Although it's not quite professional quality, QuickTime Player Pro lets you do a pretty good job of blurring a face or other body part. (For this discussion, let's assume we want to obscure the face.)
Note that this method cannot "follow" a moving face. The oval we create to obscure the face is stationary for the time it is on screen. So this method will not work if the face moves around a lot on screen. To cover a moving face, the movie could be split into several parts with a separate mask applied to each part, then the parts re-joined later into a single movie.
Essentially, you create a movie that contains two layers—two video tracks. The bottom layer is the original movie. The second layer is a portion of the same image, playing on top of the first. The second layer is a highly pixelated duplicate of the first layer, with an oval mask added to that track so only a portion of its image shows through an oval as a highly-pixelated image. The oval is created using a mask. (Note the term mask refers to a tool that lets only certain parts show through. The term has nothing to do with our covering a face. QT Player lets you add a mask to a video track so only a portion of the image plays through the mask.)
After building your multi-layered, masked movie, you export it to a new movie, which places everything in a single layer showing a pixelated face against a normal background.
To create the pixelated duplicate layer, resize the QT Player window so the movie image is only one inch wide or so. Then export to a (new) NTSC movie. Because of a feature in QT Player, the new movie will be highly pixelated. The window size determines the amount of pixilation, so resize the window as results require. You want the face of the image to be unrecognizable, yet with as little pixelation as possible so the face "blends" nicely into the background behind it.
To make the mask that covers the pixelated face, export the first frame of the pixelated movie to a pict file, open the picture in Photoshop or some other image editor, select an oval around the face. More in a moment. (The selected oval should include a substantial margin to achieve a better blend with the background.)
For the mask, you want everything inside the selected oval to be white and everything else black. If using PhotoShop, Invert the oval selection so everything outside the oval is selected, delete that image, pour black paint into it, Invert the selection again, then delete the image of the face. That's your mask, a white face against a black background. Save it as a pict file.
To add the pixelated movie to the original movie, Select All frames of the pixelated movie, Copy, activate the original movie, Select All, and Add Scaled. That adds the pixelated movie as a new video track layered over the first. Then choose Movie>Get Movie Properties, select video track 2 in the left side, Mask in the right. Click the Set button to add your mask to the track. (I forget, you may have to click the Invert button to mask the face instead of the background.)
Then Export the (multi-layered, masked) movie to a new NTSC movie or streaming DV. The new movie will contain a single layer that combines the two layers.
If the border of the blurred image is too sharp (edge sharpness is unavoidable) try selecting a wider area around the face when making the mask. If the sharp border falls against the background it is less noticeable.
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