遗传算法支持下土地利用空间分形特征尺度域的识别

针对土地利用空间分形特征只存在于有限尺度域的现象,采用无标度区内离散点拟合的离差平方和平均值最小作为目标函数,提出了一种基于遗传算法的土地利用空间分形特征尺度域的识别方法,用于准确计算分形维数的有效区间范围。以武汉市武昌区水域空间分形特征为例,利用Quickbird多光谱遥感影像提取土地利用空间信息,重点讨论了基于遗传算法识别土地利用空间分形特征尺度域范围的总体思路、适应度函数和遗传算子等环节;然后分别从测定系数、标准差和无标度区间3个角度,将其同人工判断法、相关系数法以及强化系数法进行对比讨论;并结合研究区域实际的水域空间分布格局,分析不同方法计算所得半径维数的合理性。结果表明,土地利用分形特征尺度域的范围对分形维数计算结果有较大影响;相对于传统计算方法来说,遗传算法在尺度无标度区间识别上具有更高的精度,可以为土地利用空间格局分形特征的研究提供客观指导意见。

Scale domain recognition for land use spatial fractal feature based on genetic algorithm

The spatial pattern of land use is one of the most profound human-induced alterations to the Earth's surface. Its change can lead to severe problems in urban ecological environments, such as heavy traffic, the heat island effect, and the spread of epidemics. An accurate examination of urban land use characteristics is helpful both in understanding quantitatively and comprehensively urban land use spatial patterns, and in discovering the potential rules of urban land use change. Because of its advantages in describing randomness and self-similarity, the fractal dimension has been used widely to analyze spatial patterns, and great achievements have been made in recent decades. However, the scale domain is largely ignored when the value of the fractal dimension is used to explain spatial patterns. To some extent, this leads inevitably to analysis uncertainty, because the spatial self-similarity characteristics of land use exist within a specific scale range rather than across a geographic scale range. Hence, the identification of the scale domain related to the fractal dimension is more important than the computation itself.In addressing this problem, this paper presents a model for scale domain recognition, based on a genetic algorithm, to provide a meaningful range of fractal features existing in nature. Its objective function is to minimize the average from the sum of squared residuals that is derived from the result of the fitting of a scale-free region using discrete points. It can improve the computation accuracy of the fractal dimension significantly. Because of its abundant water resources, this study took the scale domain of the water fractal feature in Wuchang district as an example. A cloud-free image obtained by the Quickbird satellite, was classified and used to extract land use information by using a combination of the decision tree method and supervised classification. A general framework and three genetic operators for the scale domain recognition of the land use spatial fractal feature were designed to identify the scale domain of the radius of the fractal dimension for water. To validate our model, its results were compared with three other methods used commonly for scale domain recognition: the artificial judgment method, the correlation coefficient method, and the strengthening coefficient method.The results indicate that different scale-less bands are derived by the four methods of scale domain identification. The scale-less band of the correlation coefficient method is significantly wider than that obtained by using the other three models. This results in a relatively small determination coefficient, indicating low accuracy. The genetic algorithm has the narrowest scale-less band and the best degree of statistical fitness of the four methods. Based on standard deviation, the four models can be ranked in the following descending order: the artificial judgment method (0.22), the correlation coefficient method (0.16), the strengthening coefficient method (0.13), and the genetic algorithm (0.08). Accordingly, the radius of the fractal dimension of water changes with the different scale-less bands derived from these four methods. The radius dimension derived from the genetic algorithm is 1.285, which suggests that the trend of the spatial distribution characteristics becomes gradually weaker moving from the center to the surroundings. This agrees with the spatial distribution of water information derived from the satellite image of Wuchang district. It reveals that it is critically important and imperative to promote the genetic algorithm for accurate identification of the scale domain of the fractal dimension. These findings are helpful for urban management departments in determining land use change, but also they provide a scientific reference for urban land use planning to ensure that land resources are used effectively.