Is punishment for leaving Islam death?

It is commonly believed that if someone leaves Islam, by Sharia law the punishment is death. Is that true? I have heard some different opinions. Dr. Zakir Naik was once asked a similar question and he responded that the punishment is death only if you tarnish Islam image in public and are publically against it. In that scenario the situation is similar to a revolt against an Army and hence punishment in that case is death. However, Islam is not an Army but a religion. What is the correct verdict in this regard?