\cvarg{orientation}{Motion gradient orientation image; calculated by the function \cvCPyCross{CalcMotionGradient}}
\cvarg{mask}{Mask image. It may be a conjunction of a valid gradient mask, obtained with \cvCPyCross{CalcMotionGradient} and the mask of the region, whose direction needs to be calculated}
\cvarg{mhi}{Motion history image}
\cvarg{timestamp}{Current time in milliseconds or other units, it is better to store time passed to \cvCPyCross{UpdateMotionHistory} before and reuse it here, because running \cvCPyCross{UpdateMotionHistory} and \cvCPyCross{CalcMotionGradient} on large images may take some time}
\cvarg{duration}{Maximal duration of motion track in milliseconds, the same as \cvCPyCross{UpdateMotionHistory}}
\end{description}
The function calculates the general
motion direction in the selected region and returns the angle between
0 degrees and 360 degrees . At first the function builds the orientation histogram
and finds the basic orientation as a coordinate of the histogram
maximum. After that the function calculates the shift relative to the
basic orientation as a weighted sum of all of the orientation vectors: the more
recent the motion, the greater the weight. The resultant angle is
a circular sum of the basic orientation and the shift.
\cvCPyFunc{CalcMotionGradient}
Calculates the gradient orientation of a motion history image.
where both $Dx(x,y)$ and $Dy(x,y)$ signs are taken into account (as in the \cvCPyCross{CartToPolar} function). After that \texttt{mask} is filled to indicate where the orientation is valid (see the \texttt{delta1} and \texttt{delta2} description).
The function finds the minimum ($m(x,y)$) and maximum ($M(x,y)$) mhi values over each pixel $(x,y)$ neighborhood and assumes the gradient is valid only if
\cvarg{curr}{Second frame, at time \texttt{t + dt}}
\cvarg{prevPyr}{Buffer for the pyramid for the first frame. If the pointer is not \texttt{NULL} , the buffer must have a sufficient size to store the pyramid from level \texttt{1} to level \texttt{level} ; the total size of \texttt{(image\_width+8)*image\_height/3} bytes is sufficient}
\cvarg{currPyr}{Similar to \texttt{prevPyr}, used for the second frame}
\cvarg{prevFeatures}{Array of points for which the flow needs to be found}
\cvarg{currFeatures}{Array of 2D points containing the calculated new positions of the input features in the second image}
\ifC
\cvarg{count}{Number of feature points}
\fi
\cvarg{winSize}{Size of the search window of each pyramid level}
\cvarg{level}{Maximal pyramid level number. If \texttt{0} , pyramids are not used (single level), if \texttt{1} , two levels are used, etc}
\cvarg{status}{Array. Every element of the array is set to \texttt{1} if the flow for the corresponding feature has been found, \texttt{0} otherwise}
\cvarg{track\_error}{Array of double numbers containing the difference between patches around the original and moved points. Optional parameter; can be \texttt{NULL}}
\cvarg{criteria}{Specifies when the iteration process of finding the flow for each point on each pyramid level should be stopped}
\cvarg{flags}{Miscellaneous flags:
\begin{description}
\cvarg{CV\_LKFLOWPyr\_A\_READY}{pyramid for the first frame is precalculated before the call}
\cvarg{CV\_LKFLOWPyr\_B\_READY}{ pyramid for the second frame is precalculated before the call}
\cvC{\cvarg{CV\_LKFLOW\_INITIAL\_GUESSES}{array B contains initial coordinates of features before the function call}}
\end{description}}
\cvPy{\cvarg{guesses}{optional array of estimated coordinates of features in second frame, with same length as \texttt{prevFeatures}}}
\end{description}
The function implements the sparse iterative version of the Lucas-Kanade optical flow in pyramids
\cite{Bouguet00}
. It calculates the coordinates of the feature points on the current video
frame given their coordinates on the previous frame. The function finds
the coordinates with sub-pixel accuracy.
Both parameters \texttt{prevPyr} and \texttt{currPyr} comply with the
following rules: if the image pointer is 0, the function allocates the
buffer internally, calculates the pyramid, and releases the buffer after
processing. Otherwise, the function calculates the pyramid and stores
it in the buffer unless the flag \texttt{CV\_LKFLOWPyr\_A[B]\_READY}
is set. The image should be large enough to fit the Gaussian pyramid
data. After the function call both pyramids are calculated and the
readiness flag for the corresponding image can be set in the next call
(i.e., typically, for all the image pairs except the very first one
\cvarg{prob\_image}{Back projection of object histogram (see \cvCPyCross{CalcBackProject})}
\cvarg{window}{Initial search window}
\cvarg{criteria}{Criteria applied to determine when the window search should be finished}
\cvarg{comp}{Resultant structure that contains the converged search window coordinates (\texttt{comp->rect} field) and the sum of all of the pixels inside the window (\texttt{comp->area} field)}
\ifC% {
\cvarg{box}{Circumscribed box for the object. If not \texttt{NULL}, it contains object size and orientation}
\else% }{
\cvarg{box}{Circumscribed box for the object.}
\fi% }
\end{description}
The function implements the CAMSHIFT object tracking algrorithm
\cite{Bradski98}.
First, it finds an object center using \cvCPyCross{MeanShift} and, after that, calculates the object size and orientation. The function returns number of iterations made within \cvCPyCross{MeanShift}.
The \texttt{CamShiftTracker} class declared in cv.hpp implements the color object tracker that uses the function.
\ifC% {
\subsection{CvConDensation}
ConDenstation state.
\begin{lstlisting}
typedef struct CvConDensation
{
int MP; //Dimension of measurement vector
int DP; // Dimension of state vector
float* DynamMatr; // Matrix of the linear Dynamics system
float* State; // Vector of State
int SamplesNum; // Number of the Samples
float** flSamples; // array of the Sample Vectors
float** flNewSamples; // temporary array of the Sample Vectors
float* flConfidence; // Confidence for each Sample
float* flCumulative; // Cumulative confidence
float* Temp; // Temporary vector
float* RandomSample; // RandomVector to update sample set
CvRandState* RandS; // Array of structures to generate random vectors
} CvConDensation;
\end{lstlisting}
The structure \texttt{CvConDensation} stores the CONditional DENSity propagATION tracker state. The information about the algorithm can be found at \url{http://www.dai.ed.ac.uk/CVonline/LOCAL\_COPIES/ISARD1/condensation.html}.
\cvCPyFunc{CreateConDensation}
Allocates the ConDensation filter structure.
\cvdefC{
CvConDensation* cvCreateConDensation( \par int dynam\_params,\par int measure\_params,\par int sample\_count );
}
\begin{description}
\cvarg{dynam\_params}{Dimension of the state vector}
\cvarg{measure\_params}{Dimension of the measurement vector}
\cvarg{sample\_count}{Number of samples}
\end{description}
The function creates a \texttt{CvConDensation} structure and returns a pointer to the structure.
\cvCPyFunc{ConDensInitSampleSet}
Initializes the sample set for the ConDensation algorithm.
The structure \texttt{CvKalman} is used to keep the Kalman filter
state. It is created by the \cvCPyCross{CreateKalman} function, updated
by the \cvCPyCross{KalmanPredict} and \cvCPyCross{KalmanCorrect} functions
\ifC
and released by the \cvCPyCross{ReleaseKalman} function
\fi
. Normally, the
structure is used for the standard Kalman filter (notation and the
formulas below are borrowed from the excellent Kalman tutorial
\cite{Welch95})
\[
\begin{array}{l}
x_k=A \cdot x_{k-1}+B \cdot u_k+w_k\\
z_k=H \cdot x_k+v_k
\end{array}
\]
where:
\[
\begin{array}{l l}
x_k\;(x_{k-1})&\text{state of the system at the moment \emph{k} (\emph{k-1})}\\
z_k &\text{measurement of the system state at the moment \emph{k}}\\
u_k &\text{external control applied at the moment \emph{k}}
\end{array}
\]
$w_k$ and $v_k$ are normally-distributed process and measurement noise, respectively:
\[
\begin{array}{l}
p(w) \sim N(0,Q)\\
p(v) \sim N(0,R)
\end{array}
\]
that is,
$Q$ process noise covariance matrix, constant or variable,
$R$ measurement noise covariance matrix, constant or variable
In the case of the standard Kalman filter, all of the matrices: A, B, H, Q and R are initialized once after the \cvCPyCross{CvKalman} structure is allocated via \cvCPyCross{CreateKalman}. However, the same structure and the same functions may be used to simulate the extended Kalman filter by linearizing the extended Kalman filter equation in the current system state neighborhood, in this case A, B, H (and, probably, Q and R) should be updated on every step.
\cvCPyFunc{CreateKalman}
Allocates the Kalman filter structure.
\cvdefC{
CvKalman* cvCreateKalman( \par int dynam\_params,\par int measure\_params,\par int control\_params=0 );
\cvarg{prob\_image}{Back projection of the object histogram (see \cvCPyCross{CalcBackProject})}
\cvarg{window}{Initial search window}
\cvarg{criteria}{Criteria applied to determine when the window search should be finished}
\cvarg{comp}{Resultant structure that contains the converged search window coordinates (\texttt{comp->rect} field) and the sum of all of the pixels inside the window (\texttt{comp->area} field)}
\end{description}
The function iterates to find the object center
given its back projection and initial position of search window. The
iterations are made until the search window center moves by less than
the given value and/or until the function has done the maximum number
of iterations. The function returns the number of iterations made.
\cvarg{coeff\_usage}{Different uses of the previous three parameters:
\begin{description}
\cvarg{CV\_VALUE}{indicates that each of \texttt{alpha, beta, gamma} is a pointer to a single value to be used for all points;}
\cvarg{CV\_ARRAY}{indicates that each of \texttt{alpha, beta, gamma} is a pointer to an array of coefficients different for all the points of the snake. All the arrays must have the size equal to the contour size.}
\cvarg{win}{Size of neighborhood of every point used to search the minimum, both \texttt{win.width} and \texttt{win.height} must be odd}
\cvarg{criteria}{Termination criteria}
\cvarg{calc\_gradient}{Gradient flag; if not 0, the function calculates the gradient magnitude for every image pixel and consideres it as the energy field, otherwise the input image itself is considered}
\end{description}
The function updates the snake in order to minimize its
total energy that is a sum of internal energy that depends on the contour
shape (the smoother contour is, the smaller internal energy is) and
external energy that depends on the energy field and reaches minimum at
the local energy extremums that correspond to the image edges in the case
of using an image gradient.
The parameter \texttt{criteria.epsilon} is used to define the minimal
number of points that must be moved during any iteration to keep the
iteration process running.
If at some iteration the number of moved points is less
than \texttt{criteria.epsilon} or the function performed
\texttt{criteria.max\_iter} iterations, the function terminates.
\cvarg{prevImg}{The first 8-bit single-channel or 3-channel input image}
\cvarg{nextImg}{The second input image of the same size and the same type as \texttt{prevImg}}
\cvarg{prevPts}{Vector of points for which the flow needs to be found}
\cvarg{nextPts}{The output vector of points containing the calculated new positions of the input features in the second image}
\cvarg{status}{The output status vector. Each element of the vector is set to 1 if the flow for the corresponding features has been found, 0 otherwise}
\cvarg{err}{The output vector that will contain the difference between patches around the original and moved points}
\cvarg{winSize}{Size of the search window at each pyramid level}
\cvarg{maxLevel}{0-based maximal pyramid level number. If 0, pyramids are not used (single level), if 1, two levels are used etc.}
\cvarg{criteria}{Specifies the termination criteria of the iterative search algorithm (after the specified maximum number of iterations \texttt{criteria.maxCount} or when the search window moves by less than \texttt{criteria.epsilon}}
\cvarg{derivLambda}{The relative weight of the spatial image derivatives impact to the optical flow estimation. If \texttt{derivLambda=0}, only the image intensity is used, if \texttt{derivLambda=1}, only derivatives are used. Any other values between 0 and 1 means that both derivatives and the image intensity are used (in the corresponding proportions).}
\cvarg{flags}{The operation flags:
\begin{description}
\cvarg{OPTFLOW\_USE\_INITIAL\_FLOW}{use initial estimations stored in \texttt{nextPts}. If the flag is not set, then initially $\texttt{nextPts}\leftarrow\texttt{prevPts}$}
\end{description}}
\end{description}
The function implements the sparse iterative version of the Lucas-Kanade optical flow in pyramids, see \cite{Bouguet00}.
\cvCppFunc{calcOpticalFlowFarneback}
Computes dense optical flow using Gunnar Farneback's algorithm
Mat\& flow, double pyrScale, int levels, int winsize,\par
int iterations, int polyN, double polySigma, int flags );}
\begin{description}
\cvarg{prevImg}{The first 8-bit single-channel input image}
\cvarg{nextImg}{The second input image of the same size and the same type as \texttt{prevImg}}
\cvarg{flow}{The computed flow image; will have the same size as \texttt{prevImg} and type \texttt{CV\_32FC2}}
\cvarg{pyrScale}{Specifies the image scale (<1) to build the pyramids for each image. \texttt{pyrScale=0.5} means the classical pyramid, where each next layer is twice smaller than the previous}
\cvarg{levels}{The number of pyramid layers, including the initial image. \texttt{levels=1} means that no extra layers are created and only the original images are used}
\cvarg{winsize}{The averaging window size; The larger values increase the algorithm robustness to image noise and give more chances for fast motion detection, but yield more blurred motion field}
\cvarg{iterations}{The number of iterations the algorithm does at each pyramid level}
\cvarg{polyN}{Size of the pixel neighborhood used to find polynomial expansion in each pixel. The larger values mean that the image will be approximated with smoother surfaces, yielding more robust algorithm and more blurred motion field. Typically, \texttt{polyN}=5 or 7}
\cvarg{polySigma}{Standard deviation of the Gaussian that is used to smooth derivatives that are used as a basis for the polynomial expansion. For \texttt{polyN=5} you can set \texttt{polySigma=1.1}, for \texttt{polyN=7} a good value would be \texttt{polySigma=1.5}}
\cvarg{flags}{The operation flags; can be a combination of the following:
\begin{description}
\cvarg{OPTFLOW\_USE\_INITIAL\_FLOW}{Use the input \texttt{flow} as the initial flow approximation}
\cvarg{OPTFLOW\_FARNEBACK\_GAUSSIAN}{Use a Gaussian $\texttt{winsize}\times\texttt{winsize}$ filter instead of box filter of the same size for optical flow estimation. Usually, this option gives more accurate flow than with a box filter, at the cost of lower speed (and normally \texttt{winsize} for a Gaussian window should be set to a larger value to achieve the same level of robustness)}
\end{description}}
\end{description}
The function finds optical flow for each \texttt{prevImg} pixel using the alorithm so that
{0}{if $\texttt{silhouette}(x,y)=0$ and $\texttt{mhi} < (\texttt{timestamp}-\texttt{duration})$}
{\texttt{mhi}(x,y)}{otherwise}
\]
That is, MHI pixels where motion occurs are set to the current \texttt{timestamp}, while the pixels where motion happened last time a long time ago are cleared.
The function, together with \cvCppCross{calcMotionGradient} and \cvCppCross{calcGlobalOrientation}, implements the motion templates technique, described in \cite{Davis97} and \cite{Bradski00}.
See also the OpenCV sample \texttt{motempl.c} that demonstrates the use of all the motion template functions.
\cvCppFunc{calcMotionGradient}
Calculates the gradient orientation of a motion history image.
\cvarg{mhi}{Motion history single-channel floating-point image}
\cvarg{mask}{The output mask image; will have the type \texttt{CV\_8UC1} and the same size as \texttt{mhi}. Its non-zero elements will mark pixels where the motion gradient data is correct}
\cvarg{orientation}{The output motion gradient orientation image; will have the same type and the same size as \texttt{mhi}. Each pixel of it will the motion orientation in degrees, from 0 to 360.}
\cvarg{delta1, delta2}{The minimal and maximal allowed difference between \texttt{mhi} values within a pixel neighorhood. That is, the function finds the minimum ($m(x,y)$) and maximum ($M(x,y)$) \texttt{mhi} values over $3\times3$ neighborhood of each pixel and marks the motion orientation at $(x, y)$ as valid only if
(in fact, \cvCppCross{fastArctan} and \cvCppCross{phase} are used, so that the computed angle is measured in degrees and covers the full range 0..360). Also, the \texttt{mask} is filled to indicate pixels where the computed angle is valid.
\cvCppFunc{calcGlobalOrientation}
Calculates the global motion orientation in some selected region.
\cvarg{orientation}{Motion gradient orientation image, calculated by the function \cvCppCross{calcMotionGradient}}
\cvarg{mask}{Mask image. It may be a conjunction of a valid gradient mask, also calculated by \cvCppCross{calcMotionGradient}, and the mask of the region, whose direction needs to be calculated}
\cvarg{mhi}{The motion history image, calculated by \cvCppCross{updateMotionHistory}}
\cvarg{timestamp}{The timestamp passed to \cvCppCross{updateMotionHistory}}
\cvarg{duration}{Maximal duration of motion track in milliseconds, passed to \cvCppCross{updateMotionHistory}}
\end{description}
The function calculates the average
motion direction in the selected region and returns the angle between
0 degrees and 360 degrees. The average direction is computed from
the weighted orientation histogram, where a recent motion has larger
weight and the motion occurred in the past has smaller weight, as recorded in \texttt{mhi}.
\cvarg{probImage}{Back projection of the object histogram; see \cvCppCross{calcBackProject}}
\cvarg{window}{Initial search window}
\cvarg{criteria}{Stop criteria for the underlying \cvCppCross{meanShift}}
\end{description}
The function implements the CAMSHIFT object tracking algrorithm
\cite{Bradski98}.
First, it finds an object center using \cvCppCross{meanShift} and then adjust the window size and finds the optimal rotation. The function returns the rotated rectangle structure that includes the object position, size and the orientation. The next position of the search window can be obtained with \texttt{RotatedRect::boundingRect()}.
See the OpenCV sample \texttt{camshiftdemo.c} that tracks colored objects.
\cvarg{probImage}{Back projection of the object histogram; see \cvCppCross{calcBackProject}}
\cvarg{window}{Initial search window}
\cvarg{criteria}{The stop criteria for the iterative search algorithm}
\end{description}
The function implements iterative object search algorithm. It takes the object back projection on input and the initial position. The mass center in \texttt{window} of the back projection image is computed and the search window center shifts to the mass center. The procedure is repeated until the specified number of iterations \texttt{criteria.maxCount} is done or until the window center shifts by less than \texttt{criteria.epsilon}. The algorithm is used inside \cvCppCross{CamShift} and, unlike \cvCppCross{CamShift}, the search window size or orientation do not change during the search. You can simply pass the output of \cvCppCross{calcBackProject} to this function, but better results can be obtained if you pre-filter the back projection and remove the noise (e.g. by retrieving connected components with \cvCppCross{findContours}, throwing away contours with small area (\cvCppCross{contourArea}) and rendering the remaining contours with \cvCppCross{drawContours})
\cvclass{KalmanFilter}
Kalman filter class
\begin{lstlisting}
class KalmanFilter
{
public:
KalmanFilter();newline
KalmanFilter(int dynamParams, int measureParams, int controlParams=0);newline
void init(int dynamParams, int measureParams, int controlParams=0);newline
Mat transitionMatrix; // state transition matrix (A)
Mat controlMatrix; // control matrix (B)
// (it is not used if there is no control)
Mat measurementMatrix; // measurement matrix (H)
Mat processNoiseCov; // process noise covariance matrix (Q)
Mat measurementNoiseCov;// measurement noise covariance matrix (R)
Mat errorCovPre; // priori error estimate covariance matrix (P'(k)):
// P'(k)=A*P(k-1)*At + Q)*/
Mat gain; // Kalman gain matrix (K(k)):
// K(k)=P'(k)*Ht*inv(H*P'(k)*Ht+R)
Mat errorCovPost; // posteriori error estimate covariance matrix (P(k)):
// P(k)=(I-K(k)*H)*P'(k)
...
};
\end{lstlisting}
The class implements standard Kalman filter \url{http://en.wikipedia.org/wiki/Kalman_filter}. However, you can modify \texttt{transitionMatrix}, \texttt{controlMatrix} and \texttt{measurementMatrix} to get the extended Kalman filter functionality. See the OpenCV sample \texttt{kalman.c}
