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Higher order SVD analysis for dynamic texture synthesis.

Roberto Costantini1, Luciano Sbaiz, Sabine Süsstrunk

  • 1School of Computer and Communication Sciences, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|January 31, 2008
PubMed
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This study introduces Higher Order Singular Value Decomposition (HOSVD) for dynamic texture synthesis. HOSVD offers a more efficient method, requiring fewer parameters than standard SVD for high-quality results.

Area of Science:

  • Computer Vision
  • Image Processing
  • Computer Graphics

Background:

  • Dynamic textures, like flames or smoke, are characterized by spatial and temporal pattern repetition.
  • Previous methods modeled dynamic textures as linear dynamic systems using Singular Value Decomposition (SVD).
  • Standard SVD unfolds video frames, limiting dimensionality reduction to the temporal domain.

Purpose of the Study:

  • To introduce Higher Order Singular Value Decomposition (HOSVD) as a superior alternative to SVD for dynamic texture modeling.
  • To demonstrate HOSVD's ability to perform dimension reduction across spatial, temporal, and chromatic domains.
  • To evaluate the efficiency and effectiveness of HOSVD for dynamic texture synthesis.

Main Methods:

  • Applied HOSVD (Tucker decomposition) to dynamic textures, treating them as multidimensional signals (tensors).

Related Experiment Videos

  • Performed dimension reduction in spatial, temporal, and chromatic domains simultaneously.
  • Compared parameter requirements and synthesis quality against standard SVD methods.

    • Main Results:

    • HOSVD decomposes dynamic textures more naturally as tensors, avoiding frame unfolding.
    • HOSVD allows for simultaneous dimension reduction across multiple domains, unlike SVD's temporal-only reduction.
    • HOSVD achieved comparable synthesis quality with approximately five times fewer parameters than standard SVD.

    Conclusions:

    • HOSVD provides a more efficient and flexible approach to dynamic texture synthesis.
    • The reduced parameter count makes HOSVD suitable for memory-constrained devices like mobile phones.
    • This technique enhances the feasibility of realistic dynamic texture generation in resource-limited environments.