言，這個演算法的利用Radon transform與傅立葉切片定理(Fourier slice theorem)的理論，把影像的二維傅立葉轉換簡化為許多一維投影序列，再運用一維序列的方式處理。得到的特徵值具有對於影像的平移、旋轉、縮放皆有良好的抑制能力，即不受空間幾何變化之影響。 本論文將這個演算法應用於一維訊號與二維影像圖樣並與傳統的方法Moment Invariants比較，實驗結果顯示這個演算法不但能夠得到較好的群落特性，而且具有更佳的雜訊免疫能力。

This thesis aims to investigate the feasibility of the Bispectral Invariant algorithm, presented by Chandran and Elgar, for feature extraction and quantification. This method is to be applied to the one-dimensional(1-D) signals as well as the two-dimensional(2-D) images. The features extracted by the algorithm, providing good noise immunity, are the quantitative results of the bispectrum of a 1-D sequence. For a 2-D image, it can be reduced to a set of projected 1-D sequences via the Radon transform, or alternatively, the Fourier transform of each 1-D projection can be obtained from a radial slice of the 2-D Fourier transform of the image according to the Fourier slice theorem. The features are shown to be translation-invariant, scale-invariant, and rotation-invariant. In other words, the quantitative result are not affected by the spatial geometrical variations. In this thesis, we also compare performance of the algorithm and that of the well-known method “moment invariants”. The results show that the bispectral invariants not only achieve better clustering characteristics but also provide superior noise immunity.