## What I learned today at SIGGRAPH 2010

• Sharp has a prototype 5-colour display (RGBYC) that is simply gorgeous, and will make people who just bought their 4-colour (RGBY) display jealous.

# Image Statistics

• If you make your image’s histogram flat, or its cumulative histogram have a roughly 45-degree slope (these are equivalent), its contrast will be higher and people will like how it looks.
• However, matching histograms between images, while it can make one image have the colour palette of another, doesn’t produce pleasing results.
• If you calculate the x and y gradients of a large volume of natural images (pictures of the real world), there is a large peak at a gradient value of zero. This implies that most of the natural world is composed of large homogenous surfaces instead of having lots of edges.
• Further, the distribution of those gradients, both in x and y, falls off very quickly, implying that those edges that exist are mostly low contrast.
• Finally, the distribution of those gradients is symmetric about 0, meaning that surfaces are mostly on top of the same background, like a window in a house.
• If you take the power spectrum of an image, on average it follows the power law: A = 1 / fβ. If you plot these spectra on a logarithmic scale, you get a straight line with a slope of β.
• Human beings are most sensitive to slopes of β = 2.8 to 3.2, but the average spectral slope of images is about 2.0. This implies that we’re tuned to see things that are really coarse, even though the average scene isn’t that way.
• If you control for orientation, you figure out what an image is a picture of very effectively just by looking at their 2D power spectra!
• PCA, Principal Component Analysis, is simply a method of computing the eigenvalues and eigenvectors of a set of data. This lets you figure out (by looking at which eigenvalue is the largest) where most of the variance of a set of data is; by sorting the values, you can figure out what your most important components are.