Sch. of Electr. and Electron. Syst. Eng., Queensland Univ. of Technol., Brisbane, Qld.
IEEE Trans Image Process. 1997;6(5):703-12. doi: 10.1109/83.568927.
A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants.
描述了一种用于从图像中提取特征以进行目标识别的新算法。该算法使用高阶谱来提供所需的不变性特性，提供抗噪声能力，并将非线性纳入特征提取过程中，从而允许使用简单的分类器。图像可以通过 Radon 变换简化为一组 1D 函数，或者根据傅里叶切片定理，从图像的二维傅里叶变换的径向切片中获取每个 1D 投影的傅里叶变换。对于每个 1D 函数计算三个傅里叶系数的乘积，称为确定性双谱，并在双频率空间中的径向线上进行积分。积分双谱的相位被证明具有平移和尺度不变性。通过在恒定半径处对这些不变量进行重新分组并进行第二阶段的不变量提取，可以实现旋转不变性。因此，旋转不变性在第二步转换为平移不变性。使用合成和实际图像的结果表明，特征空间中形成了孤立、紧凑的簇。这些簇是线性可分的，这表明从输入空间到分类空间的映射中所需的非线性已很好地纳入到特征提取阶段。使用高阶谱可获得良好的抗噪声能力，这已通过合成和真实图像得到验证。使用基于高阶谱的算法对图像进行分类与使用矩不变量方法进行分类相比具有优势。
