  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.
