Laptop monitor brightness changes depending on image displayed

Short answer: It is a feature.

This is the effect of either Intel's "Display Power Saving Technology" or AMD's "Vari-Bright" feature, the intent is to reduce power usage by reducing brightness when you look at dark images (which ostensibly would not need to be back lit so much). This technology detects whether the screen is displaying a mostly dark or mostly light image, and adjusts the back light accordingly. Unfortunately this can be annoying if important parts of the UI are light colors (like Chrome), or when dealing with highly visual applications (Photoshop, Media, etc) where changes to brightness have a negative effect on visual fidelity.

So yes, this is a feature, unfortunately this means either dealing with the effect, or forfeiting the power savings it produces.

If you dislike this feature, it can be disabled (or adjusted) it in the settings for your graphics card.

Intel:

The exact layout of Intel's options may vary from system to system, but on my machine:

Intel system tray icon > Graphics Properties > Power > On Battery > Display Power Saving Technology

It shouldn't be too hard to find, even if it isn't in the same place on your machine. You may need to look for the properties in control panel.

AMD:

Open the Catalyst Control Center (search for "CCC" in start, choose CCC - Advanced) > Graphics > Power Play > Enable Vari-Bright [Check-box] [Source]

The answer is correct but unfortunately unhelpful for when your laptop is plugged in, as Intel doesn't allow you to change the setting for AC power. Here's something else to try.

The registry key HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Class\{4d36e968-e325-11ce-bfc1-08002be10318}\0000 should have a value named DCUserPreferencePolicy.
Contrary to its name, it seems to affect the AC behavior as well.
I think the top half of the number is for AC power. So you might have something like 0x00220020. The bottom 0 means this feature is disabled for DC power, so I think changing the upper half to mirror the lower half (that is, to 0x00200020) should fix it. In my case, I just set the whole thing to 0 because I didn't particularly care what it was. You can try that or something else.

The provided solution addresses the issue but my computer did not have the intel system tray icon, but I found I could also access the configuration by right clicking on the desktop and choosing:

Intel® Graphics Settings →
 Graphics Properties →
  Power →
   On Battery →
    Display Power Saving Technology

My laptop does exactly the same thing. It's a display panel "feature" (not Windows 8 fault), Dynamic contrast . Maybe a badly implemented one.