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Why does the integrated image contain an extra row and column of zeros?

I learn how to use integrated images using opencv with the Java API, and I created a test that displays an image in grayscale before using an integrated image and after using it. the grayscale image is 10 x 10, and when I converted it to an integral image, I found it 11 x 11 with extra rows of zeros and an extra column of zeros, as shown below in the output.

please let me know why does the integrated image contain an extra row and column of zeros?

The code

    public static void main(String[] args) {
    MatFactory matFactory = new MatFactory();
    FilePathUtils.addInputPath(path_Obj);
    Mat bgrMat = matFactory.newMat(FilePathUtils.getInputFileFullPathList().get(0));
    Mat gsImg = SysUtils.rgbToGrayScaleMat(bgrMat);

    Log.D(TAG, "MainClas", "gsImg.dump(): " + gsImg.dump());
    Mat integralMat = new Mat();
    Imgproc.integral(gsImg, integralMat, CvType.CV_32F);

    Log.D(TAG, "MainClas", "sumMat.dump(): " + integralMat.dump());
}

audio output

    1: Debug: MainClass -> MainClas: gsImg.dump(): [2, 1, 7, 5, 1, 11, 2, 7, 9, 11;
        1, 2, 0, 0, 3, 20, 17, 5, 7, 8;
        4, 8, 0, 2, 6, 30, 31, 5, 2, 2;
        39, 43, 47, 44, 38, 62, 60, 37, 37, 39;
        27, 29, 52, 52, 47, 75, 67, 59, 58, 63;
        25, 21, 49, 51, 51, 78, 64, 66, 76, 80;
        40, 36, 50, 46, 41, 56, 42, 45, 47, 49;
        13, 17, 20, 15, 9, 20, 15, 19, 12, 11;
        17, 13, 8, 5, 4, 7, 13, 20, 17, 17;
        2, 4, 7, 9, 8, 6, 6, 7, 7, 8]
    2: Debug: MainClass -> MainClas: sumMat.dump(): [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
        0, 2, 3, 10, 15, 16, 27, 29, 36, 45, 56;
        0, 3, 6, 13, 18, 22, 53, 72, 84, 100, 119;
        0, 7, 18, 25, 32, 42, 103, 153, 170, 188, 209;
        0, 46, 100, 154, 205, 253, 376, 486, 540, 595, 655;
        0, 73, 156, 262, 365, 460, 658, 835, 948, 1061, 1184;
        0, 98, 202, 357, 511, 657, 933, 1174, 1353, 1542, 1745;
        0, 138, 278, 483, 683, 870, 1202, 1485, 1709, 1945, 2197;
        0, 151, 308, 533, 748, 944, 1296, 1594, 1837, 2085, 2348;
        0, 168, 338, 571, 791, 991, 1350, 1661, 1924, 2189, 2469;
        0, 170, 344, 584, 813, 1021, 1386, 1703, 1973, 2245, 2533]
+4
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2 answers

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