Ripplet transform type II transform for feature extraction

Current image representation schemes have limited capability of representing two-dimensional (2D) singularities (e.g. edges in an image). Wavelet transform has better performance in representing one-dimensional (1D) singularities than Fourier transform. Recently invented ridgelet and curvelet transform achieve better performance in resolving 2D singularities than wavelet transform. To further improve the capability of representing 2D singularities, this study proposes a new transform called ripplet transform type II (ripplet-II). The new transform is able to capture 2D singularities along a family of curves in images. In fact, ridgelet transform is a special case of ripplet-II transform with degree 1. Ripplet-II transform provides the freedom in parameter settings, which can be optimised for specific problems. Ripplet-II transform can be used for feature extraction because of its efficiency in representing edges and textures. Experiments in texture classification and image retrieval demonstrate that the ripplet-II transform-based scheme outperforms wavelet and ridgelet transform-based approaches.