Verizon shows the camera icon on the locked [not home] screen. On the S4 Mini...[at least on my unit] the camera is not on the screen. So, to take a pix, one needs to unlock, then select the camera icon...then shoot.
How to solve this?
Can't guarantee the accuracy but here's a link. Read the 4 comments in addition to the instructions:
http://androidwidgetcenter.com/android-tips/how-to-add-camera-shortcut-on-galaxy-s4-lock-screen/http://
Bad link above. This one seems to work with cntrl/clk. Sucks that a post can't be edited.
http://androidwidgetcenter.com/android-tips/how-to-add-camera-shortcut-on-galaxy-s4-lock-screen