传统的2维几何矩算法着眼于单个矩形窗口，但当关心的矩形区域在大地图上滑动时，传统算法效率不高。为提高2维几何矩运算速度，提出了一种新的快速迭代算法。由于该算法能够充分利用相邻滑动窗重叠的像素信息，从而可以大大提高2维几何矩的计算效率。该算法所需的乘法和加法运算复杂度完全与滑动窗尺寸N×L无关，都为O(1)。与传统算法的2维几何矩运算复杂度O(N×L)相比，该算法运算速度可以比传统算法提高接近N×L倍。计算机仿真结果验证了该结论。该速度可以满足大多数实时应用的需要。

The traditional algorithms for geometric moment focus on the single rectangle windows. It has very low efficiency in the sliding window applications. This issue prompts a new fast algorithm for 2 D geometric moment. It could efficiently reuse the overlapping pixels between conjoint sliding windows, and achieves much higher computation efficiency. The average number of the multiplications and additions is O(1), regardless of the sliding windows size. Compared to the operation complexity of the traditional algorithm, known as O(N×L) in 2 D case, the new algorithm derived by this paper can improve its speed by the factor of nearly N×L. A number of computer experiments are performed to validate this conclusion. This operation speed of this new algorithm can satisfy the requirements of most real time applications.