mirror of
https://github.com/opencv/opencv.git
synced 2024-12-14 00:39:13 +08:00
157 lines
6.8 KiB
Markdown
157 lines
6.8 KiB
Markdown
|
Optical Flow {#tutorial_optical_flow}
|
||
|
============
|
||
|
|
||
|
Goal
|
||
|
----
|
||
|
|
||
|
In this chapter,
|
||
|
- We will understand the concepts of optical flow and its estimation using Lucas-Kanade
|
||
|
method.
|
||
|
- We will use functions like **cv.calcOpticalFlowPyrLK()** to track feature points in a
|
||
|
video.
|
||
|
- We will create a dense optical flow field using the **cv.calcOpticalFlowFarneback()** method.
|
||
|
|
||
|
Optical Flow
|
||
|
------------
|
||
|
|
||
|
Optical flow is the pattern of apparent motion of image objects between two consecutive frames
|
||
|
caused by the movemement of object or camera. It is 2D vector field where each vector is a
|
||
|
displacement vector showing the movement of points from first frame to second. Consider the image
|
||
|
below (Image Courtesy: [Wikipedia article on Optical Flow](http://en.wikipedia.org/wiki/Optical_flow)).
|
||
|
|
||
|
![image](images/optical_flow_basic1.jpg)
|
||
|
|
||
|
It shows a ball moving in 5 consecutive frames. The arrow shows its displacement vector. Optical
|
||
|
flow has many applications in areas like :
|
||
|
|
||
|
- Structure from Motion
|
||
|
- Video Compression
|
||
|
- Video Stabilization ...
|
||
|
|
||
|
Optical flow works on several assumptions:
|
||
|
|
||
|
-# The pixel intensities of an object do not change between consecutive frames.
|
||
|
2. Neighbouring pixels have similar motion.
|
||
|
|
||
|
Consider a pixel \f$I(x,y,t)\f$ in first frame (Check a new dimension, time, is added here. Earlier we
|
||
|
were working with images only, so no need of time). It moves by distance \f$(dx,dy)\f$ in next frame
|
||
|
taken after \f$dt\f$ time. So since those pixels are the same and intensity does not change, we can say,
|
||
|
|
||
|
\f[I(x,y,t) = I(x+dx, y+dy, t+dt)\f]
|
||
|
|
||
|
Then take taylor series approximation of right-hand side, remove common terms and divide by \f$dt\f$ to
|
||
|
get the following equation:
|
||
|
|
||
|
\f[f_x u + f_y v + f_t = 0 \;\f]
|
||
|
|
||
|
where:
|
||
|
|
||
|
\f[f_x = \frac{\partial f}{\partial x} \; ; \; f_y = \frac{\partial f}{\partial y}\f]\f[u = \frac{dx}{dt} \; ; \; v = \frac{dy}{dt}\f]
|
||
|
|
||
|
Above equation is called Optical Flow equation. In it, we can find \f$f_x\f$ and \f$f_y\f$, they are image
|
||
|
gradients. Similarly \f$f_t\f$ is the gradient along time. But \f$(u,v)\f$ is unknown. We cannot solve this
|
||
|
one equation with two unknown variables. So several methods are provided to solve this problem and
|
||
|
one of them is Lucas-Kanade.
|
||
|
|
||
|
### Lucas-Kanade method
|
||
|
|
||
|
We have seen an assumption before, that all the neighbouring pixels will have similar motion.
|
||
|
Lucas-Kanade method takes a 3x3 patch around the point. So all the 9 points have the same motion. We
|
||
|
can find \f$(f_x, f_y, f_t)\f$ for these 9 points. So now our problem becomes solving 9 equations with
|
||
|
two unknown variables which is over-determined. A better solution is obtained with least square fit
|
||
|
method. Below is the final solution which is two equation-two unknown problem and solve to get the
|
||
|
solution.
|
||
|
|
||
|
\f[\begin{bmatrix} u \\ v \end{bmatrix} =
|
||
|
\begin{bmatrix}
|
||
|
\sum_{i}{f_{x_i}}^2 & \sum_{i}{f_{x_i} f_{y_i} } \\
|
||
|
\sum_{i}{f_{x_i} f_{y_i}} & \sum_{i}{f_{y_i}}^2
|
||
|
\end{bmatrix}^{-1}
|
||
|
\begin{bmatrix}
|
||
|
- \sum_{i}{f_{x_i} f_{t_i}} \\
|
||
|
- \sum_{i}{f_{y_i} f_{t_i}}
|
||
|
\end{bmatrix}\f]
|
||
|
|
||
|
( Check similarity of inverse matrix with Harris corner detector. It denotes that corners are better
|
||
|
points to be tracked.)
|
||
|
|
||
|
So from the user point of view, the idea is simple, we give some points to track, we receive the optical
|
||
|
flow vectors of those points. But again there are some problems. Until now, we were dealing with
|
||
|
small motions, so it fails when there is a large motion. To deal with this we use pyramids. When we go up in
|
||
|
the pyramid, small motions are removed and large motions become small motions. So by applying
|
||
|
Lucas-Kanade there, we get optical flow along with the scale.
|
||
|
|
||
|
Lucas-Kanade Optical Flow in OpenCV
|
||
|
-----------------------------------
|
||
|
|
||
|
OpenCV provides all these in a single function, **cv.calcOpticalFlowPyrLK()**. Here, we create a
|
||
|
simple application which tracks some points in a video. To decide the points, we use
|
||
|
**cv.goodFeaturesToTrack()**. We take the first frame, detect some Shi-Tomasi corner points in it,
|
||
|
then we iteratively track those points using Lucas-Kanade optical flow. For the function
|
||
|
**cv.calcOpticalFlowPyrLK()** we pass the previous frame, previous points and next frame. It
|
||
|
returns next points along with some status numbers which has a value of 1 if next point is found,
|
||
|
else zero. We iteratively pass these next points as previous points in next step. See the code
|
||
|
below:
|
||
|
|
||
|
@add_toggle_cpp
|
||
|
- **Downloadable code**: Click
|
||
|
[here](https://github.com/opencv/opencv/tree/3.4/samples/cpp/tutorial_code/video/optical_flow/optical_flow.cpp)
|
||
|
|
||
|
- **Code at glance:**
|
||
|
@include samples/cpp/tutorial_code/video/optical_flow/optical_flow.cpp
|
||
|
@end_toggle
|
||
|
|
||
|
@add_toggle_python
|
||
|
- **Downloadable code**: Click
|
||
|
[here](https://github.com/opencv/opencv/tree/3.4/samples/python/tutorial_code/video/optical_flow/optical_flow.py)
|
||
|
|
||
|
- **Code at glance:**
|
||
|
@include samples/python/tutorial_code/video/optical_flow/optical_flow.py
|
||
|
@end_toggle
|
||
|
|
||
|
(This code doesn't check how correct are the next keypoints. So even if any feature point disappears
|
||
|
in image, there is a chance that optical flow finds the next point which may look close to it. So
|
||
|
actually for a robust tracking, corner points should be detected in particular intervals. OpenCV
|
||
|
samples comes up with such a sample which finds the feature points at every 5 frames. It also run a
|
||
|
backward-check of the optical flow points got to select only good ones. Check
|
||
|
samples/python/lk_track.py).
|
||
|
|
||
|
See the results we got:
|
||
|
|
||
|
![image](images/opticalflow_lk.jpg)
|
||
|
|
||
|
Dense Optical Flow in OpenCV
|
||
|
----------------------------
|
||
|
|
||
|
Lucas-Kanade method computes optical flow for a sparse feature set (in our example, corners detected
|
||
|
using Shi-Tomasi algorithm). OpenCV provides another algorithm to find the dense optical flow. It
|
||
|
computes the optical flow for all the points in the frame. It is based on Gunner Farneback's
|
||
|
algorithm which is explained in "Two-Frame Motion Estimation Based on Polynomial Expansion" by
|
||
|
Gunner Farneback in 2003.
|
||
|
|
||
|
Below sample shows how to find the dense optical flow using above algorithm. We get a 2-channel
|
||
|
array with optical flow vectors, \f$(u,v)\f$. We find their magnitude and direction. We color code the
|
||
|
result for better visualization. Direction corresponds to Hue value of the image. Magnitude
|
||
|
corresponds to Value plane. See the code below:
|
||
|
|
||
|
@add_toggle_cpp
|
||
|
- **Downloadable code**: Click
|
||
|
[here](https://github.com/opencv/opencv/tree/3.4/samples/cpp/tutorial_code/video/optical_flow/optical_flow_dense.cpp)
|
||
|
|
||
|
- **Code at glance:**
|
||
|
@include samples/cpp/tutorial_code/video/optical_flow/optical_flow_dense.cpp
|
||
|
@end_toggle
|
||
|
|
||
|
@add_toggle_python
|
||
|
- **Downloadable code**: Click
|
||
|
[here](https://github.com/opencv/opencv/tree/3.4/samples/python/tutorial_code/video/optical_flow/optical_flow_dense.py)
|
||
|
|
||
|
- **Code at glance:**
|
||
|
@include samples/python/tutorial_code/video/optical_flow/optical_flow_dense.py
|
||
|
@end_toggle
|
||
|
|
||
|
|
||
|
See the result below:
|
||
|
|
||
|
![image](images/opticalfb.jpg)
|