Analogy to a dictionary attack
The similarly to the dictionary attack on the blurred image attack lies in the fact that blurring an image is a one-way encryption scheme. You are converting the image you have into another image designed to be unreadable. However, since account numbers only typically go up to the millions, we can assemble a "dictionary" of possible account numbers - that is, all the numbers from 0000001 to 9999999, for example, use an automated image processor to photoshop each of those numbers onto a photo of a blank check, and blur each image. At that point, one can simply compare the blurred pixels to see what most closely matches the original blurred photo we have.
Solution
The solution is simple: Don't blur your images! Instead, just color over them :-)