原始算法                      列优化                             行优化

分析：
行优化最优，相比于列优化，更符合图像数据在计算机中的存储顺序，因此并且在计算过程中无需申请额外空间保存各列像素之和，只需一个变量保存行像素之和便可！详见开源软件scantailor里的push函数。

3. 在反汇编中，max和min充分利用了条件按传送指令比如cmovg,cmovl，而一般的if语句很大程度上会调用jmp指令的（当然和常数比较一般编译也会用条件传送替代的，比如和0比较），jmp指令是比较耗时的。

开源软件scantailor里的积分图算法的实现：
（调用的时候先调用beginRow定位行指针，然后循环调用push推入该行的像素值，所有行循环完毕就计算完成，然后可以调用sum计算区域累加和。）

/**
 * \brief Provides the sum of values in a sub-rectangle of a 2D array in constant time.
 *
 * Suppose you have a MxN array of some values.  Now if we are not going to
 * alter it, but are going to calculate the sum of values in various
 * rectangular sub-regions, it's best to use an integral image for this purpose.
 * We construct it once, with complexity of O(M*N), and then obtain the sum
 * of values in a rectangular sub-region in O(1).
 *
 * \note Template parameter T must be large enough to hold the sum of all
 *       values in the array.
 */
template<typename T>
class IntegralImage
{
    DECLARE_NON_COPYABLE(IntegralImage)
public:
    IntegralImage(int width, int height);

    explicit IntegralImage(QSize const& size);

    ~IntegralImage();

    /**
     * \brief To be called before pushing new row data.
     */
    void beginRow();

    /**
     * \brief Push a single value to the integral image.
     *
     * Values must be pushed row by row, starting from row 0, and from
     * column to column within each row, starting from column 0.
     * At the beginning of a row, a call to beginRow() must be made.
     *
     * \note Pushing more than width * height values results in undefined
     *       behavior.
     */
    void push(T val);

    /**
     * \brief Calculate the sum of values in the given rectangle.
     *
     * \note If the rectangle exceeds the image area, the behaviour is
     *       undefined.
     */
    T sum(QRect const& rect) const;
private:
    void init(int width, int height);

    T* m_pData;
    T* m_pCur;
    T* m_pAbove;
    T m_lineSum;
    int m_width;
    int m_height;

};

template<typename T>
IntegralImage<T>::IntegralImage(int const width, int const height)
:   m_lineSum() // init with 0 or with default constructor.
{
    // The first row and column are fake.
    init(width + 1, height + 1);
}

template<typename T>
IntegralImage<T>::IntegralImage(QSize const& size)
:   m_lineSum() // init with 0 or with default constructor.
{
    // The first row and column are fake.
    init(size.width() + 1, size.height() + 1);
}

template<typename T>
IntegralImage<T>::~IntegralImage()
{
    delete[] m_pData;
}

template<typename T>
void
IntegralImage<T>::init(int const width, int const height)
{
    m_width = width;
    m_height = height;

    m_pData = new T[width * height];

    // Initialize the first (fake) row.
    // As for the fake column, we initialize its elements in beginRow().
    T* p = m_pData;
    for (int i = 0; i < width; ++i, ++p) {
        *p = T();
    }

    m_pAbove = m_pData;
    m_pCur = m_pAbove + width; // Skip the first row.
}

template<typename T>
void
IntegralImage<T>::push(T const val)
{
    m_lineSum += val;
    *m_pCur = *m_pAbove + m_lineSum;
    ++m_pCur;
    ++m_pAbove;
}

template<typename T>
void
IntegralImage<T>::beginRow()
{
    m_lineSum = T();

    // Initialize and skip the fake column.
    *m_pCur = T();
    ++m_pCur;
    ++m_pAbove;
}

template<typename T>
inline T
IntegralImage<T>::sum(QRect const& rect) const
{
    // Keep in mind that row 0 and column 0 are fake.
    int const pre_left = rect.left();
    int const pre_right = rect.right() + 1; // QRect::right() is inclusive.
    int const pre_top = rect.top();
    int const pre_bottom = rect.bottom() + 1; // QRect::bottom() is inclusive.
    T sum(m_pData[pre_bottom * m_width + pre_right]);
    sum -= m_pData[pre_top * m_width + pre_right];
    sum += m_pData[pre_top * m_width + pre_left];
    sum -= m_pData[pre_bottom * m_width + pre_left];
    return sum;
}