Martin Luther King Jr. understood the importance of "self-purification." Although it is indeed more than introspection and dialogue. It is also learning, practicing, and developing the skill, that is, nonviolent direct action that requires a person to essentially override their survival instinct; to remain nonviolent, vulnerable, and open to attack in situations that may be life-threatening.
Self-purification involves learning practices such as role-play, so that activists' nonviolent responses become automated. When a person violently attack you, a natural response would be to retaliate with force. Nonviolent direct action requires re-training that instinct so that you respond differently. Through drills, community role-play, and other exercises, nonviolent activists learned a new response to violence. Without such prolonged intentional practice, nonviolent activists could not have completed their work to any degree of effectiveness.