积分图的优化

原文：13行代码实现最快速最高效的积分图像算法。
Tips：
1.某个点的积分图反应的是原图中此位置左上角所有像素之和，这里是的累加和是不包括这个点像素本身的，那么，对于原图的第一行和第一列的所有像素，其对应位置的积分图就应该是0, 这样考虑到所有的像素，为了能容纳最后一列和最后一行的情况，最终的积分图就应该是 (W + 1) X (H + 1)大小。

2.优化方式：

         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>voidIntegralImage<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>voidIntegralImage<T>::push(T const val){    m_lineSum += val;    *m_pCur = *m_pAbove + m_lineSum;    ++m_pCur;    ++m_pAbove;}template<typename T>voidIntegralImage<T>::beginRow(){    m_lineSum = T();    // Initialize and skip the fake column.    *m_pCur = T();    ++m_pCur;    ++m_pAbove;}template<typename T>inline TIntegralImage<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;}