Centered background image is partly hidden by a border after reboot (dual display configuration, different screen resolutions)

Steps to reproduce (Ubuntu 12.04.1):

1.1. Go to System Settings / Hardware / Displays

1.2. Switch "Mirror displays" off.

1.3. Set up different screen resolution for displays
(My case: 1600 x 900 for native laptop monitor and 1920 x 1080 for external HDMI monitor.)

2. Find or download a wallpaper image with size that corresponds to the larger resolution (1920 x 1080 in my case).

3.1. Go to System Settings / Personal / Appearance / Look

3.2. Add your wallpaper image and set it as a background.

3.3. Choose "Center" option in the "Tile/Zoom/Center/Scale/..." list.

Result:
The image is fully visible on the display with larger resolution and partly visible on the smaller display.
There are no any borders (i.e. image spans fully on each display).
Image is not scaled; it is shown with pixel-to-pixel correspondence on both displays.

4. Reboot the system (or log out) and log back in as the same user.

Result:
On the smaller display the result is the same as described above (item 3.3).
On the larger display image is partly visible (visible is exactly the same part of image
which is visible on the smaller screen); image is not scaled, its part is just shown with
pixel-to-pixel correspondence at the center of display; around the image there is a border
that fills space where the rest of the image should be.

Expected result: The same as described in item 3.3.

Workaround:

W.1. Go to System Settings / Personal / Appearance / Look

W.2. Choose "Tile" option in the "Tile/Zoom/Center/Scale/..." list.

W.3. Choose "Center" option in the "Tile/Zoom/Center/Scale/..." list.

W.4. Repeat each time after you log in.

The bug was observed in Ubuntu 11.10, and still persists after upgrade to Ubuntu 12.04.1.

ProblemType: Bug
DistroRelease: Ubuntu 12.04
Package: xorg 1:7.6+12ubuntu1
ProcVersionSignature: Ubuntu 3.2.0-32.51-generic 3.2.30
Uname: Linux 3.2.0-32-generic x86_64
.tmp.unity.support.test.0:

ApportVersion: 2.0.1-0ubuntu13
Architecture: amd64
CompizPlugins: [core,composite,opengl,compiztoolbox,decor,regex,mousepoll,vpswitch,grid,move,snap,place,resize,session,animation,imgpng,gnomecompat,wall,workarounds,fade,expo,scale,unitymtgrabhandles,ezoom,unityshell,switcher]
CompositorRunning: compiz
Date: Mon Oct 15 16:09:57 2012
DistUpgraded: 2012-10-15 09:44:05,298 DEBUG got a conffile-prompt from dpkg for file: '/etc/bash.bashrc'
DistroCodename: precise
DistroVariant: ubuntu
DkmsStatus:
 virtualbox, 4.1.12, 3.0.0-26-generic, x86_64: installedError! Could not locate dkms.conf file.
 File: does not exist.
  (WARNING! Diff between built and installed module!)
 virtualbox, 4.1.12, 3.2.0-32-generic, x86_64: installed
GraphicsCard:
 Intel Corporation 2nd Generation Core Processor Family Integrated Graphics Controller [8086:0116] (rev 09) (prog-if 00 [VGA controller])
   Subsystem: Samsung Electronics Co Ltd Device [144d:c0c1]
   Subsystem: Samsung Electronics Co Ltd Device [144d:c0c1]
InstallationMedia: Ubuntu 11.10 "Oneiric Ocelot" - Release amd64 (20111012)
MachineType: SAMSUNG ELECTRONICS CO., LTD. RC530/RC730
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-3.2.0-32-generic root=UUID=7ab06e14-ffd7-4e18-b756-2c246e0b6fc1 ro quiet splash vt.handoff=7
SourcePackage: xorg
Symptom: display
UpgradeStatus: Upgraded to precise on 2012-10-15 (0 days ago)
dmi.bios.date: 08/10/2011
dmi.bios.vendor: American Megatrends Inc.
dmi.bios.version: 02WD.M007.20110810.PSA
dmi.board.asset.tag: To be filled by O.E.M.
dmi.board.name: RC530/RC730
dmi.board.vendor: SAMSUNG ELECTRONICS CO., LTD.
dmi.board.version: 02WD
dmi.chassis.asset.tag: No Asset Tag
dmi.chassis.type: 9
dmi.chassis.vendor: SAMSUNG ELECTRONICS CO., LTD.
dmi.chassis.version: N/A
dmi.modalias: dmi:bvnAmericanMegatrendsInc.:bvr02WD.M007.20110810.PSA:bd08/10/2011:svnSAMSUNGELECTRONICSCO.,LTD.:pnRC530/RC730:pvr02WD:rvnSAMSUNGELECTRONICSCO.,LTD.:rnRC530/RC730:rvr02WD:cvnSAMSUNGELECTRONICSCO.,LTD.:ct9:cvrN/A:
dmi.product.name: RC530/RC730
dmi.product.version: 02WD
dmi.sys.vendor: SAMSUNG ELECTRONICS CO., LTD.
version.compiz: compiz 1:0.9.7.8-0ubuntu1.4
version.ia32-libs: ia32-libs 20090808ubuntu36
version.libdrm2: libdrm2 2.4.32-1ubuntu1
version.libgl1-mesa-dri: libgl1-mesa-dri 8.0.3+8.0.2-0ubuntu3.2
version.libgl1-mesa-dri-experimental: libgl1-mesa-dri-experimental N/A
version.libgl1-mesa-glx: libgl1-mesa-glx 8.0.3+8.0.2-0ubuntu3.2
version.xserver-xorg-core: xserver-xorg-core 2:1.11.4-0ubuntu10.8
version.xserver-xorg-input-evdev: xserver-xorg-input-evdev 1:2.7.0-0ubuntu1.2
version.xserver-xorg-video-ati: xserver-xorg-video-ati 1:6.14.99~git20111219.aacbd629-0ubuntu2
version.xserver-xorg-video-intel: xserver-xorg-video-intel 2:2.17.0-1ubuntu4.1
version.xserver-xorg-video-nouveau: xserver-xorg-video-nouveau 1:0.0.16+git20111201+b5534a1-1build2