Parallel Wavelet Schemes for Images

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    20-Feb-2017
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Transcript of Parallel Wavelet Schemes for Images

  • Parallel Wavelet Schemes for Images

  • Filter Bank

    H(z1) a

    d

    2

    +

    G(z1) 2

    2 H(z)

    2 G(z)

  • Lifting Scheme

    a

    d

    split P (z1)T P (z) merge

    P (z)T =

    K>k>0

    [1 U (k)(z)0 1

    ] [1 0

    P (k)(z) 1

    ]

  • CDF 9/7 Wavelet

    input

    output

    steps

    even samples

    odd samples

    P (z) =

    [1

    (1 + z1

    )0 1

    ] [1 0

    (1 + z) 1

    ] [1

    (1 + z1

    )0 1

    ] [1 0

    (1 + z) 1

    ] [ 00 1/

    ]

  • 2-D Discrete Wavelet Transform

  • Objective

  • State of the Art: Separable Convolution

    NH

    NH

    NV NV

    y = NV |NH | x

  • State of the Art: Separable Lifting

    THP TVP S

    HU S

    VU

    y = SVU SHU TVP THP x

  • Our Solution: Separable Polyconvolution

    NH

    NV NH NV

    y = NVP,U |NHP,U | x

  • Our Solution: Non-Separable Convolution

    N N

    y = N x

  • Our Solution: Non-Separable Convolution

    N N

    y = N x

  • Our Solution: Non-Separable Polyconvolution

    NP,U NP,U

    y = NP,U x

  • Our Solution: Non-Separable Polyconvolution

    NP,U NP,U

    y = NP,U x

  • Our Solution: Non-Separable Lifting

    TP TP SU SU

    y = SUTP x

  • Our Solution: Non-Separable Implosion

    TIP RIP,U S

    IU

    y = SIURIP,U TIP x

  • Our Solution: Non-Separable Explosion

    TEP REP,U S

    EU

    y = SEUREP,U TEP x

  • Platforms

    feature shaders OpenCL

    results exchanged off-chip memory on-chip memorypassing in registers no yesSIMD available no yes, SIMD-32transform view global view block-based

  • Results: Properties

    Table : Arithmetic Operations / Steps for CDF 9/7

    separability scheme shaders OpenCL

    separable convolution 58 / 2 56 / 1separable polyconvolution 42 / 4 20 / 2separable lifting 32 / 8 32 / 4

    non-separable convolution 200 / 1 152 / 1non-separable polyconvolution 62 / 2 46 / 2non-separable lifting 36 / 4 36 / 4non-separable implosion 39 / 6 36 / 6non-separable explosion 37 / 6 36 / 6

  • Results: Performance in Shaders

    2

    3

    4

    5

    6

    7

    8

    9

    10

    11

    12

    13

    10.0kpx 100.0kpx 1.0Mpx 10.0Mpx 100.0Mpx 1.0Gpx

    GB/s

    Separable LiftingNon-Separable Lifting

    Non-Separable ImplosionNon-Separable Explosion

    Non-Separable Polyconv.Separable Polyconv.

    Non-Separable ConvolutionSeparable Convolution