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Singularity-Exponent-Domain Image Feature Transform

Combining the generalized fractal theory and the time-frequency distribution, the image feature decomposition in the singularity exponent domain is studied in this paper. With the theoretical derivation and quantitative analysis, the singularity-exponent-domain image feature transform (SIFT) method is proposed to analyze and process images from new feature dimensions. If one derives from the generalized fractal characteristics of the image, the two-dimensional frequency variables of the 2D time-frequency transform of the image can be used to estimate the two-dimensional singularity power spectrum (SPS) in the space dimension. As a consequence, it leads to the SPS distribution of the original image in the spatial domain, i.e., SIFT images. Based on the SIFT, the feature transform images with different singularity exponent and feature curves of singularity power spectrum with respect to different physical regions can thus be obtained. The SIFT is rigorously derived from the 2D-SPS and the Pseudo Wigner-Ville distribution (PWVD). In addition, the feature images based on the SIFT is proved to be the SNR independence in the GWN background. In order to validate the effectiveness of feature extraction, the proposed methodology is tested on the breast ultrasound images, the visual images, and the synthetic aperture radar (SAR) images. Furthermore, the SAR target detection method based on the SIFT images is proposed, and the experiment results indicate that the proposed algorithm is superior in performance to the traditional CFAR or 2D-SPS method. In fact, this new SIFT is promising to provide a technical approach for image feature extraction, target detection, and recognition.