Fractional Wavelet Scattering Network and Applications

Objective: The present study introduces a fractional wavelet scattering network (FrScatNet), which is a generalized translation invariant version of the classical wavelet scattering network (ScatNet). Methods: In our approach, the FrScatNet is constructed based on the fractional wavelet transform (FRWT). The fractional scattering coefficients are iteratively computed using FRWTs and modulus operators. The feature vectors constructed by fractional scattering coefficients are usually used for signal classification. In this work, an application example of FrScatNet is provided in order to assess its performance on pathological images. Firstly, the FrScatNet extracts feature vectors from patches of the original histological images under different orders. Then we classify those patches into target (benign or malignant) and background groups. And the FrScatNet property is analyzed by comparing error rates computed from different fractional orders respectively. Based on the above pathological image classification, a gland segmentation algorithm is proposed by combining the boundary information and the gland location. Results: The error rates for different fractional orders of FrScatNet are examined and show that the classification accuracy is significantly improved in fractional scattering domain. We also compare the FrScatNet based gland segmentation method with those proposed in the 2015 MICCAI Gland Segmentation Challenge and our method achieves comparable results. Conclusion: The FrScatNet is shown to achieve accurate and robust results. More stable and discriminative fractional scattering coefficients are obtained by the FrScatNet in this work. Significance: The added fractional order parameter is able to analyze the image in the fractional scattering domain.