Gaussian Blur is a common effect in normal gui development. Qt provide a class, QGraphicsBlurEffect, for QWidget to this effect.
However, what about QImage?
This is the code snippet I found in \qt\src\gui\image\qpixmapfilter.cpp:

QImage blurred(const QImage& image, const QRect& rect, int radius, bool alphaOnly = false)
{
    int tab[] = { 14, 10, 8, 6, 5, 5, 4, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2 };
    int alpha = (radius < 1)  ? 16 : (radius > 17) ? 1 : tab[radius-1];

    QImage result = image.convertToFormat(QImage::Format_ARGB32_Premultiplied);
    int r1 = rect.top();
    int r2 = rect.bottom();
    int c1 = rect.left();
    int c2 = rect.right();

    int bpl = result.bytesPerLine();
    int rgba[4];
    unsigned char* p;

    int i1 = 0;
    int i2 = 3;

    if (alphaOnly)
        i1 = i2 = (QSysInfo::ByteOrder == QSysInfo::BigEndian ? 0 : 3);

    for (int col = c1; col <= c2; col++) {
        p = result.scanLine(r1) + col * 4;
        for (int i = i1; i <= i2; i++)
            rgba[i] = p[i] << 4;

        p += bpl;
        for (int j = r1; j < r2; j++, p += bpl)
            for (int i = i1; i <= i2; i++)
                p[i] = (rgba[i] += ((p[i] << 4) - rgba[i]) * alpha / 16) >> 4;
    }

    for (int row = r1; row <= r2; row++) {
        p = result.scanLine(row) + c1 * 4;
        for (int i = i1; i <= i2; i++)
            rgba[i] = p[i] << 4;

        p += 4;
        for (int j = c1; j < c2; j++, p += 4)
            for (int i = i1; i <= i2; i++)
                p[i] = (rgba[i] += ((p[i] << 4) - rgba[i]) * alpha / 16) >> 4;
    }

    for (int col = c1; col <= c2; col++) {
        p = result.scanLine(r2) + col * 4;
        for (int i = i1; i <= i2; i++)
            rgba[i] = p[i] << 4;

        p -= bpl;
        for (int j = r1; j < r2; j++, p -= bpl)
            for (int i = i1; i <= i2; i++)
                p[i] = (rgba[i] += ((p[i] << 4) - rgba[i]) * alpha / 16) >> 4;
    }

    for (int row = r1; row <= r2; row++) {
        p = result.scanLine(row) + c2 * 4;
        for (int i = i1; i <= i2; i++)
            rgba[i] = p[i] << 4;

        p -= 4;
        for (int j = c1; j < c2; j++, p -= 4)
            for (int i = i1; i <= i2; i++)
                p[i] = (rgba[i] += ((p[i] << 4) - rgba[i]) * alpha / 16) >> 4;
    }

    return result;
}

And a demo:

int main(int argc, char *argv[])
{
    QApplication a(argc, argv);
    QLabel label;
    QImage image("image.png");
    image =  blurred(image,image.rect(),10,false);
    label.setPixmap(QPixmap::fromImage(image));
    label.show();

    return a.exec();
}

Nice and simple, huh?