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    Area of Science:

    • Image analysis
    • Signal processing
    • Machine learning

    Background:

    • Classical wavelet scattering networks offer translation invariance for signal analysis.
    • Pathological image analysis requires robust feature extraction for accurate classification and segmentation.

    Purpose of the Study:

    • Introduce a generalized translation-invariant network, the fractional wavelet scattering network (FrScatNet).
    • Assess FrScatNet's performance in pathological image classification and gland segmentation.
    • Investigate the impact of fractional orders on feature extraction and classification accuracy.

    Main Methods:

    • Construct FrScatNet using the fractional wavelet transform (FRWT) and modulus operators.
    • Iteratively compute fractional scattering coefficients for feature vector generation.
    • Apply FrScatNet to histological image patches for classification (benign/malignant) and gland segmentation.

    Main Results:

    • FrScatNet demonstrates improved classification accuracy in the fractional scattering domain.
    • The proposed gland segmentation algorithm achieves results comparable to state-of-the-art methods.
    • Analysis of error rates across different fractional orders validates the method's effectiveness.

    Conclusions:

    • FrScatNet provides accurate and robust results for pathological image analysis.
    • The fractional order parameter enables enhanced image analysis in the fractional scattering domain.
    • FrScatNet yields more stable and discriminative fractional scattering coefficients.