[Galaxy Note 3 Accessories] nerys71:
it depends on the sport and I would be cautious about getting it wet AT ALL but yes I can think of one way to easily use it as an action cam for some 4k loving.

FIRST install the hack that allows you to up the "bit rate" of the video. CAUTION while this hack allows you to remove the 5 minute limit unless you format your card to something like exfat or ntfs or something (people more expert at this will chime in) your going to run into the 4gb limit. at 50MB your probably looking at 4-5 minutes anyway at 100 MB bit rate your at around 2.5 minutes!! so be aware. you will hit the 4gb wall FAST at 4k

at minimum do 50mb and 256kbit audio mod!

now. onwards. BUY a case that includes a holster cover plate.

I would suggest Zero Lemon's Zero Shock case. (yes you can use it without the zero lemon battery its $24) I WOULD suggest buying the zero lemon battery ($60 gets you battery and case) with a 10 AMP battery you could probably go an entire weekend without recharging it no mater how much video you record. (yes its that impressive)

You would use some webbing and build yourself a "chest harness" something with a nice "backing plate" that would press hard against your chest.

Second figure out the appropriate angle. if you put it flat against your chest your probably going to get lots of sky so your probably going to want to angle it down a bit.

remove the "clip" from the holster and secure (screw?) the holster to your custom chest mount.

I would also install a screw top and bottom in the wood so you can stretch a rubber band over the two screws across the phone as a little bit of extra insurance IE install a velcro strap for a more pro and permanent look and function.

at home you would rig and set up your chest strap rig. at the site you would done the chest mount (like a go pro chest mount but more heavy duty since your phone weighs a lot more) keep it all black and you won't look like a "dork" so to speak. and use a black case as well.

at the top of your run you would hit "go" on the video snap it into the chest mount holster case slap your velcro security strap in place and GO.

this is a VERY good idea consider how nice the 4k video is!

Here are some pics and vid describing how I might do it. if I have time I may just build a rig.

Here is the zero lemon case for my note II (similar for the Note III) you can of course get all black I HATE black so I had to get pink purple since that is the only other color they make :) its not bad. since you want invisible get all black.

Here is the holster it snaps into

Here it is snapped into the holster plate

The other side mounted

I would remove the clip and use a couple washer and a screw to secure it to your chest plate (be sure not to BEND IT as you screw it in use spacers as needed if you distort the holster it might not hold the phone as firmly. also be sure to install a beefy velcro security strap as backup.

Mount it roughly their and your good to go. Be sure to set ANGLE proper or your gonna get a lot of sky shots :) you want level with horizon or even slightly "down" so when you "lean back" your still getting good footage.

https://www.youtube.com/watch?v=WaJ46EFdKo8

If you want a HEAD mounted action cam I would go with the SONY HDR series (the 10 is cheaper but lacks wifi connectivity which is really nice since you can use your phone as a viewfinder for the cam in real time!!)

I stalked ebay and scored mine for $129. there is another vendor who makes a 3D printer "strap mount" for the cam you DEFINITELY want this otherwise you have to stick the cam in its water proof case to "mount" it to anything.

I really like the video and fantastic audio from the sony.

NOW the contour are also VERY nice units and they have the advantage (the newer ones) of being waterproof WITHOUT an additional case.

they are also more compact than a go pro !! the go pro is smaller but its a landscape format camera. while the contour and sony units are "pistol style"

for chest mounting go pro is king since its landscape (like your phone) but for HEAD mounting unless you are mounting on top of your helmet the contour and sony units are much better.