Multi-scale Kernel PCA and Its Application to Curvelet-Based Feature Extraction for Mammographic Mass Characterization

Accurate characterization of mammographic masses plays a key role in effective mammogram classification and retrieval. Because of their high performance in multi-resolution texture analysis, several curvelet-based features have been proposed to describe mammograms, but without satisfactory results in distinguishing between malignant and benign masses. This paper tackles the problem of extracting a reduced set of discriminative curvelet texture features for mammographic mass characterization. The contribution of this paper is twofold. First, to overcome the weakness of PCA to cope with the nonlinearity of curvelet coefficient distributions, we investigate the use of kernel principal components analysis (KPCA) with a Gaussian kernel over curvelet coefficients for mammogram characterization. Second, a new multi-scale Gaussian kernel is introduced to overcome the shortcoming of single Gaussian kernels. Indeed, giving that faraway points may contain useful information for mammogram characterization, the kernel must emphasis neighbor points without neglecting faraway ones. Gaussian kernels either fail to emphasis neighborhood (high sigma values) or ignore faraway points (low sigma values). To emphasis neighborhood without neglecting faraway points, we propose to use a linear combination of Gaussian kernels with several sigma values, as a kernel in KPCA. Experiments performed on the DDSM database showed that KPCA outperforms state-of-the-art curvelet-based methods including PCA and moments and that the multi-scale gaussian kernel outperforms single gaussian kernels.