MQD Algorithm

The Minimum Quadric Differences (MQD) algorithm is to simply calculate the pixel value differences between the search windows.

$$C(\Delta X, \Delta Y) = \sum_{i=1}^{N}\sum_{j=1}^{N} \lef... ..._1(X_i,Y_j) - f_2(X_i + \Delta X, Y_j + \Delta Y) \right\vert$$ (2)

The location of the minimum value in $C$ is used as the particle displacement. Note that MQD is sometimes referred as `gray level difference accumulation'. The criteria to retain the calculated vectors is similar to that in the correlation algorithm, i.e., by checking the ratio of the two highest peaks and the signal to noise ratio of the highest peak.

The accuracy of the cross-correlation algorithm and the MQD algorithm are almost the same. However, the MQD algorithm may be more robust than the correlation algorithm in certain situations. For example, the correlation algorithm does not work well for images containing no particles such as speckle images. However, there is a price to pay - the MQD algorithm is in general slower than the correlation algorithm.