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I have two ideas and want to put them into one construction.

  1. The clusters representing objects are then extracted by introducing set of shape constraints.
  2. shape constraints describe the global shape of an object.

after combining them,

The clusters representing objects are then extracted by introducing set of shape constraints (describe/describing) the global shape of an object.

So, I am not sure what verb form should I used. i.e. either describe or describing. Any suggestions please.

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Try this:

The clusters representing objects are then extracted by introducing a set of shape constraints that describe the global shape of an object.

or this:

The clusters which represent objects are then extracted by introducing a set of shape constraints that describe the global shape of an object.

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