You emphasize getting to know the person in a broader sense, who is the offender. Yet, what if the other is unknown to me? How am I supposed to widen my view of this stranger?
We tend to emphasize three cognitive approaches in the forgiveness process. The first is the Personal Perspective, in which the forgiver examines the personal history of the offending person, examining incidents in which this person has been hurt by others. If you do not know the one who offended, then you cannot answer the questions in the Personal Perspective. Yet, we also have what we call the Global Perspective in which the forgiver sees the shared inherent worth of both the offending person and the self. After all, each is a person and all persons are unique, which makes each special and irreplaceable. A third perspective, for those who have transcendent beliefs, is the Cosmic Perspective. For example, a Jewish or Christian person can understand that all people are made in the image and likeness of God, as stated in Genesis 1 of the Bible. So, even though you do not know the one who hurt you, both the Global and Cosmic Perspectives are available for you to do the cognitive work of forgiveness.