Quantity of motion of an arbitrary number of inputs

In video analysis I have been working with what is often referred to as “quantity of motion” (which should not be confused with momentum, the product of mass and velocity p=mv), i.e. the sum of all active pixels in a motion image. In this sense, QoM is 0 if there is no motion, and has a positive value if there is motion in any direction.

Working with various types of sensor and motion capture systems, I see the same need to know how much motion there is in the system, independent of the number of variables and dimensions in the system studied. Thus, whether we use a single 1-dimensional MIDI slider or 32 6-dimensional sensors in a motion capture system, we still need to be able to say whether there is any movement in the system, and approximately how much movement there is.

So I have made a small abstraction in Max that sums up all incoming values, divides by the number of values, finds the first derivative and takes the absolute value of this.

I had two optimization questions while working on the patch:

  1. Does it matter whether derivation is done before or after summing up the values?
  2. Is it more efficient to use Max objects than Jitter objects?


  1. No, it does not matter.
  2. Max objects are ~3 times faster

A screenshot of the efficiency test patch is shown below, and a zip-file of the patches.


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Alexander Refsum Jensenius is a music researcher and research musician living in Oslo, Norway.