Cryptage d'images à l'aide d'un masque jetable

Données du chat  (45x45)

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            0.258061, 0.258061, 0.193545, 0. , 0. , 0. , 0.322576, 0.322576, 
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            0.258061, 0.258061, 0.225803, 0. , 0. , 0. , 0. , 0.258061, 
            0.354833, 0.354833, 0.322576, 0.322576, 0.12903, 0.0967727, 
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            0.258061, 0.258061, 0.193545, 0.225803, 0.193545, 0.193545, 0. , 
            0. , 0. , 0. , 0.322576, 0.322576, 0.354833, 0.387091, 0.387091, 
            0.483864, 0.354833, 0.290318, 0.225803, 0.258061}, {0.451606, 
            0.354833, 0.387091, 0.354833, 0.290318, 0.354833, 0.354833, 
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            0.258061, 0.387091, 0.354833, 0.387091, 0.322576, 0.451606, 
            0.258061, 0.258061, 0.193545, 0.161288, 0.225803, 0.193545, 
            0.258061, 0.322576, 0. , 0. , 0. , 0. , 0. , 0.354833, 0.354833, 
            0.322576, 0.354833, 0.322576, 0.258061, 0.322576}, {0.290318, 
            0.387091, 0.322576, 0.322576, 0.290318, 0.258061, 0.354833, 
            0.451606, 0.516136, 0.387091, 0.387091, 0.483864, 0.354833, 
            0.225803, 0.193545, 0.225803, 0.290318, 0.258061, 0.258061, 
            0.290318, 0.387091, 0.290318, 0.387091, 0.322576, 0.354833, 
            0.258061, 0.258061, 0.193545, 0.225803, 0.225803, 0.225803, 
            0.258061, 0.387091, 0.322576, 0.354833, 0.354833, 0.322576, 0. , 
            0. , 0. , 0. , 0.322576, 0.290318, 0.322576, 
            0.290318}, {0.354833, 0.322576, 0.387091, 0.258061, 0.322576, 
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            0.322576, 0.258061, 0.225803, 0.225803, 0.258061, 0.225803, 
            0.193545, 0.225803, 0.258061, 0.290318}, {0.419348, 0.354833, 
            0.322576, 0.290318, 0.322576, 0.322576, 0.387091, 0.451606, 
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            0.225803, 0.225803, 0.258061, 0.419348, 0.290318, 0.290318, 
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            0.258061, 0.354833, 0.387091, 0.354833, 0.387091, 0.516136, 
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            0.451606, 0.419348, 0.516136, 0.419348, 0.451606, 0.322576, 
            0.258061, 0.290318, 0.225803, 0.290318, 0.322576, 0.258061, 
            0.387091, 0.322576, 0.322576, 0.322576, 0.290318, 0.290318, 
            0.225803, 0.225803, 0.161288, 0.161288, 0.193545, 0.193545, 
            0.225803}, {0.258061, 0.290318, 0.290318, 0.290318, 0.322576, 
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            0.290318, 0.354833, 0.387091, 0.387091, 0.322576, 0.354833, 
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            0.290318, 0.354833, 0.322576, 0.354833, 0.451606, 0.580652, 
            0.612909, 0.580652, 0.548394, 0.387091, 0.483864, 0.419348, 
            0.322576, 0.354833, 0.322576, 0.322576, 0.322576, 0.258061, 
            0.290318, 0.322576, 0.322576, 0.290318, 0.387091, 0.290318, 
            0.258061, 0.258061, 0.225803, 0.225803, 0.225803, 0.258061, 
            0.225803}, {0.322576, 0.322576, 0.354833, 0.322576, 0.354833, 
            0.483864, 0.451606, 0.387091, 0.225803, 0.258061, 0.193545, 
            0.258061, 0.290318, 0.354833, 0.387091, 0.354833, 0.354833, 
            0.387091, 0.451606, 0.612909, 0.548394, 0.709682, 0.645167, 
            0.483864, 0.451606, 0.387091, 0.354833, 0.322576, 0.387091, 
            0.354833, 0.322576, 0.258061, 0.225803, 0.193545, 0.290318, 
            0.322576, 0.354833, 0.258061, 0.322576, 0.290318, 0.193545, 
            0.193545, 0.161288, 0.225803, 0.225803}, {0.225803, 0.258061, 
            0.322576, 0.322576, 0.387091, 0.387091, 0.419348, 0.354833, 
            0.225803, 0.193545, 0.193545, 0.225803, 0.161288, 0.322576, 
            0.516136, 0.387091, 0.451606, 0.516136, 0.612909, 0.645167, 
            0.612909, 0.645167, 0.548394, 0.677424, 0.516136, 0.419348, 
            0.548394, 0.483864, 0.451606, 0.419348, 0.290318, 0.258061, 
            0.258061, 0.12903, 0.193545, 0.225803, 0.225803, 0.225803, 
            0.258061, 0.322576, 0.225803, 0.225803, 0.225803, 0.161288, 
            0.12903}, {0.225803, 0.258061, 0.290318, 0.290318, 0.322576, 
            0.354833, 0.322576, 0.354833, 0.225803, 0.193545, 0.193545, 
            0.225803, 0.258061, 0.322576, 0.451606, 0.483864, 0.548394, 
            0.451606, 0.677424, 0.709682, 0.580652, 0.580652, 0.612909, 
            0.677424, 0.548394, 0.483864, 0.516136, 0.483864, 0.483864, 
            0.354833, 0.387091, 0.290318, 0.225803, 0.0967727, 0.193545, 
            0.258061, 0.193545, 0.225803, 0.225803, 0.290318, 0.161288, 
            0.193545, 0.193545, 0.12903, 0.193545}, {0.258061, 0.193545, 
            0.258061, 0.290318, 0.290318, 0.290318, 0.258061, 0.290318, 
            0.225803, 0.161288, 0.258061, 0.258061, 0.225803, 0.354833, 
            0.354833, 0.741939, 0.741939, 0.516136, 0.645167, 0.580652, 
            0.548394, 0.548394, 0.580652, 0.645167, 0.548394, 0.580652, 
            0.516136, 0.548394, 0.516136, 0.419348, 0.387091, 0.225803, 
            0.193545, 0.193545, 0.193545, 0.225803, 0.161288, 0.161288, 
            0.193545, 0.225803, 0.12903, 0.161288, 0.12903, 0.12903, 
            0.161288}};

Dimensions[dataChat45x45]

ListDensityPlot[dataChat45x45, AspectRatio -> Automatic, 
        Mesh -> False];

Données de la lettre mu (45x45)

dataMu45x45 = {{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 0.74902, 0.498039, 0.623529, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.87451, 0, 0, 0, 0.498039, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.560784, 0, 
            0, 0, 0.25098, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 0.498039, 0, 0, 0, 0.439216, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0.811765, 1, 1, 1, 
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            1, 0.498039, 0, 0, 0.560784, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
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            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 
            0.376471, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 0.686275, 0, 0.686275, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.74902, 0, 0.937255, 1, 1, 
            0.74902, 0.498039, 0.498039, 0.623529, 0.87451, 1, 1, 1, 1, 1, 1, 
            1, 1, 0.87451, 0.498039, 0.498039, 0.686275, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.74902, 
            0.188235, 1, 0.811765, 0.12549, 0, 0, 0, 0, 0, 0.376471, 
            0.937255, 1, 1, 1, 1, 1, 0.439216, 0, 0, 0, 0, 0.12549, 0.811765, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            0.74902, 0.376471, 0.87451, 0.0627451, 0, 0, 0, 0.188235, 
            0.25098, 0.0627451, 0, 0.188235, 0.937255, 1, 1, 1, 0.560784, 0, 
            0, 0, 0.0627451, 0.25098, 0.0627451, 0.12549, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.74902, 0.498039, 
            0.25098, 0, 0, 0.0627451, 0.811765, 1, 1, 1, 0.560784, 0, 
            0.188235, 1, 1, 1, 0.0627451, 0, 0, 0, 0.811765, 1, 0.937255, 
            0.0627451, 0.686275, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 0.498039, 0.376471, 0, 0, 0, 0.560784, 1, 1, 1, 
            1, 1, 0.623529, 0, 0.623529, 1, 0.686275, 0, 0, 0, 0.25098, 1, 1, 
            1, 0.439216, 0.439216, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 0.498039, 0.0627451, 0, 0, 0, 0.74902, 1, 1, 
            1, 1, 1, 1, 0.439216, 0.12549, 1, 0.498039, 0, 0, 0, 0.498039, 1, 
            1, 1, 0.686275, 0.25098, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 0.937255, 1, 1, 1, 1, 
            1, 1, 0.937255, 0.0627451, 0.686275, 0.25098, 0, 0, 0, 0.498039, 
            1, 1, 1, 0.74902, 0.25098, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 
            1, 1, 0.376471, 0.313725, 0.25098, 0, 0, 0, 0.498039, 1, 1, 1, 
            0.87451, 0.623529, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 
            0.811765, 0, 0.25098, 0, 0, 0, 0.498039, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 
            0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.12549, 0, 0, 0, 0, 
            0.498039, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 0.313725, 0, 0, 0, 0, 0.498039, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 
            0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 0.498039, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            0.74902, 0, 0, 0, 0, 0.498039, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 0.74902, 0, 0, 0, 0, 0.498039, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 
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            0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0.498039, 1, 1, 
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            1, 1, 1, 1, 1, 0, 0, 0, 0, 0.498039, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 
            0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0.498039, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 0.498039, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 
            0, 0, 0.498039, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 0, 0, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 0, 0, 0, 0, 0.498039, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.498039, 0, 0, 
            0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0.498039, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 0.74902, 0.498039, 0.498039, 0.498039, 0.498039, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 0.498039, 0.498039, 0.498039, 0.498039, 
            0.74902, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
            1, 1, 1, 1, 1, 1, 1, 1, 1}};

Dimensions[dataMu45x45];

ListDensityPlot[dataMu45x45, AspectRatio -> Automatic, 
        Mesh -> False];

"Addition" des deux images

Regardez ce qui se passe si l'on "additionne" deux images  ("dataChat45x45" et "dataMu45x45"). Avant d'effecteur l'addition, on multiplie la matrice "dataMu45x45" par 1/coeff.

coeff = 64;
superposition = dataChat45x45 + dataMu45x45/coeff;
pixelSuperposition[x_, 
          y_] := {If[superposition[[y, x]] > 1, 
            superposition[[y, x]] = 1];  
          GrayLevel[superposition[[y, x]]], 
          Polygon[{{x, y}, {x + 1, y}, {x + 1, y + 1}, {x, 
                y + 1}}]};
resultat = 
        Table[pixelSuperposition[x, y], {x, 1, 45}, {y, 1, 45}];
Show[Graphics[resultat], AspectRatio -> Automatic, 
        Axes -> False];
soustraction = (superposition - dataChat45x45)*coeff;
pixelSoustraction[x_, 
          y_] := {If[soustraction[[y, x]] > 1, 
            soustraction[[y, x]] = 1];  
          GrayLevel[soustraction[[y, x]]], 
          Polygon[{{x, y}, {x + 1, y}, {x + 1, y + 1}, {x, 
                y + 1}}]};
original = 
        Table[pixelSoustraction[x, y], {x, 1, 45}, {y, 1, 45}];
Show[Graphics[original], AspectRatio -> Automatic, 
        Axes -> False];

Exercice

Faites varier le coefficient "coeff" entre 0.25 et 64, observez les différents résultats et commentez-les.