No, this image doesn't prove anything. Two snapshots do not convey trajectory over time. And in some cases, people will use such snapshots as evidence against global warming. For example, if you take a summer 1980 photo compared to a winter 2012, it may not look like there is any difference at all. Of course, you have to compare winter to winter to have any meaning.
Point is, that to really convey a useful measure of sea ice change, one must consider the change over time and the change in volume (not just the 2D extent). The attached image, for example, shows the change in ice volume over time (as anomaly).
Also, the change in ice still doesn't by itself prove anything. It is one piece of a much larger and complex puzzle and needs to be considered within that context.
And yes, according to scientists who study and understand that larger complex puzzle, global warming and climate change are occurring and are mostly a result of human activity.
Image source: Polar Science Center: http://psc.apl.washington.edu/wordpress/research/p...