Understanding forest fire spread in any region of Canada is critical to promoting forest health, and protecting human life and infrastructure. Quantifying fire spread from noisy images, where regions of a fire are separated by change-point boundaries, is critical to faithfully estimating fire spread rates. In this research, we develop a statistically consistent smooth estimator that allows us to denoise fire spread imagery from micro-fire experiments. We develop an anisotropic smoothing method for change-point data that uses estimates of the underlying data generating process to inform smoothing. We show that the anisotropic local constant regression estimator is consistent with convergence rate $O\left(n^{-1/{(q+2)}}\right)$. We demonstrate its effectiveness on simulated one- and two-dimensional change-point data and fire spread imagery from micro-fire experiments.

翻译：了解加拿大任何地区的森林火灾蔓延对于促进森林健康、保护人类生命和基础设施至关重要。用噪音图像中的火灾传播量来量化火灾,将火灾区域由变化点边界分隔开来,对于忠实地估计火灾蔓延率至关重要。在这个研究中,我们开发了一个统计上一致的平稳测算器,使我们能够将微型火灾试验的火灾扩散量隐藏起来。我们开发了一种变化点数据的异常平滑方法,该方法利用对基本数据生成过程的估计来提供平稳信息。我们显示,厌食性地方恒定回归估计仪与折合率(n ⁇ 1/{(q+2){right)一致。我们展示了模拟的一维和二维变化点数据以及微火实验的火灾传播图像的有效性。