Shaped local regression and its application to color transforms

Local linear regression is widely used in describing input-output relationships and has been applied with reasonable success to computational problems in color imaging such as approximating printer-models and device color characterization transforms. A popular flavor of local regression is one where locality is achieved by using a weight function which decays as a function of the distance from the regression data point. This paper proposes an improved method for local regression by introducing the notion of "shaping" in the localizing weight function. We make two novel contributions: I) a parameterization of the regression weight function via a shaping matrix, and 2) a method to optimize shape by explicitly introducing the shaping matrix parameters in the regression error measure. Experiments reveal dramatic improvements in approximating printer color transforms by using shaped local linear regression. A particularly pronounced benefit is gained in the case of sparse training sets, which are fairly common in color characterization applications due to the effort and/or cost associated with acquiring color measurements.