If you’re doing image processing, you’ve probably had to transform your image from one color space to another. In video coding, for example, the RGB image is transformed into YPrPb or YCrCb so that most of the visually relevant information is packed into the Y component which is essentially brightness. Subsampling the chroma bands (Cr and Cb) provides additional means for compression with little perceptual quality loss. While the human eye is very good at detecting brightness variation, it’s not very good at detecting subtle changes in chroma, either saturation or hue.
The thing is that very often, there are color space transformation matrices found in text book but they’re not, due to rounding (and other possible errors), always exactly inverses of each other. This week, I will discuss how we can use projections onto convex sets (POCS) to make sure that reduced precision matrices are exactly (within a given precision) reversible.