A couple of years ago Habré slipped two articles that mentioned an interesting algorithm. Articles, however, were written nechitabilno. In the style of "news» ( 1 , 2 ), but the link to the site was present, it was possible to find out details on place (algorithm for authorship MIT). And there was magic. Absolutely magical algorithm that allows to see the invisible. Both authors Habré did not notice it and focus on the fact that the algorithm allows us to see the pulse. Having missed the most important thing.

The algorithm allows us to strengthen the movement, invisible eye, to show things that have never been seen alive. Video slightly higher - presentation c cfqnf MIT second part of the algorithm. Microsaccades, which are listed starting from the 29th of a second, previously observed only as a reflection of the mirrors mounted on the pupils. And here they are seen through the eyes.

A couple of weeks ago, I again came across the articles. I immediately became curious: what people did in those two years to prepare? But ... the void. It has defined the following fun week and a half. I want to make the same algorithm and find out what you can do with it and why it is still not in every smartphone, at least for a pulse.

The article will be a lot of mat videos, pictures, a bit of code and answers to the questions.

Let's start with the math (I will not stick to any one particular article, and will interfere in different parts of the different articles, for a smoother narrative). A research group has two major works on the algorithmic part:

1) Eulerian Video Magnification for Revealing Subtle Changes in the World

2) Phase-Based Video Motion Processing

In the first study realized amplitude approach, more rough and fast. I took it as a basis. In the second paper except the amplitude of the signal phase is used. This allows for a much more realistic and clear picture. The video above was applied specifically to this work. Minus - a more complex algorithm and processing, deliberately departing from the real-time without the use of the video card.

#### begin? H4> What is the gain of movement? Strengthening movement, is when we predict in which direction the signal will mix and move it farther in that direction.

Suppose we have a one-dimensional receiver. At the receiver, we see that the signal I (x, t) = f (x). In the picture drawn on a black (to some point t) .In the next time signal I (x, t + 1) = f (x + Δ) (blue). Amplify this signal, which means receive a signal I '(x, t + 1) = f (x + (1 + α) Δ). Here α - gain. Expanding it in a Taylor series it can be expressed as:

Let:

What is B? Roughly speaking it is I (x, t + 1) - I (x, t). Draw:

Of course, this is inaccurate, but as a rough approximation descend (blue graph pokazyaet form such "priblizhenongo" signal). If we multiply B by (1 + α) and it will be "strengthening" of the signal. Get (red graph):

In real frame may contain several movements, each of which will go at different speeds. The above method - linear prediction, without elaboration, he breaks off. But, there is a classical approach to solve this problem, which was used in the work - to spread the movement from the frequency response (both spatial and temporal).

In the first stage decomposition image spatial frequency. This stage also implements receive differential ∂f (x) / ∂x. In first work not tell how they implement it. In second work, by using a phase approach, the amplitude and phase filters Gabbora considered a different order:

About what I did, taking the filter:

And normalized the value to

Here l - the distance of the pixel from the center of the filter. Of course, I'm a little faked taking a filter for only one window value σ. This has accelerated computing. This gives a slightly more blurred picture, but I decided not to strive for accuracy.

Returning to formulas. Suppose we want to amplify the signal, giving a characteristic response at the frequency ω in the temporary frame sequence. We have already picked up the characteristic spatial filter with a window σ. This gives us an approximate differential at each point. As is clear from the formula - there is only a temporary function giving feedback on our progress and gain. Multiplied by the sine of the frequency you want to strengthen (and it will function giving the response time). We obtain:

Of course, much easier than in the original article, but a little less of a problem with the speed.

#### Code and the result. H4> source to the first article laid out in open access to Matlab :. It would seem, why reinvent the wheel and write your own? But there were a number of reasons, largely tied to Matlab:

As a result, the logic operation is obtained:

It's simple to outrageous. For example incremental summation with the frame so generally realized:

#### A little bit about the beauty h4> course at MIT love beautiful results. And, therefore, try to make them as the most beautiful way. As a result, the viewer gets the impression that this particular, it is an integer. Unfortunately not. Swells the vein can be seen only when properly set lighting (shadow should draw pattern of the skin). Change the color of the face - just a good camera without auto-correction, with the right light and put the man in which there are clear problems with the heart (in the video is a large man and Preterm birth). For example in the example with the negro, whose heart all right, do not you see the brightness fluctuations of the skin, and the gain changes the shade of micromotion (shadow lies neatly from the top down).

#### Quantitative characteristics h4> Still. In the video clearly visible breathing and pulse. Let's try to get them. The simplest thing that comes to mind - summed difference between adjacent frames. Since when breathing fluctuates almost the entire body - this characteristic should be visible.

The resulting graph passage through Fourier transformation, considering the spectrum (in the graph collect statistics somewhere in 5 minutes by summing the spectra calculated at 16-second intervals).

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Visible clear peak at a frequency of 0.6-1.3, is not characteristic of the noise. Since breathing is not sinusoidal process, and the process of having two distinct spike (with breaths), the frequency difference images must equal double the frequency of breathing. Respiratory rate I was somewhere 10 breaths in 30 seconds (0.3 HZ). Its doubling - 0.6HZ. That is approximately equal to the revealed trace maximum. But, of course, the exact value can not speak. Besides breathing pulled plenty of fine motor skills of the body, which greatly spoils the picture.

There is an interesting peak at 2.625HZ. Apparently it makes its way to the power leveling matrix. The matrix creep band that successfully produce a maximum at this frequency.

Incidentally, the double pulse frequency should lie approximately in the same range, and thus the method should not work on it. And indeed:

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This spectrum can not find a pulse.

In one of his works is given MIT is another way to measure heart rate, calculate flow on the face and determine its frequency of this flow. So I did (on the schedule too spectra):

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Best seen in the chart on which I put the number of maxima of the spectrum:

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Why maximum heart rate * 3 I do not know how to explain it, but this precisely is the maximum and is tied to the pulse :)

I would like to mention only that for the pulse in this way need to sit up straight and do not move. In a game of Starcraft is not possible, the frequency is not removed. Oh ... And this idea! We'll have to get a heart rate monitor, it's interesting now become!

#### So, the result h4> As a result, I am quite clearly formed an opinion about the boundaries of the algorithm, it became clear what his limitations:

** Why he did not become popular for measuring the pulse rate? B> Quality for Web-cameras computer grabs at the border, or even lacking. In android is clearly not enough performance. Remain special equipment for the professional measurement. But they are very expensive and not stable to external conditions (illumination, flickering light, darkness, shaking), and the quality will be lower than those proven tools shooting pulse. **

** Why is not the algorithm used to evaluate the fluctuations of houses, bridges, cranes? B> Again. Special devices are cheaper and provide greater accuracy. **

** And where it can be used and whether it is possible at all? B> I think you can. Wherever necessary visibility. Scientific shooting a movie, educational programs. The training of psychiatrists, psychologists, pick up artist (see the tiniest of human movement, increased facial expressions). For the analysis of the negotiations. Of course, it is not necessary to use a simpler version of the algorithm, and the version that they have in the last work and is based on a phased approach. In this real-time all of this will be difficult to see, the performance will not be enough, except that everything vidyuhi rasparalelit. But you can see after the fact. **

** Nothing new under the sun h4> When you read the work of comrades and watch videos sneaking suspicion. Somewhere I saw it all. Here you look and think, think. And then they show a video of how using the same algorithm take and stabilize motion of the Moon, removing noise atmosphere. And then in a flash: "Yes this is the noise suppression algorithm, only with positive feedback !!". And instead of suppressing spurious motion, it strengthens them. If we take α & lt; 1, then the connection again and negative movement away! **

Of course, in the suppression algorithm of motion and shaking slightly different math and slightly different approach. But in fact exactly the same spectral analysis of space-time tube.

While saying that there svisnul algorithm silly. At MIT really noticed one little interesting feature, developed it and got a whole theory with such beautiful and magical images.

** And finally: the programmer, be careful! H4> algorithm, according to the notes on the site of a patent. Use allowed for educational purposes. Of course, in Russia there is no patenting algorithms. But be careful, if you can do something based on it. Outside of Russia, it may be illegal. **

** Basement h4> **

* Z.YU. And tell me the heart rate monitor, which could throw off the data on the PC and, preferably, a thread interface for Android had? I> *

Source:

The algorithm allows us to strengthen the movement, invisible eye, to show things that have never been seen alive. Video slightly higher - presentation c cfqnf MIT second part of the algorithm. Microsaccades, which are listed starting from the 29th of a second, previously observed only as a reflection of the mirrors mounted on the pupils. And here they are seen through the eyes.

A couple of weeks ago, I again came across the articles. I immediately became curious: what people did in those two years to prepare? But ... the void. It has defined the following fun week and a half. I want to make the same algorithm and find out what you can do with it and why it is still not in every smartphone, at least for a pulse.

The article will be a lot of mat videos, pictures, a bit of code and answers to the questions.

Let's start with the math (I will not stick to any one particular article, and will interfere in different parts of the different articles, for a smoother narrative). A research group has two major works on the algorithmic part:

1) Eulerian Video Magnification for Revealing Subtle Changes in the World

2) Phase-Based Video Motion Processing

In the first study realized amplitude approach, more rough and fast. I took it as a basis. In the second paper except the amplitude of the signal phase is used. This allows for a much more realistic and clear picture. The video above was applied specifically to this work. Minus - a more complex algorithm and processing, deliberately departing from the real-time without the use of the video card.

Suppose we have a one-dimensional receiver. At the receiver, we see that the signal I (x, t) = f (x). In the picture drawn on a black (to some point t) .In the next time signal I (x, t + 1) = f (x + Δ) (blue). Amplify this signal, which means receive a signal I '(x, t + 1) = f (x + (1 + α) Δ). Here α - gain. Expanding it in a Taylor series it can be expressed as:

Let:

What is B? Roughly speaking it is I (x, t + 1) - I (x, t). Draw:

Of course, this is inaccurate, but as a rough approximation descend (blue graph pokazyaet form such "priblizhenongo" signal). If we multiply B by (1 + α) and it will be "strengthening" of the signal. Get (red graph):

In real frame may contain several movements, each of which will go at different speeds. The above method - linear prediction, without elaboration, he breaks off. But, there is a classical approach to solve this problem, which was used in the work - to spread the movement from the frequency response (both spatial and temporal).

In the first stage decomposition image spatial frequency. This stage also implements receive differential ∂f (x) / ∂x. In first work not tell how they implement it. In second work, by using a phase approach, the amplitude and phase filters Gabbora considered a different order:

About what I did, taking the filter:

And normalized the value to

Here l - the distance of the pixel from the center of the filter. Of course, I'm a little faked taking a filter for only one window value σ. This has accelerated computing. This gives a slightly more blurred picture, but I decided not to strive for accuracy.

Returning to formulas. Suppose we want to amplify the signal, giving a characteristic response at the frequency ω in the temporary frame sequence. We have already picked up the characteristic spatial filter with a window σ. This gives us an approximate differential at each point. As is clear from the formula - there is only a temporary function giving feedback on our progress and gain. Multiplied by the sine of the frequency you want to strengthen (and it will function giving the response time). We obtain:

Of course, much easier than in the original article, but a little less of a problem with the speed.

- If you then come to mind to do something reasonable and applicable to the Matlab code much harder to use than C # + OpenCV, ported in a couple of hours with ++.
- The original code was guided to work with saved video that has a constant bitrate. To be able to use the camera is connected to a computer having a variable bit rate need to change the logic.
- The original code implements the easiest of their algorithms without buns. Implement a slightly more sophisticated version with buns - already half the work. Moreover, despite the fact that the algorithm was the original, its input parameters are not those articles.
- The original code periodically led to a dead hang computer (even without the blue screen). Maybe just me, but you uncomfortable.
- In the original code was only console mode. Do everything in visual Matlab, which I know is much worse VS, it would be much longer than rewrite everything. Sources < / a> I posted on github.com and commented in detail. The program implements capture video from the camera and its analysis in real time. Optimization turned slightly to the left, but you can get locked up, expanding options. That circumcised in the name of optimization:
- Use a frame with a reduced size. Greatly speeds up the work. On the form did not manage to deduce the size of the frame, but if you open the code, the line: & quot; _capture.QueryFrame (). Convert & lt; Bgr, float & gt; (). PyrDown (). PyrDown (); & quot; this is it

As a result, the logic operation is obtained:

It's simple to outrageous. For example incremental summation with the frame so generally realized:

& lt; code & gt; for (int x = 0; x & lt; Ic [ccp] .I.Width; x ++) for (int y = 0; y & lt; Ic [ccp] .I.Height; y ++) { FF2.Data [y, x, 0] = Alpha * FF2.Data [y, x, 0] / counter; ImToDisp.Data [y, x, 0] = (byte) Math.Max (0, Math.Min ((FF2.Data [y, x, 0] + ImToDisp.Data [y, x, 0]), 255) ); } & Lt; / code & gt; pre> (Yes, I know that with OpenCV is not the best way)

Somewhere in the 90% of the code is not the kernel, I kit around it. But the realization of the nucleus gives already a good result. It is seen as inflated chest for a few tens of centimeters in breathing, is seen as swells Vienna as shakes his head in time with the pulse.

Here is explained in detail why the bobble head of the pulse. In fact it returns from stuffing of blood in heart:

The resulting graph passage through Fourier transformation, considering the spectrum (in the graph collect statistics somewhere in 5 minutes by summing the spectra calculated at 16-second intervals).

Visible clear peak at a frequency of 0.6-1.3, is not characteristic of the noise. Since breathing is not sinusoidal process, and the process of having two distinct spike (with breaths), the frequency difference images must equal double the frequency of breathing. Respiratory rate I was somewhere 10 breaths in 30 seconds (0.3 HZ). Its doubling - 0.6HZ. That is approximately equal to the revealed trace maximum. But, of course, the exact value can not speak. Besides breathing pulled plenty of fine motor skills of the body, which greatly spoils the picture.

There is an interesting peak at 2.625HZ. Apparently it makes its way to the power leveling matrix. The matrix creep band that successfully produce a maximum at this frequency.

Incidentally, the double pulse frequency should lie approximately in the same range, and thus the method should not work on it. And indeed:

This spectrum can not find a pulse.

In one of his works is given MIT is another way to measure heart rate, calculate flow on the face and determine its frequency of this flow. So I did (on the schedule too spectra):

Best seen in the chart on which I put the number of maxima of the spectrum:

Why maximum heart rate * 3 I do not know how to explain it, but this precisely is the maximum and is tied to the pulse :)

I would like to mention only that for the pulse in this way need to sit up straight and do not move. In a game of Starcraft is not possible, the frequency is not removed. Oh ... And this idea! We'll have to get a heart rate monitor, it's interesting now become!

Of course, in the suppression algorithm of motion and shaking slightly different math and slightly different approach. But in fact exactly the same spectral analysis of space-time tube.

While saying that there svisnul algorithm silly. At MIT really noticed one little interesting feature, developed it and got a whole theory with such beautiful and magical images.

Source:

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