Combine the first three ingredients to make a tomato sauce. Mix and set aside.
Combine cream cheese and the next 5 ingredients in the food processor. Pulse a few times until combined. Fold in the crab meat to the cream cheese mixture. Set aside.
Sauté artichokes with salt, pepper and garlic over medium high heat for 2-3 minutes. Set aside.
Pour tomato mixture into a baking dish. Pour cream cheese mixture on top. Gently fold in artichokes into the mixtures.
Bake at 400 F for 20 minutes, or until heated through. Garnish with tomatoes and parsley.
Serve hot with lightly salted tortilla chips.