Identifying Discontinuities in Trend Surfaces Using Bilateral Kernel Regression |
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| Authors: | Chris Brunsdon |
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| Institution: | Department of Geography, University of Leicester |
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| Abstract: | Following a brief review of the kernel regression approach to estimating surface models of the form z=f(x,y) +ε, 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. |
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