# Motion Analysis and Object Tracking

## Overview

// global functions

void
cv::accumulate(
InputArray src,
InputOutputArray dst,
InputArray mask = noArray()
);

void
cv::accumulateProduct(
InputArray src1,
InputArray src2,
InputOutputArray dst,
InputArray mask = noArray()
);

void
cv::accumulateSquare(
InputArray src,
InputOutputArray dst,
InputArray mask = noArray()
);

void
cv::accumulateWeighted(
InputArray src,
InputOutputArray dst,
double alpha,
InputArray mask = noArray()
);

void
cv::createHanningWindow(
OutputArray dst,
Size winSize,
int type
);

Point2d
cv::phaseCorrelate(
InputArray src1,
InputArray src2,
InputArray window = noArray(),
double* response = 0
);


## Detailed Documentation

### Global Functions

void
cv::accumulate(
InputArray src,
InputOutputArray dst,
InputArray mask = noArray()
)


Adds an image to the accumulator.

The function adds src or some of its elements to dst :

$\texttt{dst} (x,y) \leftarrow \texttt{dst} (x,y) + \texttt{src} (x,y) \quad \text{if} \quad \texttt{mask} (x,y) \ne 0$

The function supports multi-channel images. Each channel is processed independently.

The functions accumulate* can be used, for example, to collect statistics of a scene background viewed by a still camera and for the further foreground-background segmentation.

Parameters:

 src Input image of type CV_8UC(n), CV_16UC(n), CV_32FC(n) or CV_64FC(n), where n is a positive integer. dst Accumulator image with the same number of channels as input image, and a depth of CV_32F or CV_64F. mask Optional operation mask.

void
cv::accumulateProduct(
InputArray src1,
InputArray src2,
InputOutputArray dst,
InputArray mask = noArray()
)


Adds the per-element product of two input images to the accumulator.

The function adds the product of two images or their selected regions to the accumulator dst :

$\texttt{dst} (x,y) \leftarrow \texttt{dst} (x,y) + \texttt{src1} (x,y) \cdot \texttt{src2} (x,y) \quad \text{if} \quad \texttt{mask} (x,y) \ne 0$

The function supports multi-channel images. Each channel is processed independently.

Parameters:

 src1 First input image, 1- or 3-channel, 8-bit or 32-bit floating point. src2 Second input image of the same type and the same size as src1 . dst Accumulator with the same number of channels as input images, 32-bit or 64-bit floating-point. mask Optional operation mask.

void
cv::accumulateSquare(
InputArray src,
InputOutputArray dst,
InputArray mask = noArray()
)


Adds the square of a source image to the accumulator.

The function adds the input image src or its selected region, raised to a power of 2, to the accumulator dst :

$\texttt{dst} (x,y) \leftarrow \texttt{dst} (x,y) + \texttt{src} (x,y)^2 \quad \text{if} \quad \texttt{mask} (x,y) \ne 0$

The function supports multi-channel images. Each channel is processed independently.

Parameters:

 src Input image as 1- or 3-channel, 8-bit or 32-bit floating point. dst Accumulator image with the same number of channels as input image, 32-bit or 64-bit floating-point. mask Optional operation mask.

void
cv::accumulateWeighted(
InputArray src,
InputOutputArray dst,
double alpha,
InputArray mask = noArray()
)


Updates a running average.

The function calculates the weighted sum of the input image src and the accumulator dst so that dst becomes a running average of a frame sequence:

$\texttt{dst} (x,y) \leftarrow (1- \texttt{alpha} ) \cdot \texttt{dst} (x,y) + \texttt{alpha} \cdot \texttt{src} (x,y) \quad \text{if} \quad \texttt{mask} (x,y) \ne 0$

That is, alpha regulates the update speed (how fast the accumulator “forgets” about earlier images). The function supports multi-channel images. Each channel is processed independently.

Parameters:

 src Input image as 1- or 3-channel, 8-bit or 32-bit floating point. dst Accumulator image with the same number of channels as input image, 32-bit or 64-bit floating-point. alpha Weight of the input image. mask Optional operation mask.

void
cv::createHanningWindow(
OutputArray dst,
Size winSize,
int type
)


This function computes a Hanning window coefficients in two dimensions.

See (http://en.wikipedia.org/wiki/Hann_function) and (http://en.wikipedia.org/wiki/Window_function) for more information.

An example is shown below:

// create hanning window of size 100x100 and type CV_32F
Mat hann;
createHanningWindow(hann, Size(100, 100), CV_32F);


Parameters:

 dst Destination array to place Hann coefficients in winSize The window size specifications type Created array type
Point2d
cv::phaseCorrelate(
InputArray src1,
InputArray src2,
InputArray window = noArray(),
double* response = 0
)


The function is used to detect translational shifts that occur between two images.

The operation takes advantage of the Fourier shift theorem for detecting the translational shift in the frequency domain. It can be used for fast image registration as well as motion estimation. For more information please see http://en.wikipedia.org/wiki/Phase_correlation

Calculates the cross-power spectrum of two supplied source arrays. The arrays are padded if needed with getOptimalDFTSize.

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.

• Next it computes the forward DFTs of each source array:

$\mathbf{G}_a = \mathcal{F}\{src_1\}, \; \mathbf{G}_b = \mathcal{F}\{src_2\}$

where $$\mathcal{F}$$ is the forward DFT.

• It then computes the cross-power spectrum of each frequency domain array:

$R = \frac{ \mathbf{G}_a \mathbf{G}_b^*}{|\mathbf{G}_a \mathbf{G}_b^*|}$
• Next the cross-correlation is converted back into the time domain via the inverse DFT:

$r = \mathcal{F}^{-1}\{R\}$
• Finally, it computes the peak location and computes a 5x5 weighted centroid around the peak to achieve sub-pixel accuracy.

$(\Delta x, \Delta y) = \texttt{weightedCentroid} \{\arg \max_{(x, y)}\{r\}\}$
• If non-zero, the response parameter is computed as the sum of the elements of r within the 5x5 centroid around the peak location. It is normalized to a maximum of 1 (meaning there is a single peak) and will be smaller when there are multiple peaks.

Parameters:

 src1 Source floating point array (CV_32FC1 or CV_64FC1) src2 Source floating point array (CV_32FC1 or CV_64FC1) window Floating point array with windowing coefficients to reduce edge effects (optional). response Signal power within the 5x5 centroid around the peak, between 0 and 1 (optional).

Returns:

detected phase shift (sub-pixel) between the two arrays.