Mathematical properties of pyramid-transform-based resolution conversion and its applications. (English) Zbl 1539.68353
Summary: In this paper, we aim to clarify the statistical and geometric properties of linear resolution conversion for registration between different resolutions observed using the same modality. The pyramid transform is achieved by smoothing and downsampling. The dual operation of the pyramid transform is achieved by linear smoothing after upsampling. The rational-order pyramid transform is decomposed into upsampling for smoothing and the conventional integer-order pyramid transform. By controlling the ratio between upsampling for smoothing and downsampling in the pyramid transform, the rational-order pyramid transform is computed. The tensor expression of the multiway pyramid transform implies that the transform yields orthogonal base systems for any ratio of the rational pyramid transform. The numerical evaluation of the transform shows that the rational-order pyramid transform preserves the normalised distribution of greyscale in images.
MSC:
| 68U10 | Computing methodologies for image processing |
| 65F99 | Numerical linear algebra |
| 65T60 | Numerical methods for wavelets |
| 94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
Keywords:
resolution conversion; multiresolution analysis; pyramid transform; tensor decomposition; volumetric image; histogram distanceReferences:
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