In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to compare two spatial sequences along a 45°line. The proposed coefficient was explored for the bivariate Matérn and Wendland covariance functions. The asymptotic normality of a sample version of the spatial concordance coefficient for an increasing domain sampling framework was established for the Wendland covariance function. To work with large digital images, we developed a local approach for estimating the concordance that uses local spatial models on non-overlapping windows. Monte Carlo simulations were used to gain additional insights into the asymptotic properties for finite sample sizes. As an illustrative example, we applied this methodology to two similar images of a deciduous forest canopy. The images were recorded with different cameras but similar fields-of-view and within minutes of each other. Our analysis showed that the local approach helped to explain a percentage of the non-spatial concordance and provided additional information about its decay as a function of the spatial lag.

在这项工作中，我们定义了用于二阶平稳过程的空间一致性系数。这个问题已经在非空间环境中得到了广泛解决，但是这里我们考虑一个系数，该系数对于固定的空间滞后可以使一个人沿着45°线比较两个空间序列。探索了拟议的系数为二元Matérn和Wendland协方差函数。针对Wendland协方差函数，建立了针对递增域采样框架的空间一致性系数样本版本的渐近正态性。为了处理大型数字图像，我们开发了一种局部方法来估计在非重叠窗口上使用局部空间模型的一致性。蒙特卡洛模拟用于获得对有限样本大小的渐近性质的更多见解。作为说明性示例，我们将此方法应用于落叶林冠层的两个相似图像。图像是用不同的相机记录的，但视野相似且彼此之间的间隔仅为几分钟。我们的分析表明，局部方法有助于解释非空间一致性的百分比，并提供有关其衰减与空间滞后的函数的其他信息。