Can I add motion blur to make animation less jerky?

Question

I am doing an animation, and if I do things the easy way, fast moving objects end up jerking across the screen, rather than appearing to move smoothly – in other words, I have a temporal aliasing problem. One possible solution is to oversample the animation and blend the frames back together at the output frame rate.

To illustrate, at 24 frames per second:

frame
  0    **
  1        **
  2            **
  3                **
 ...                   **

Oversampled at double speed (though realistically I'd probably oversample quite a bit more than double):

frame
  0    **
 0.6     **
  1        **
 1.5         **
  2            **
 2.5             **
  3                **
 3.5                 **
 ...                   **

Blended back to 24 frames per second (all mixed with the background):

frame
  0    ****
  1        ****
  2            ****
  3                ****
 ...                   ****

The problem with oversampling is that if I just use Premiere Elements 14, if I take the oversampled clip and slow it back down to regular speed, it appears to just skip frames rather than blending them.

This seems like something that ffmpeg probably does, but I've barely started trying to understand it, and my reading of the documentation, tutorials, and the forum messages that have turned up with web searches hasn't been enough to figure out what switches would do the job.

So, questions:

1. Is there an option in Premiere Elements 14 to blend frames from an oversampled clip, rather than just skipping frames?
2. If ffmpeg is the smart way to do this, what kind of switches do I need to use to get the job done?
3. Is there some other reasonably easy-to-use software that could do the frame blending instead of skipping them? (And if so, how do I use that?)

Even if there's a way to do it directly in Premiere Elements, answers to #2 and #3 are likely to be helpful to people who use other editors.

Answer 1

I can't test the ffmpeg method below now but it notionally does what you ask:

Let's say your source is 25 fps.

ffmpeg -i in.mp4 -vf minterpolate=50,tblend=all_mode=average,framestep=2 out.mp4

Answer 2

Newer ffmpeg since version 4.1 includes new tmix video filter that mixes N adjacent frames together using weights.

Now it is possible to do exactly what you have suggested: take an animation rendered with a N times higher framerate, merge every N frames together and lower framerate N times down to normal one, dropping out extra frames.

Here's a script I created to test this flow:

#!/bin/bash

let WIDTH=640
let HEIGHT=480

let MID=$WIDTH/2

let BUFFER=16
let FRAMERATE=30

let XRATE=$BUFFER\*$FRAMERATE

let DURATION=8
let FPERIOD=$XRATE\*$DURATION


ffmpeg \
  -filter_complex \
  " \
    color=white:${WIDTH}x${HEIGHT}:d=$DURATION:r=$XRATE,format=rgb24[bg];  \
    color=black:8x${HEIGHT}:d=$DURATION:r=$XRATE,format=rgb24[bar];  \
    [bg][bar]overlay=x='$MID + $MID * sin(8 * PI * n / $FPERIOD)':y=0:format=yuv444,format=yuv420p[motion]; \
    [motion]tmix=frames=$BUFFER \
  " \
  -c:v libx264  \
  -r $FRAMERATE  \
  -an  \
  -hide_banner \
  -y  \
  output.mp4

It creates an 8-seconds long animation of a black bar running left-right in a sine speed motion. See it on YouTube.

Thanks Gyan for the tip on achieving smooth animation by forcing full chroma sampling.