Motion Analysis and Object Tracking¶

Acc¶

Acc(image, sum, mask=NULL) → None¶

Adds a frame to an accumulator.

Parameters:	image (`CvArr`) – Input image, 1- or 3-channel, 8-bit or 32-bit floating point. (each channel of multi-channel image is processed independently) sum (`CvArr`) – Accumulator with the same number of channels as input image, 32-bit or 64-bit floating-point mask (`CvArr`) – Optional operation mask

The function adds the whole image image or its selected region to the accumulator sum :

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

CalcGlobalOrientation¶

CalcGlobalOrientation(orientation, mask, mhi, timestamp, duration) → float¶

Calculates the global motion orientation of some selected region.

Parameters:

orientation (CvArr) – Motion gradient orientation image; calculated by the function CalcMotionGradient
mask (CvArr) – Mask image. It may be a conjunction of a valid gradient mask, obtained with CalcMotionGradient and the mask of the region, whose direction needs to be calculated
mhi (CvArr) – Motion history image
timestamp (float) – Current time in milliseconds or other units, it is better to store time passed to UpdateMotionHistory before and reuse it here, because running UpdateMotionHistory and CalcMotionGradient on large images may take some time
duration (float) – Maximal duration of motion track in milliseconds, the same as UpdateMotionHistory

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.

CalcMotionGradient¶

CalcMotionGradient(mhi, mask, orientation, delta1, delta2, apertureSize=3) → None¶

Calculates the gradient orientation of a motion history image.

Parameters:

mhi (CvArr) – Motion history image
mask (CvArr) – Mask image; marks pixels where the motion gradient data is correct; output parameter
orientation (CvArr) – Motion gradient orientation image; contains angles from 0 to ~360 degrees
delta1 (float) – See below
delta2 (float) – See below
apertureSize (int) – Aperture size of derivative operators used by the function: CV _ SCHARR, 1, 3, 5 or 7 (see Sobel )

The function calculates the derivatives $Dx$ and $Dy$ of mhi and then calculates gradient orientation as:

$\texttt{orientation} (x,y)= \arctan{\frac{Dy(x,y)}{Dx(x,y)}}$

where both $Dx(x,y)$ and $Dy(x,y)$ signs are taken into account (as in the CartToPolar function). After that mask is filled to indicate where the orientation is valid (see the delta1 and 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

$\min ( \texttt{delta1} , \texttt{delta2} ) \le M(x,y)-m(x,y) \le \max ( \texttt{delta1} , \texttt{delta2} ).$

CalcOpticalFlowBM¶

CalcOpticalFlowBM(prev, curr, blockSize, shiftSize, max_range, usePrevious, velx, vely) → None¶

Calculates the optical flow for two images by using the block matching method.

Parameters:

prev (CvArr) – First image, 8-bit, single-channel
curr (CvArr) – Second image, 8-bit, single-channel
blockSize (CvSize) – Size of basic blocks that are compared
shiftSize (CvSize) – Block coordinate increments
max_range (CvSize) – Size of the scanned neighborhood in pixels around the block
usePrevious (int) – Uses the previous (input) velocity field
velx (CvArr) –
Horizontal component of the optical flow of

$\left \lfloor \frac{\texttt{prev->width} - \texttt{blockSize.width}}{\texttt{shiftSize.width}} \right \rfloor \times \left \lfloor \frac{\texttt{prev->height} - \texttt{blockSize.height}}{\texttt{shiftSize.height}} \right \rfloor$

size, 32-bit floating-point, single-channel
vely (CvArr) – Vertical component of the optical flow of the same size velx , 32-bit floating-point, single-channel

The function calculates the optical flow for overlapped blocks $\texttt{blockSize.width} \times \texttt{blockSize.height}$ pixels each, thus the velocity fields are smaller than the original images. For every block in prev the functions tries to find a similar block in curr in some neighborhood of the original block or shifted by (velx(x0,y0),vely(x0,y0)) block as has been calculated by previous function call (if usePrevious=1 )

CalcOpticalFlowHS¶

CalcOpticalFlowHS(prev, curr, usePrevious, velx, vely, lambda, criteria) → None¶

Calculates the optical flow for two images.

Parameters:

prev (CvArr) – First image, 8-bit, single-channel
curr (CvArr) – Second image, 8-bit, single-channel
usePrevious (int) – Uses the previous (input) velocity field
velx (CvArr) – Horizontal component of the optical flow of the same size as input images, 32-bit floating-point, single-channel
vely (CvArr) – Vertical component of the optical flow of the same size as input images, 32-bit floating-point, single-channel
lambda (float) – Lagrangian multiplier
criteria (CvTermCriteria) – Criteria of termination of velocity computing

The function computes the flow for every pixel of the first input image using the Horn and Schunck algorithm Horn81 .

CalcOpticalFlowLK¶

CalcOpticalFlowLK(prev, curr, winSize, velx, vely) → None¶

Calculates the optical flow for two images.

Parameters:

prev (CvArr) – First image, 8-bit, single-channel
curr (CvArr) – Second image, 8-bit, single-channel
winSize (CvSize) – Size of the averaging window used for grouping pixels
velx (CvArr) – Horizontal component of the optical flow of the same size as input images, 32-bit floating-point, single-channel
vely (CvArr) – Vertical component of the optical flow of the same size as input images, 32-bit floating-point, single-channel

The function computes the flow for every pixel of the first input image using the Lucas and Kanade algorithm Lucas81 .

CalcOpticalFlowPyrLK¶

CalcOpticalFlowPyrLK(prev, curr, prevPyr, currPyr, prevFeatures, winSize, level, criteria, flags, guesses = None) -> (currFeatures, status, track_error)¶

Calculates the optical flow for a sparse feature set using the iterative Lucas-Kanade method with pyramids.

Parameters:

prev (CvArr) – First frame, at time t
curr (CvArr) – Second frame, at time t + dt
prevPyr (CvArr) – Buffer for the pyramid for the first frame. If the pointer is not NULL , the buffer must have a sufficient size to store the pyramid from level 1 to level level ; the total size of (image_width+8)*image_height/3 bytes is sufficient
currPyr (CvArr) – Similar to prevPyr , used for the second frame
prevFeatures (CvPoint2D32f) – Array of points for which the flow needs to be found
currFeatures (CvPoint2D32f) – Array of 2D points containing the calculated new positions of the input features in the second image
winSize (CvSize) – Size of the search window of each pyramid level
level (int) – Maximal pyramid level number. If 0 , pyramids are not used (single level), if 1 , two levels are used, etc
status (str) – Array. Every element of the array is set to 1 if the flow for the corresponding feature has been found, 0 otherwise
track_error (float) – Array of double numbers containing the difference between patches around the original and moved points. Optional parameter; can be NULL
criteria (CvTermCriteria) – Specifies when the iteration process of finding the flow for each point on each pyramid level should be stopped
flags (int) –
Miscellaneous flags:
- CV_LKFLOWPyr_A_READY pyramid for the first frame is precalculated before the call
- CV_LKFLOWPyr_B_READY pyramid for the second frame is precalculated before the call
guesses (CvPoint2D32f) – optional array of estimated coordinates of features in second frame, with same length as prevFeatures

The function implements the sparse iterative version of the Lucas-Kanade optical flow in pyramids 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 prevPyr and 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 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 CV_LKFLOWPyr_A_READY is set).

CamShift¶

CamShift(prob_image, window, criteria)-> (int, comp, box)¶

Finds the object center, size, and orientation.

Parameters:

prob_image (CvArr) – Back projection of object histogram (see CalcBackProject )
window (CvRect) – Initial search window
criteria (CvTermCriteria) – Criteria applied to determine when the window search should be finished
comp (CvConnectedComp) – Resultant structure that contains the converged search window coordinates ( comp->rect field) and the sum of all of the pixels inside the window ( comp->area field)
box (CvBox2D) – Circumscribed box for the object.

The function implements the CAMSHIFT object tracking algrorithm Bradski98 . First, it finds an object center using MeanShift and, after that, calculates the object size and orientation. The function returns number of iterations made within MeanShift .

The CamShiftTracker class declared in cv.hpp implements the color object tracker that uses the function.

CvKalman¶

class CvKalman¶

Kalman filter state.

MP¶

number of measurement vector dimensions

DP¶

number of state vector dimensions

CP¶

number of control vector dimensions

state_pre¶

predicted state (x’(k)): x(k)=A*x(k-1)+B*u(k)

state_post¶

corrected state (x(k)): x(k)=x’(k)+K(k)*(z(k)-H*x’(k))

transition_matrix¶

state transition matrix (A)

control_matrix¶

control matrix (B) (it is not used if there is no control)

measurement_matrix¶

measurement matrix (H)

process_noise_cov¶

process noise covariance matrix (Q)

measurement_noise_cov¶

measurement noise covariance matrix (R)

error_cov_pre¶

priori error estimate covariance matrix (P’(k)): P’(k)=A*P(k-1)*At + Q

gain¶

Kalman gain matrix (K(k)): K(k)=P’(k)*Ht*inv(H*P’(k)*Ht+R)

error_cov_post¶

posteriori error estimate covariance matrix (P(k)): P(k)=(I-K(k)*H)*P’(k)

The structure CvKalman is used to keep the Kalman filter state. It is created by the CreateKalman function, updated by the KalmanPredict and KalmanCorrect functions . Normally, the structure is used for the standard Kalman filter (notation and the formulas below are borrowed from the excellent Kalman tutorial 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 CvKalman structure is allocated via 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.

CreateKalman¶

CreateKalman(dynam_params, measure_params, control_params=0) → CvKalman¶

Allocates the Kalman filter structure.

Parameters:	dynam_params (int) – dimensionality of the state vector measure_params (int) – dimensionality of the measurement vector control_params (int) – dimensionality of the control vector

The function allocates CvKalman and all its matrices and initializes them somehow.

KalmanCorrect¶

KalmanCorrect(kalman, measurement) → cvmat¶

Adjusts the model state.

Parameters:	kalman (`CvKalman`) – Kalman filter object returned by CreateKalman measurement (`CvMat`) – CvMat containing the measurement vector

The function adjusts the stochastic model state on the basis of the given measurement of the model state:

$\begin{array}{l} K_k=P'_k \cdot H^T \cdot (H \cdot P'_k \cdot H^T+R)^{-1} \\ x_k=x'_k+K_k \cdot (z_k-H \cdot x'_k) \\ P_k=(I-K_k \cdot H) \cdot P'_k \end{array}$

where

$z_k$	given measurement ( `mesurement` parameter)
$K_k$	Kalman “gain” matrix.

The function stores the adjusted state at kalman->state_post and returns it on output.

KalmanPredict¶

KalmanPredict(kalman, control=None) → cvmat¶

Estimates the subsequent model state.

Parameters:	kalman (`CvKalman`) – Kalman filter object returned by CreateKalman control (`CvMat`) – Control vector $u_k$ , should be NULL iff there is no external control ( `control_params` =0)

The function estimates the subsequent stochastic model state by its current state and stores it at kalman->state_pre :

$\begin{array}{l} x'_k=A \cdot x_{k-1}+B \cdot u_k \\ P'_k=A \cdot P_{k-1}+A^T + Q \end{array}$

where

$x'_k$	is predicted state `kalman->state_pre` ,
$x_{k-1}$	is corrected state on the previous step `kalman->state_post` (should be initialized somehow in the beginning, zero vector by default),
$u_k$	is external control ( `control` parameter),
$P'_k$	is priori error covariance matrix `kalman->error_cov_pre`
$P_{k-1}$	is posteriori error covariance matrix on the previous step `kalman->error_cov_post` (should be initialized somehow in the beginning, identity matrix by default),

The function returns the estimated state.

KalmanUpdateByMeasurement¶

Synonym for KalmanCorrect

KalmanUpdateByTime¶

Synonym for KalmanPredict

MeanShift¶

MeanShift(prob_image, window, criteria) → comp¶

Finds the object center on back projection.

Parameters:

prob_image (CvArr) – Back projection of the object histogram (see CalcBackProject )
window (CvRect) – Initial search window
criteria (CvTermCriteria) – Criteria applied to determine when the window search should be finished
comp (CvConnectedComp) – Resultant structure that contains the converged search window coordinates ( comp->rect field) and the sum of all of the pixels inside the window ( comp->area field)

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.

MultiplyAcc¶

MultiplyAcc(image1, image2, acc, mask=NULL) → None¶

Adds the product of two input images to the accumulator.

Parameters:	image1 (`CvArr`) – First input image, 1- or 3-channel, 8-bit or 32-bit floating point (each channel of multi-channel image is processed independently) image2 (`CvArr`) – Second input image, the same format as the first one acc (`CvArr`) – Accumulator with the same number of channels as input images, 32-bit or 64-bit floating-point mask (`CvArr`) – Optional operation mask

The function adds the product of 2 images or their selected regions to the accumulator acc :

$\texttt{acc} (x,y) \leftarrow \texttt{acc} (x,y) + \texttt{image1} (x,y) \cdot \texttt{image2} (x,y) \quad \text{if} \quad \texttt{mask} (x,y) \ne 0$

RunningAvg¶

RunningAvg(image, acc, alpha, mask=NULL) → None¶

Updates the running average.

Parameters:	image (`CvArr`) – Input image, 1- or 3-channel, 8-bit or 32-bit floating point (each channel of multi-channel image is processed independently) acc (`CvArr`) – Accumulator with the same number of channels as input image, 32-bit or 64-bit floating-point alpha (float) – Weight of input image mask (`CvArr`) – Optional operation mask

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

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

where $\alpha$ regulates the update speed (how fast the accumulator forgets about previous frames).

SegmentMotion¶

SegmentMotion(mhi, seg_mask, storage, timestamp, seg_thresh) → None¶

Segments a whole motion into separate moving parts.

Parameters:

mhi (CvArr) – Motion history image
seg_mask (CvArr) – Image where the mask found should be stored, single-channel, 32-bit floating-point
storage (CvMemStorage) – Memory storage that will contain a sequence of motion connected components
timestamp (float) – Current time in milliseconds or other units
seg_thresh (float) – Segmentation threshold; recommended to be equal to the interval between motion history “steps” or greater

The function finds all of the motion segments and marks them in seg_mask with individual values (1,2,...). It also returns a sequence of CvConnectedComp structures, one for each motion component. After that the motion direction for every component can be calculated with CalcGlobalOrientation using the extracted mask of the particular component Cmp .

SnakeImage¶

SnakeImage(image, points, alpha, beta, gamma, win, criteria, calc_gradient=1) → new_points¶

Changes the contour position to minimize its energy.

Parameters:

image (IplImage) – The source image or external energy field
points (CvPoints) – Contour points (snake)
alpha (sequence of float) – Weight[s] of continuity energy, single float or a list of floats, one for each contour point
beta (sequence of float) – Weight[s] of curvature energy, similar to alpha
gamma (sequence of float) – Weight[s] of image energy, similar to alpha
win (CvSize) – Size of neighborhood of every point used to search the minimum, both win.width and win.height must be odd
criteria (CvTermCriteria) – Termination criteria
calc_gradient (int) – 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

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 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 criteria.epsilon or the function performed criteria.max_iter iterations, the function terminates.

The function returns the updated list of points.

SquareAcc¶

SquareAcc(image, sqsum, mask=NULL) → None¶

Adds the square of the source image to the accumulator.

Parameters:	image (`CvArr`) – Input image, 1- or 3-channel, 8-bit or 32-bit floating point (each channel of multi-channel image is processed independently) sqsum (`CvArr`) – Accumulator with the same number of channels as input image, 32-bit or 64-bit floating-point mask (`CvArr`) – Optional operation mask

The function adds the input image image or its selected region, raised to power 2, to the accumulator sqsum :

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

UpdateMotionHistory¶

UpdateMotionHistory(silhouette, mhi, timestamp, duration) → None¶

Updates the motion history image by a moving silhouette.

Parameters:	silhouette (`CvArr`) – Silhouette mask that has non-zero pixels where the motion occurs mhi (`CvArr`) – Motion history image, that is updated by the function (single-channel, 32-bit floating-point) timestamp (float) – Current time in milliseconds or other units duration (float) – Maximal duration of the motion track in the same units as `timestamp`

The function updates the motion history image as following:

$\texttt{mhi} (x,y)= \forkthree{\texttt{timestamp}}{if $\texttt{silhouette}(x,y) \ne 0$}{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 timestamp, while the pixels where motion happened far ago are cleared.

Motion Analysis and Object Tracking¶

Acc¶

CalcGlobalOrientation¶

CalcMotionGradient¶

CalcOpticalFlowBM¶

CalcOpticalFlowHS¶

CalcOpticalFlowLK¶

CalcOpticalFlowPyrLK¶

CamShift¶

CvKalman¶

CreateKalman¶

KalmanCorrect¶

KalmanPredict¶

KalmanUpdateByMeasurement¶

KalmanUpdateByTime¶

MeanShift¶

MultiplyAcc¶

RunningAvg¶

SegmentMotion¶

SnakeImage¶

SquareAcc¶

UpdateMotionHistory¶

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Motion Analysis and Object Tracking¶

Acc¶

CalcGlobalOrientation¶

CalcMotionGradient¶

CalcOpticalFlowBM¶

CalcOpticalFlowHS¶

CalcOpticalFlowLK¶

CalcOpticalFlowPyrLK¶

CamShift¶

CvKalman¶

CreateKalman¶

KalmanCorrect¶

KalmanPredict¶

KalmanUpdateByMeasurement¶

KalmanUpdateByTime¶

MeanShift¶

MultiplyAcc¶

RunningAvg¶

SegmentMotion¶

SnakeImage¶

SquareAcc¶

UpdateMotionHistory¶

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