wenergy2

Energy for 2-D wavelet decomposition

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    Syntax

    [Ea,Eh,Ev,Ed] = wenergy2(C,S)
    [Ea,EDetail] = wenergy2(C,S)

    Description

    [Ea,Eh,Ev,Ed] = wenergy2(C,S) returns, for the 2-D wavelet decomposition structure C, S:

    • Ea — Percentage of energy corresponding to the approximation.

    • Eh, Ev, and Ed — Vectors which contain the percentages of energy corresponding to the horizontal, vertical, and diagonal details, respectively.

    example

    [Ea,EDetail] = wenergy2(C,S) returns EDetail, the sum of the energies corresponding to the horizontal, vertical, and diagonal details.

    Examples

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    Open Live Script

    Load and display an image.

    load detail
image(X)
colormap(map)

    Figure contains an axes object. The axes object contains an object of type image.

    Obtain the level 4 wavelet decomposition of the image using the sym4 wavelet.

    load detail
[C,S] = wavedec2(X,4,"sym4");

    Obtain the percentages of energy in the approximation, and all detail levels and orientations.

    [Ea,Eh,Ev,Ed] = wenergy2(C,S)
    Ea = 
86.9903

    Eh = 1×4

    1.1921    1.7396    1.8062    1.0492


    Ev = 1×4

    1.0084    1.6559    1.5394    1.0467


    Ed = 1×4

    0.4793    0.6951    0.5449    0.2528

    Confirm the percentage of energy of the combined details equals the sum of the percentages of the individual detail orientations.

    [~,EDetail] = wenergy2(C,S)
    EDetail = 1×4

    2.6799    4.0906    3.8904    2.3488


    sum([Eh;Ev;Ed])
    ans = 1×4

    2.6799    4.0906    3.8904    2.3488

    Input Arguments

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    Wavelet decomposition vector, specified as a vector. C contains the approximation and detail coefficients organized by level. The bookkeeping matrix S is used to parse C. For more information, see wavedec2.

    Example: [C,S] = wavedec2(X,3,"db4") returns the level 4 wavelet decomposition of X using the db4 wavelet.

    Data Types: double

    Bookkeeping matrix, specified as an integer-valued matrix. The matrix S contains the dimensions of the wavelet coefficients by level and is used to parse the wavelet decomposition vector C. For more information, see wavedec2.

    Data Types: double

    Output Arguments

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    Percentage of energy corresponding to the approximation, returned as a scalar.

    Data Types: double

    Percentage of energy corresponding to the horizontal, vertical, and diagonal details, respectively, returned as 1-by-L vectors, where L is the level of the wavelet decomposition. The kth element of the vector is the percentage of energy at the kth level.

    Data Types: double

    Percentage of energy corresponding to the details, respectively, returned as a 1-by-L vector, where L is the level of the wavelet decomposition. The kth element of the vector is the percentage of energy at the kth level. EDetail is the sum of the vectors Eh, Ev, and Ed.

    Data Types: double

    Version History

    Introduced before R2006a

    See Also