diff --git a/modules/imgproc/doc/motion_analysis_and_object_tracking.rst b/modules/imgproc/doc/motion_analysis_and_object_tracking.rst index 34dae1ef5..8a4d0507d 100644 --- a/modules/imgproc/doc/motion_analysis_and_object_tracking.rst +++ b/modules/imgproc/doc/motion_analysis_and_object_tracking.rst @@ -161,34 +161,34 @@ Return value: detected phase shift (sub-pixel) between the two arrays. The function performs the following equations -* - First it applies a Hanning window (see http://en.wikipedia.org/wiki/Hann\_function) to each image to remove possible edge effects. This window is cached until the array size changes to speed up processing time. +* First it applies a Hanning window (see http://en.wikipedia.org/wiki/Hann\_function) to each image to remove possible edge effects. This window is cached until the array size changes to speed up processing time. -* - Next it computes the forward DFTs of each source array: - .. math:: +* Next it computes the forward DFTs of each source array: + + .. math:: \mathbf{G}_a = \mathcal{F}\{src_1\}, \; \mathbf{G}_b = \mathcal{F}\{src_2\} - where - :math:`\mathcal{F}` is the forward DFT. + where + :math:`\mathcal{F}` is the forward DFT. + +* It then computes the cross-power spectrum of each frequency domain array: -* - It then computes the cross-power spectrum of each frequency domain array: .. math:: - R = \frac{ \mathbf{G}_a \mathbf{G}_b^*}{|\mathbf{G}_a \mathbf{G}_b^*|} + R = \frac{ \mathbf{G}_a \mathbf{G}_b^*}{|\mathbf{G}_a \mathbf{G}_b^*|} + +* Next the cross-correlation is converted back into the time domain via the inverse DFT: -* - Next the cross-correlation is converted back into the time domain via the inverse DFT: .. math:: - r = \mathcal{F}^{-1}\{R\} -* - Finally, it computes the peak location and computes a 5x5 weighted centroid around the peak to achieve sub-pixel accuracy. + r = \mathcal{F}^{-1}\{R\} + +* Finally, it computes the peak location and computes a 5x5 weighted centroid around the peak to achieve sub-pixel accuracy. + .. math:: - (\Delta x, \Delta y) = \texttt{weighted_centroid}\{\arg \max_{(x, y)}\{r\}\} + (\Delta x, \Delta y) = \texttt{weightedCentroid} \{\arg \max_{(x, y)}\{r\}\} .. seealso:: :ocv:func:`dft`,