Following a brief review of the kernel regression approach to estimating surface models of the form z = f(x,y) + e, this article will consider the situation where f is not a continuous surface function, and in particular where the discontinuities take the form of one-dimensional breaks in the surface, and are not specified a priori. This form of model is particularly useful when visualizing some social and economic data where very rapid changes in geographical characteristics may occur – such as crime rates or house prices. The article briefly reviews approaches to this problem and proposes a novel approach (Bilateral Kernel Regression) adapting an algorithm from the field field of image processing (Bilateral Filtering), giving example analyses of synthetic and real-world data. Techniques for enhancing the basic algorithm are also considered.