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    Area of Science:

    • Computer Graphics
    • Image Processing
    • Wavelet Theory

    Background:

    • Biorthogonal Catmull-Clark subdivision wavelet transforms improve geometric model processing.
    • Progressive interpolation enhances compression and noise filtering but struggles with reconstruction precision and detail preservation.
    • Existing methods face limitations in handling sharp features and maintaining detail during noise reduction.

    Purpose of the Study:

    • To present a unified Catmull-Clark subdivision based biorthogonal wavelet construction with shape control parameters.
    • To address the limitations of existing methods in reconstruction precision and noise-filtering performance.
    • To improve the processing of 3D models with sharp-feature constraints.

    Main Methods:

    • Customizing local orthogonalizing coefficients based on vertex valences of quadrilateral patches.
    • Integrating local and in-place lifting operations for reduced memory and computation.
    • Developing a novel wavelet transform with shape control for 3D model processing.

    Main Results:

    • The proposed wavelet transform achieves higher compression ratios compared to state-of-the-art methods.
    • Demonstrates more stable noise-filtering effects and better progressive transmission quality.
    • Significantly decreases Bits/vertex for 3D meshes and improves Peak Signal-to-Noise Ratio (PSNR).

    Conclusions:

    • The novel wavelet transform offers superior performance in compression, noise filtering, and progressive transmission for 3D models.
    • Customizable shape control parameters and efficient lifting operations lead to reduced computational complexity and memory consumption.
    • The method effectively preserves model details and enhances overall quality in geometric processing applications.