The $C(r,s)$ values to consider the 1-Dimensional Gaussian curve fits, identified by the whole-pixel $C(r,s)$ maxima of $r = 5$, $s = 0$. Figure 3 demonstrates this concept, where the correlation plane values along $s = 0$ and $r = 5$ are highlighted in red and yellow respectively.įigure 3. If we ‘cut’ the correlation plane at each of these full-pixel maximum locations, we can estimate the 1 dimensional curves in each direction. This result is good, and close to the true value of $r = 5.5$, $s = 0$. Visually inspecting Figure 2, we recognize that the maximum value of our correlation plane is at $r = 5$, $s = 0$. The correlation plane for the interrogation region pair in Figure 1.

The correlation plane $C(r,s)$ for this image pair is demonstrated by Figure 2.įigure 2. A synthetic interrogation region pair with $x$ and $y$ displacement of 0 and 5.5 pixels respectively. Note: these results are in image coordinates, and the $y$ is flipped from conventional orientation.įigure 1.

1, generated with a uniform movement of no $x$-direction displacement and +5.5 pixels $y$ direction displacement. To illustrate this idea, we take an image pair as shown in Fig. With this assumption, we will fit our curve in the $r$ direction independently, then the $s$ direction independently. To do this computation quickly, we will further assume that the $r$ and $s$ directions are each a 1-dimensional Gaussian distribution. If we assume this correlation peak shape, then we can fit a Gaussian distribution to this correlation peak using the values nearest our maximum $C(r,s)$. While the overall peak shape is difficult to determine, a common approximation is that the correlation peak follows a Gaussian (or normal) distribution. Fortunately, there are several ways to increase our vector output resolution by first making an educated guess about the overall shape of the correlation plane, fitting the curve of this guess to the correlation plane points which are identified by $C(r,s)$, and finally finding the peak of our fitted curve(s).

One limitation of finding our vector values with only the maximum peak of our correlation plane $C(r,s)$ is that this would limit the range of possible output values to a maximum resolution of 1 pixel (i.e., the resolution of our correlation plane).

Imagej piv