So, here's a bad chart:
The source describes a real and important phenomenon: Americans are broadly and significantly wrong about crime rates. But the chart. The chart is bad.
Why is the chart bad?
The central issue is that the double y axes are representing drastically different variables. Generally, putting two lines on the same chart where the scale is the same is good. Both scales go from 0 to 100. But when just one scale is a percentage it actually masks the very different variables being measured here.
What are those variables? The orange line is the national violent crime rate, from 0 to 100. Out of what? 1,000? 100,000? 1 million? A little searching suggests that the rate is out of 1,000 but you wouldn't know this here.
The blue line is the "percentage of survey respondents who said that crime has increased locally over the past year." Here's the thing. People can absolutely be correct that the crime rates have increased locally while they drop nationally. In fact, almost everyone could say correctly that crime rates have increased locally while they decrease nationally, as long as crime rates are decreasing significantly enough in certain parts of the country. This isn't a perception gap if people are correctly identifying local trends while national trends go in the other direction.
Even if we (incorrectly) interpret the blue line to represent what percentage of respondents say crime is increasing nationally over the past year, there are several years where people are correctly identifying crime rates. From 2005 to 2006 and from 2010 to 2012 crime does increase nationally. So survey respondents who say crime rates are increasing over the last year in 2006, 2011, and 2012 are correct! There's a perception gap here, but it's on the part of survey respondents who deny that crime rates are increasing.
The large yellow area ominously labeled "PERCEPTION GAP" suggests that there's some permanent (since 9/11, roughly) disconnect between what Americans believe the crime rate is and what it actually is. And this is likely true. But the chart doesn't show that!
There are still plenty of interesting questions to ask about these lines and the gap between reality and our perception of it. Why does the blue line spike and drop when it does? Why does public perception seem to restabilize and basically flatten after 2005? Is the blue line bump in 2009 due to Obama's inauguration (and the racist backlash that followed) or is the blue line just delayed by a few years and the bump is due to the actual crime rate bump in 2006?
I'm also in broad agreement that Americans' views about violent crime are way off-base. However, charts like this one give us the appearance that something exists while actually representing something else entirely. That's a more worrisome perception gap.