opticalFlowLKDoG

Object for estimating optical flow using Lucas-Kanade derivative of Gaussian method

Description

Create an optical flow object for estimating the direction and speed of moving objects using the Lucas-Kanade derivative of Gaussian (DoG) method. Use the object function estimateFlow to estimate the optical flow vectors. Using the reset object function, you can reset the internal state of the optical flow object.

Creation

Syntax

opticFlow = opticalFlowLKDoG

opticFlow = opticalFlowLKDoG(Name,Value)

Description

opticFlow = opticalFlowLKDoG returns an optical flow object that you can use to estimate the direction and speed of the moving objects in a video. The optical flow is estimated using the Lucas-Kanade derivative of Gaussian (DoG) method.

opticFlow = opticalFlowLKDoG(Name,Value) returns an optical flow object with properties specified as one or more Name,Value pair arguments. Any unspecified properties have default values. Enclose each property name in quotes.

For example, opticalFlowLKDoG('NumFrames',3)

Properties

NumFrames — Number of buffered frames

3 (default) | positive integer-valued scalar

Number of buffered frames for temporal smoothing, specified as a positive integer-valued scalar. As you increase this number, the optical flow estimation method becomes less robust to abrupt changes in the trajectory of the moving objects. The amount of delay in flow estimation depends on the value of NumFrames. The output flow corresponds to the image at t_flow = t_current − 0.5(NumFrames-1), where t_current is the time of the current image.

ImageFilterSigma — Standard deviation for image smoothing filter

1.5 | positive scalar

Standard deviation for image smoothing filter, specified as a positive scalar.

GradientFilterSigma — Standard deviation for gradient smoothing filter

1 | positive scalar

Standard deviation for gradient smoothing filter, specified as a positive scalar.

NoiseThreshold — Threshold for noise reduction

0.0039 (default) | positive scalar

Threshold for noise reduction, specified as a positive scalar. As you increase this number, the movement of the objects has less impact on optical flow calculation.

Object Functions

estimateFlow	Estimate optical flow
reset	Reset the internal state of the optical flow estimation object

Examples

Compute Optical Flow Using Lucas-Kanade DoG Method

Read a video file. Specify the timestamp of the frame to be read.

vidReader = VideoReader('visiontraffic.avi','CurrentTime',11);

Create an optical flow object for estimating the optical flow using Lucas-Kanade DoG method. Specify the threshold for noise reduction. The output is an optical flow object specifying the optical flow estimation method and its properties.

opticFlow = opticalFlowLKDoG('NoiseThreshold',0.0005)

opticFlow = 
  opticalFlowLKDoG with properties:

              NumFrames: 3
       ImageFilterSigma: 1.5000
    GradientFilterSigma: 1
         NoiseThreshold: 5.0000e-04

Create a custom figure window to visualize the optical flow vectors.

h = figure;
movegui(h);
hViewPanel = uipanel(h,'Position',[0 0 1 1],'Title','Plot of Optical Flow Vectors');
hPlot = axes(hViewPanel);

Read the image frames and convert to grayscale images. Estimate the optical flow from consecutive image frames. Display the current image frame and plot the optical flow vectors as quiver plot.

while hasFrame(vidReader)
    frameRGB = readFrame(vidReader);
    frameGray = im2gray(frameRGB);
    flow = estimateFlow(opticFlow,frameGray);
    imshow(frameRGB)
    hold on
    plot(flow,'DecimationFactor',[5 5],'ScaleFactor',35,'Parent',hPlot);
    hold off
    pause(10^-3)
end

Algorithms

To compute the optical flow between two images, you must solve this optical flow constraint equation:

$$I_{x}u+I_{y}v+I_t=0$$

.

• $$I_x$$, $$I_y$$, and $$I_t$$ are the spatiotemporal image brightness derivatives.

• u is the horizontal optical flow.

• v is the vertical optical flow.

Lucas-Kanade Derivative of Gaussian Method

The Lucas-Kanade method computes $$I_t$$ using a derivative of Gaussian filter.

To solve the optical flow constraint equation for u and v:

1. Compute $$I_x$$ and $$I_y$$ using the following steps:

   1. Use a Gaussian filter to perform temporal filtering. Specify the temporal filter characteristics such as the standard deviation and number of filter coefficients using the NumFrames property.

   2. Use a Gaussian filter and the derivative of a Gaussian filter to smooth the image using spatial filtering. Specify the standard deviation and length of the image smoothing filter using the ImageFilterSigma property.

2. Compute $$I_t$$ between images 1 and 2 using the following steps:

   1. Use the derivative of a Gaussian filter to perform temporal filtering. Specify the temporal filter characteristics such as the standard deviation and number of filter coefficients using the NumFrames property.

   2. Use the filter described in step 1b to perform spatial filtering on the output of the temporal filter.

3. Smooth the gradient components, $$I_x$$, $$I_y$$, and $$I_t$$, using a gradient smoothing filter. Use the GradientFilterSigma property to specify the standard deviation and the number of filter coefficients for the gradient smoothing filter.

4. Solve the 2-by-2 linear equations for each pixel using the following method:

   • If $$A=\left[\begin{array}{cc}a& b\\ b& c\end{array}\right]=\left[\begin{array}{cc}{\displaystyle \sum W^2{I}_x^2}& {\displaystyle \sum W^2{I}_x{I}_y}\\ {\displaystyle \sum W^2{I}_y{I}_x}& {\displaystyle \sum W^2{I}_y^2}\end{array}\right]$$

     Then the eigenvalues of A are $${\lambda }_i=\frac{a+c}{2}\pm \frac{\sqrt{4b^2+{(a-c)}^2}}{2};i=1,2$$

   • When the algorithm finds the eigenvalues, it compares them to the threshold, $$\tau$$, that corresponds to the value you enter for the NoiseThreshold property. The results fall into one of the following cases:

     Case 1: $${\lambda }_1\ge \tau$$ and $${\lambda }_2\ge \tau$$

     A is nonsingular, so the algorithm solves the system of equations using Cramer's rule.

     Case 2: $${\lambda }_1\ge \tau$$ and $${\lambda }_2<\tau$$

     A is singular (noninvertible), so the algorithm normalizes the gradient flow to calculate u and v.

     Case 3: $${\lambda }_1<\tau$$ and $${\lambda }_2<\tau$$

     The optical flow, u and v, is 0.

References

[1] Barron, J. L., D. J. Fleet, S. S. Beauchemin, and T. A. Burkitt. “ Performance of optical flow techniques.” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR),236-242. Champaign, IL: CVPR, 1992.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced in R2015a