user6316: I have a video containing a single person facing the camera. I would like to black-out everything in this video except for a small rectangular box around the person's eyes. I'm sure there are many approaches that might work for this, but I'm having trouble figuring out where to even begin. Preferably it can be done using free software for OS X.
Edit: To clarify, the person's head moves around significantly and unpredictably, so I'm asking how to do this with some sort of motion tracking.

user3295: You can use Lightworks (multi-plattform) for that or alternatively iMovie. Both offer either masking and or cropping.
One of the most basic features in a video editor. Just watch one of the dozens of beginner tutorials for the tool that fits you the most.
When you go with the cropping approach you just duplicate the video layer and crop each layer down to one of the eyes.
Edit: With motion tracking it gets much more complicated (in the sense of software complexity, motion tracking is super easy nowadays). You will have to reside to a paid tool in that case. I can't think of freeware that integrates all that in to a free package.
The go to tools for motion tracking and masking work are After Effects, Nuke and Apple Motion (not that much actually but just to name an prominent Apple tool). With After Effects being the most prominent one out there and with a shitload of tutorials available to get going.

user5546: I agree with the two previous answers:  You'll need paid motion-tracking software such as After Effects.
I wanted to add that in addition to tracking the X-Y position in the frame, you will most likely need to track the "rotation" of the 2 eyes as well.  That is, a horizontal rectangular mask will work for the eyes of a person facing forward with his/her head upright, but if he/she tips his/her head to the left or right, the rectangle will have to similarly tip to the left or the right in order to expose both eyes (since one will be "above" the other in the frame at that point).

user2836: Unfortunately, this requires motion tracking and there isn't much out there that can handle it for free.  (As Jason Conrad pointed out, DaVinci Resolve Lite can.)  Motion tracking is pretty elaborate because it has to use complex computer vision systems to identify objects within the image and track where they move from frame to frame.  
After Effects is probably the cheapest option on the list of tools that are often used for motion tracking, but it is still either several hundred dollars for a stand alone copy of the slightly older CS6 version or $20 a month to rent the newest version from Adobe.
With such a motion tracking capable tool, you can track the motion of the scene and then either stabilize it such that the eyes remain stationary or you can use the tracking data to have a rectangular mask follow the eyes and only reveal the contents of the mask.  After Effects (or really any other program that supports this kind of tracking) is pretty advanced and gives lots of options for how to accomplish your goal, though you should also be aware that they are pretty advanced packages and there is a potentially significant learning curve.

user3592: Davinci Resolve lite is free, and it contains an excellent motion tracker.  By combining the motion tracker with a power window, and adding a color correction (to darken everything outside of the power window), you should be able to achieve the results you're after very quickly.  For tutorials on Davinci Resolve, search youtube for Alexis Van Hurkman.  He literally wrote the book on it (the instruction manual), and provides a generous amount of tutorials online for free.  Of course, he also has a complete course for sale through ripple training.  You can download Resolve lite here.  

6316: <p>I have a video containing a single person facing the camera. I would like to black-out everything in this video except for a small rectangular box around the person's eyes. I'm sure there are many approaches that might work for this, but I'm having trouble figuring out where to even begin. Preferably it can be done using free software for OS X.</p>

<p>Edit: To clarify, the person's head moves around significantly and unpredictably, so I'm asking how to do this with some sort of motion tracking.</p>
 3295: <p>You can use <a href="http://www.lwks.com/" rel="nofollow">Lightworks</a> (multi-plattform) for that or alternatively iMovie. Both offer either masking and or cropping.
One of the most basic features in a video editor. Just watch one of the dozens of beginner tutorials for the tool that fits you the most.</p>

<p>When you go with the cropping approach you just duplicate the video layer and crop each layer down to one of the eyes.</p>

<p><strong>Edit:</strong> With motion tracking it gets much more complicated (in the sense of software complexity, motion tracking is super easy nowadays). You will have to reside to a paid tool in that case. I can't think of freeware that integrates all that in to a free package.</p>

<p>The go to tools for motion tracking and masking work are After Effects, Nuke and Apple Motion (not that much actually but just to name an prominent Apple tool). With After Effects being the most prominent one out there and with a shitload of tutorials available to get going.</p>
 5546: <p>I agree with the two previous answers:  You'll need paid motion-tracking software such as After Effects.</p>

<p>I wanted to add that in addition to tracking the X-Y position in the frame, you will most likely need to track the "rotation" of the 2 eyes as well.  That is, a horizontal rectangular mask will work for the eyes of a person facing forward with his/her head upright, but if he/she tips his/her head to the left or right, the rectangle will have to similarly tip to the left or the right in order to expose both eyes (since one will be "above" the other in the frame at that point).</p>
 2836: <p>Unfortunately, this requires motion tracking and there isn't much out there that can handle it for free.  (As Jason Conrad pointed out, DaVinci Resolve Lite can.)  Motion tracking is pretty elaborate because it has to use complex computer vision systems to identify objects within the image and track where they move from frame to frame.  </p>

<p>After Effects is probably the cheapest option on the list of tools that are often used for motion tracking, but it is still either several hundred dollars for a stand alone copy of the slightly older CS6 version or $20 a month to rent the newest version from Adobe.</p>

<p>With such a motion tracking capable tool, you can track the motion of the scene and then either stabilize it such that the eyes remain stationary or you can use the tracking data to have a rectangular mask follow the eyes and only reveal the contents of the mask.  After Effects (or really any other program that supports this kind of tracking) is pretty advanced and gives lots of options for how to accomplish your goal, though you should also be aware that they are pretty advanced packages and there is a potentially significant learning curve.</p>
 3592: <p>Davinci Resolve lite is free, and it contains an excellent motion tracker.  By combining the motion tracker with a power window, and adding a color correction (to darken everything outside of the power window), you should be able to achieve the results you're after very quickly.  For tutorials on Davinci Resolve, search youtube for Alexis Van Hurkman.  He literally wrote the book on it (the instruction manual), and provides a generous amount of tutorials online for free.  Of course, he also has a complete course for sale through <a href="http://www.rippletraining.com" rel="nofollow">ripple training</a>.  You can download Resolve lite <a href="https://www.blackmagicdesign.com/support" rel="nofollow">here</a>.  </p>
