opticalFlowLK

Object for estimating optical flow using Lucas-Kanade method

Description

Create an optical flow object for estimating the direction and speed of a moving object using the Lucas-Kanade 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 = opticalFlowLK

opticFlow = opticalFlowLK('NoiseThreshold',threshold)

Description

opticFlow = opticalFlowLK 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 method.

opticFlow = opticalFlowLK('NoiseThreshold',threshold) returns an optical flow object with the property 'NoiseThreshold' specified as a Name,Value pair. Enclose the property name in quotes.

For example, opticalFlowLK('NoiseThreshold',0.05)

example

Properties

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`threshold` — 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

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Compute Optical Flow Using Lucas-Kanade Algorithm

Open Live Script

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 method. Specify the threshold for noise reduction. The output is an optical flow object specifying the optical flow estimation method and its properties.

opticFlow = opticalFlowLK('NoiseThreshold',0.009);

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',10,'Parent',hPlot);
    hold off
    pause(10^-3)
end

Figure contains an axes object and an object of type uipanel. The hidden axes object contains 2 objects of type image, quiver.

Algorithms

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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 Method

To solve the optical flow constraint equation for u and v, the Lucas-Kanade method divides the original image into smaller sections and assumes a constant velocity in each section. Then it performs a weighted, least-square fit of the optical flow constraint equation to a constant model for ${[\begin{matrix} u & v \end{matrix}]}^{T}$ in each section $Ω$ . The method achieves this fit by minimizing this equation:

$\sum_{x \in Ω} W^{2} {[I_{x} u + I_{y} v + I_{t}]}^{2}$

W is a window function that emphasizes the constraints at the center of each section. The solution to the minimization problem is

$[\begin{matrix} \sum W^{2} I_{x}^{2} & \sum W^{2} I_{x} I_{y} \\ \sum W^{2} I_{y} I_{x} & \sum W^{2} I_{y}^{2} \end{matrix}] [\begin{matrix} u \\ v \end{matrix}] = - [\begin{matrix} \sum W^{2} I_{x} I_{t} \\ \sum W^{2} I_{y} I_{t} \end{matrix}]$

The Lucas-Kanade method computes $I_{t}$ using a difference filter, [-1 1].

u and v are solved as follows:

Compute $I_{x}$ and $I_{y}$ using the kernel $[\begin{matrix} - 1 & 8 & 0 & \begin{matrix} - 8 & 1 \end{matrix} \end{matrix}] / 12$ and its transposed form.
Compute $I_{t}$ between images 1 and 2 using the $[\begin{matrix} - 1 & 1 \end{matrix}]$ kernel.
Smooth the gradient components, $I_{x}$ , $I_{y}$ , and $I_{t}$ , using a separable and isotropic 5-by-5 element kernel whose effective 1-D coefficients are $[\begin{matrix} \begin{matrix} 1 & 4 \end{matrix} & 6 & 4 & 1 \end{matrix}] / 16$ .
Solve the 2-by-2 linear equations for each pixel using the following method:
- If $A = [\begin{matrix} a & b \\ b & c \end{matrix}] = [\begin{matrix} \sum W^{2} I_{x}^{2} & \sum W^{2} I_{x} I_{y} \\ \sum W^{2} I_{y} I_{x} & \sum W^{2} I_{y}^{2} \end{matrix}]$
  Then the eigenvalues of A are $λ_{i} = \frac{a + c}{2} \pm \frac{\sqrt{4 b^{2} + {(a - c)}^{2}}}{2}; i = 1, 2$
- The eigenvalues are compared to the threshold, $τ$ , that corresponds to the value you enter for the threshold for noise reduction. The results fall into one of the following cases:
  Case 1: $λ_{1} \geq τ$ and $λ_{2} \geq τ$
  A is nonsingular, the system of equations are solved using Cramer's rule.
  Case 2: $λ_{1} \geq τ$ and $λ_{2} < τ$
  A is singular (noninvertible), the gradient flow is normalized to calculate u and v.
  Case 3: $λ_{1} < τ$ and $λ_{2} < τ$
  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

opticalFlowLK

Description

Creation

Syntax

Description

Properties

threshold — Threshold for noise reduction 0.0039 (default) | positive scalar

Object Functions

Examples

Compute Optical Flow Using Lucas-Kanade Algorithm

Algorithms

Lucas-Kanade Method

References

Extended Capabilities

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

Version History

See Also

`threshold` — Threshold for noise reduction
`0.0039` (default) | positive scalar

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