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    This study introduces a novel tensor decomposition method to compress integral histograms (IH), significantly reducing memory usage for multidimensional data analysis. The approach enables rapid, accurate histogram retrieval for various regions of interest, accelerating visualization and graphics applications.

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    Area of Science:

    • Computer Science
    • Data Visualization
    • Scientific Computing

    Background:

    • Histograms are essential for multidimensional data analysis and visualization.
    • Integral histograms (IH) accelerate calculations for rectangular regions but require substantial storage.
    • Existing methods face challenges with large datasets and memory constraints.

    Purpose of the Study:

    • To develop a novel compression and approximate retrieval algorithm for integral histograms (IH).
    • To reduce the memory footprint of IH by several orders of magnitude while maintaining user-defined accuracy.
    • To accelerate histogram computation for regions of interest (ROI) in large-scale data.

    Main Methods:

    • Utilized tensor train decomposition for compressing large-scale integral histograms.
    • Developed an incremental tensor decomposition algorithm for efficient compression.
    • Proposed a method to encode ROI borders in the compressed domain for rapid histogram reconstruction.
    • Generalized the algorithm for arbitrary region shapes and histogram field computation.

    Main Results:

    • Achieved memory reduction of several orders of magnitude for integral histograms.
    • Demonstrated high-speed histogram reconstruction, independent of region size.
    • Successfully compressed integral histograms exceeding hundreds of gigabytes.
    • Validated the method on diverse multidimensional datasets, showing significant speedups.

    Conclusions:

    • The proposed tensor-compressed integral histogram method drastically reduces memory requirements.
    • It enables significantly faster histogram queries compared to traditional methods.
    • The approach is versatile, supporting arbitrary shapes and batch computations, making it valuable for large-scale data processing.