user5416: When I watched videos on GoPro's youtube profile, they seem to me almost perfectly stable. And when I attached my action cam to helmet and tried to record during skiing, the video was very shaky.
I am aware, that videos on their profile are advertising videos made by pros. So my question is to pros - can you tell if the videos were stabilized with some software? Do consumer products have such capabilities? 
If the videos were not stabilized, what can be done, to achieve more stable videos, when recording from helmet or hand held (pole-mounted) camera?

user3029: There is also Prodrenalin - PC based standalone tool for GoPro videos, includes stabilization and other features

user5764: I would like to add that any software that can track points can be used for stabilisation. Biggest problem with software stabilisation is that you loose part of your frame. Personally i just use my 3d trackers solution as stabilisation  datasource because its by far the best solver i have.
I would recommend physical stabilisation. For consumers the best way to stabilize things is to add more weight. Something that is moderately rigid and hard to rotate is a good choice. Like a pole with weight on relatively far below your grip is good. The innertia of the object makes the shot more stable.

image 1: Three types of planar noise. In three dimensions you have 2 more rotations.
To better understand what to stabilize one has to look at how different noise affects the camera, this is illustrated in Image 1. There are 2 kinds of noise noise due to rotational vibration and noise due to translational vibration. 
The rotational vibration is much much worse than translational vibration because it grows the further you are from the camera. As a result you want to make the weight counter rotation as much as possible. It turns out that moment of inertia grows with the distance from pivot. So you need to put the weight as far as possible. Bust still not so far that pivoting the camera becomes impossible. 
This is also why gyro stabilization works as it turns out that you can store inertia in rotation so at big speeds even small masses have high moment of inertia. The gyro stabilization does nearly nothing to the translational noise.
The translational vibration is also something that the software stabilization is much better at removing. The same mass that's stabilizes the rotation will however also stabilize the translational noise. Mainly because you need more force to get the camera moving eliminating the highest frequencies of noise. 
The second thing to do is to ensure that your connection to a noise source is isolated. Heavy rubber pieces are good. You want the inertia to be able to filter the noise, too rigid connection makes it impossible.
Physical stabilization also makes the results of software stabilization easier and much better in quality. Even very little stabilization helps a lot.
other resources:

14$ camera stabilizer


user5763: Software that I know of:

Virtualdub with Deshaker plugin:
http://www.guthspot.se/video/deshaker.htm
Sony Vegas Pro since version 10 has a built-in stabilization plugin
Depan for Avisynth - http://avisynth.org.ru/depan/depan.html - it can get quite complicated but there are sample scripts to help getting started.

Youtube can detect if the footage is shaky, though it's not always working so well and it applies to the whole video.
My personal favorite is the Virtualdub route. Just remember to save it to a lossless format if you plan on editing it further.

5416: <p>When I watched videos on <a href="https://www.youtube.com/channel/UCqhnX4jA0A5paNd1v-zEysw">GoPro's youtube profile</a>, they seem to me almost perfectly stable. And when I attached my action cam to helmet and tried to record during skiing, the video was very shaky.</p>

<p>I am aware, that videos on their profile are advertising videos made by pros. So my question is to pros - <strong>can you tell if the videos were stabilized with some software?</strong> Do consumer products have such capabilities? </p>

<p>If the videos were not stabilized, <strong>what can be done, to achieve more stable videos</strong>, when recording from helmet or hand held (pole-mounted) camera?</p>
 3029: <p>There is also <a href="http://vegasaur.com/ProDRENALIN" rel="nofollow">Prodrenalin</a> - PC based standalone tool for GoPro videos, includes stabilization and other features</p>
 5764: <p>I would like to add that any software that can track points can be used for stabilisation. Biggest problem with software stabilisation is that you loose part of your frame. Personally i just use my 3d trackers solution as stabilisation  datasource because its by far the best solver i have.</p>

<p>I would recommend physical stabilisation. For consumers the best way to stabilize things is to add more weight. Something that is moderately rigid and hard to rotate is a good choice. Like a pole with weight on relatively far below your grip is good. The innertia of the object makes the shot more stable.</p>

<p><img src="https://i.stack.imgur.com/GqjQ2.png" alt="enter image description here">
<strong>image 1:</strong> Three types of planar noise. In three dimensions you have 2 more rotations.</p>

<p>To better understand what to stabilize one has to look at how different noise affects the camera, this is illustrated in <em>Image 1</em>. There are 2 kinds of noise noise due to rotational vibration and noise due to translational vibration. </p>

<p>The rotational vibration is much much worse than translational vibration because it grows the further you are from the camera. As a result you want to make the weight counter rotation as much as possible. It turns out that <a href="http://en.wikipedia.org/wiki/Moment_of_inertia" rel="nofollow noreferrer">moment of inertia</a> grows with the distance from pivot. So you need to put the weight as far as possible. Bust still not so far that pivoting the camera becomes impossible. </p>

<p>This is also why gyro stabilization works as it turns out that you can store inertia in rotation so at big speeds even small masses have high moment of inertia. The gyro stabilization does nearly nothing to the translational noise.</p>

<p>The translational vibration is also something that the software stabilization is much better at removing. The same mass that's stabilizes the rotation will however also stabilize the translational noise. Mainly because you need more force to get the camera moving eliminating the highest frequencies of noise. </p>

<p>The second thing to do is to ensure that your connection to a noise source is isolated. Heavy rubber pieces are good. You want the inertia to be able to filter the noise, too rigid connection makes it impossible.</p>

<p>Physical stabilization also makes the results of software stabilization easier and much better in quality. Even very little stabilization helps a lot.</p>

<p><strong>other resources:</strong></p>

<ul>
<li><a href="http://littlegreatideas.com/stabilizer/diy/" rel="nofollow noreferrer">14$ camera stabilizer</a></li>
</ul>
 5763: <p>Software that I know of:</p>

<ul>
<li>Virtualdub with Deshaker plugin:
<a href="http://www.guthspot.se/video/deshaker.htm">http://www.guthspot.se/video/deshaker.htm</a></li>
<li>Sony Vegas Pro since version 10 has a built-in stabilization plugin</li>
<li>Depan for Avisynth - <a href="http://avisynth.org.ru/depan/depan.html">http://avisynth.org.ru/depan/depan.html</a> - it can get quite complicated but there are sample scripts to help getting started.</li>
</ul>

<p>Youtube can detect if the footage is shaky, though it's not always working so well and it applies to the whole video.
My personal favorite is the Virtualdub route. Just remember to save it to a lossless format if you plan on editing it further.</p>
