Fix #1
The installation process is now split into two pieces. The Chromium extension, and the Companion.
The Companion uses Chrome's Native Messaging API to gather clipboard images externally to the browser (#1 (comment)). It only runs when called by Chrome, not on startup. It also does not require admin/root privileges to install.
More details are provided in the README.
Edit: Rereleased due to a change in the git tag naming scheme.
To install the Companion host, follow the instructions in the README. If you are on Windows, you can simply run the installer below. It does not require admin privileges.