If you take a photo with the built-in camera of the Samsung Galaxy S4, then a camera sound is heard with a sort of "click". If you do not want to hear this sound when the shutter is released, then you have only the following possibility on your Samsung Galaxy S4 without root privileges:
Before you start the camera, pull down the status bar and tap once on the "speaker" icon. The smartphone is now switched to “Vibration mode” in which all sounds, including ringtones and alert tones are deactivated.
Of course, also the camera shutter sound is set to silent when vibration mode is activated. Now open the camera app with your Samsung Galaxy S4 and you will hear no sound when the shutter button is pressed for taking a picture or video.
Once you have the picture shot, do not forget to provide your phone back to "loud" to. Pull the status bar down again and tap double on the speaker icon.
This variant is the only way to make pictures without the shutter sound on the Samsung Galaxy S4 but this solution works very quickly and you need no rooted smartphone.