If the mother sees you in the yard she will not come near. In addition, if a bird is injured, it needs help and cannot be placed back in the nest. You should assume Birds that are cat caught are injured although they may not appear to be. If a bird is featherless, it needs heat. Holding a featherless baby bird in your hand will warm it effectively.
Doves make very poor nests which get blown down easily.
Pigeons usually don't make nests. Juvenile pigeons are fully feathered and very docile, and rely on their parents for a long time. If you're not sure the bird needs attention, call a rehabilitator. Rabies has been produced in birds experimentally, however, it has never been found in wild bird populations. There are two common methods you can use to catch wild animals, the box method and the sheet method.