How do phase values are able to capture motion from video?

In summary, the phase spectrum of an image contains important structural information and plays a crucial role in analyzing video signals. The temporal variations of phase values can capture the dynamic characteristics of a video sequence, such as global motion. This is because the Fourier Transform, which is used to compute the phase spectrum, has a property where the phase of a signal changes depending on its spatial position. Therefore, as an object moves through an image, the phase values will change, allowing for the detection of motion. However, this technique may not be effective for detecting rotational motion, as the phase values for this type of movement may remain unchanged.
  • #1
ramdas
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hi everyone,i know that the phase spectrum contains most of the structural information about the image.But i want to know more about importance of phase spectrum related to video signals.

I have read that temporal variations of phase values are able to capture most of the dynamical characteristics of the video sequence like global motion in the video.But i don't understand how it does?
so can anybody explain the relation between motion and phase? It will be very useful for my project.thank you..
 
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  • #2
I'm not familiar with this; do you have a reference to the technique? An article would be nice.
 
  • #5
global motion in images is a simple translation of all pixels.
ƒ(x-x0, y-y0)

when you apply the Fourier transform, the intensity spectrum F(u,v) stays exactly the same.
Only the phase spectrum changes, e-j2∏(ux0/m, vy0/N).
The only thing not completely described by the phase angle are the gained/lossed pixels along the edge.
 
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  • #6
@MrSparkle thank u sir for your explanation .but will please explain it with any real time or simple example so that my concept will get cleared properly .thank you very much
 
  • #7
let us consider an example ...

please consider any real time example say video of rotating wheel or wave (or video of traffic on road.) if i compute its phase spectrum using Fourier Transform,the phase values captures motion of rotating wheel (or complex motion of moving car on road). but i don't understand how it does?By which property of Fourier transform could u explain it to me?
 
  • #8
I personally can't explain it any better than by saying it is simply a basic property of the Fourier Transform. This is what you get when you do the math.

ƒ(x-x0, y-y0) ⇔ F(u,v)e-j2∏(ux0/M, vy0/N)

Do you have access to MATLAB? It you want real world examples, I highly recommend it since you can pretty easily create your own. Here is a link for the basic commands. http://matlabgeeks.com/tips-tutorials/how-to-do-a-2-d-fourier-transform-in-matlab/ I'm sure you could do the same stuff in R or Octave, but I don't have much experience with those.
 
  • #9
@MrSparkle ok i will look at what you are talking about.thank you for helping ;-)
 
  • #10
To understand the effect first consider the simple case of a one dimensional line of length TwoPi. Along that line we consider values of a simple cosine wave of unit amplitude and frequency. When we take the FT of the cosine signal that is spaced along the line, we get a value of 1 for the cosine coefficient of spatial frequency 1. The sine coefficient for spatial frequency 1, along with all other spatial frequency components, should remain zero. The phase vector for the fundamental frequency cosine wave will lie initially along the +x axis.

As the cosine wave is shifted sideways in space, the phase of the spatial frequency component will sweep in a circle from the +cosine through the +sine, then to -cosine, through -sine and back to +cosine. In effect the phasor rotates once each time the wave is moved sideways by one spatial period. The direction of spatial frequency vector rotation is decided by the direction of spatial movement. (This is the "fourier shift theorem" at work).

If the whole of a complex pattern moves sideways the phase of the fundamental will change at a rate proportional to the rate of image movement. Small movements may show up better in higher harmonics, but the highest harmonics will look like noise as the image content will change significantly with larger movements, (unless the panorama wraps around).

A small object that crosses a large fixed background will cause only a small difference in the real cos(1) and imaginary sin(1) coefficients. The point of the phase vectors will move in a small circle due to the small contribution of the part of the image that moves. If you plot all the phase vectors on an Argand diagram then as the image pans, you will see the entire constellation of phase vectors rotating about the centre. But if only a small object moves across the background you will see all the phase vectors rotate in small circles about the tips of their average background values. The rate of rotation will be proportional to the spatial frequency.

The principle of superposition does not usually apply to spatial images because an object that moves against the background does not sum to the background, it replaces background with an object. In effect the moving object removes other information temporarily while substituting it's own. Likewise, when a camera pans, information is lost on one side of the image as new information appears on the other.

So it is easy to detect a transverse movement through phase, but a rotating wheel is hard to detect using phase in a 2D spatial transform, unless it rolls across the image.
 
  • #11
thanks sir for your feed but i have doubt.

Baluncore said:
To understand the effect first consider the simple case of a one dimensional line of length TwoPi. Along that line we consider values of a simple cosine wave of unit amplitude and frequency. When we take the FT of the cosine signal that is spaced along the line, we get a value of 1 for the cosine coefficient of spatial frequency 1. The sine coefficient for spatial frequency 1, along with all other spatial frequency components, should remain zero. The phase vector for the fundamental frequency cosine wave will lie initially along the +x axis.

As the cosine wave is shifted sideways in space, the phase of the spatial frequency component will sweep in a circle from the +cosine through the +sine, then to -cosine, through -sine and back to +cosine. In effect the phasor rotates once each time the wave is moved sideways by one spatial period. The direction of spatial frequency vector rotation is decided by the direction of spatial movement. (This is the "fourier shift theorem" at work).

If the whole of a complex pattern moves sideways the phase of the fundamental will change at a rate proportional to the rate of image movement. Small movements may show up better in higher harmonics, but the highest harmonics will look like noise as the image content will change significantly with larger movements, (unless the panorama wraps around).

A small object that crosses a large fixed background will cause only a small difference in the real cos(1) and imaginary sin(1) coefficients. The point of the phase vectors will move in a small circle due to the small contribution of the part of the image that moves. If you plot all the phase vectors on an Argand diagram then as the image pans, you will see the entire constellation of phase vectors rotating about the centre. But if only a small object moves across the background you will see all the phase vectors rotate in small circles about the tips of their average background values. The rate of rotation will be proportional to the spatial frequency.

The principle of superposition does not usually apply to spatial images because an object that moves against the background does not sum to the background, it replaces background with an object. In effect the moving object removes other information temporarily while substituting it's own. Likewise, when a camera pans, information is lost on one side of the image as new information appears on the other.

So it is easy to detect a transverse movement through phase, but a rotating wheel is hard to detect using phase in a 2D spatial transform, unless it rolls across the image.

thank you very much sir for your feedback.but i have one doubt.can i say here that due to motion , moving part pixel magnitude (intensity) values becomes dominant (means its intensity values are increased so much for waveform or moving wheel or cars) compared to stationary(background or stationary road) part magnitude (intensities) in frames ? ? ? please correct me if i am going wrong...Thank u again
 
  • #12
The Fourier Transform is orthogonal, it spreads all spatial pixel values into all spatial frequency vectors.
If the moving part is significantly brighter than the background, then the movement will be easier to detect.

You need to do numerical experiments with moving one dimensional patterns to see the phase rotation effect.
Alternatively, you can approach the effect from the mathematical side by investigating the Fourier Shift Theorem.
 
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1. What are phase values in the context of video motion capture?

Phase values refer to the specific angles or positions of an object or body part captured in a video frame. They can be used to represent and track the movement of an object or body part over time.

2. How do phase values differ from other methods of motion capture?

Phase values differ from other methods of motion capture, such as optical motion capture or marker-based motion capture, in that they do not require physical markers or sensors. Instead, they use algorithms to analyze changes in pixel values and patterns in video frames to track motion.

3. How do phase values capture motion from video?

Phase values capture motion from video by analyzing changes in the phase of pixel values over time. This is achieved through Fourier analysis, which breaks down the video signal into its component frequencies and calculates the phase of each frequency. By tracking changes in phase over time, the movement of an object or body part can be accurately captured.

4. What are the advantages of using phase values for motion capture?

One advantage of using phase values for motion capture is that they do not require physical markers or sensors, making the process less intrusive and more convenient. Additionally, phase values can be captured from standard video footage, eliminating the need for specialized equipment. They also allow for more accurate and precise tracking of motion compared to other methods.

5. Are there any limitations to using phase values for motion capture?

While phase values have many advantages for motion capture, they do have some limitations. They may not be suitable for capturing extremely fast or complex movements, as they rely on changes in pixel values and may not be able to accurately track rapid movements. Additionally, changes in lighting or background may affect the accuracy of phase value tracking.

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