Scale analysis in remote sensing based on wavelet transform and multifractal modeling

With the development of Geographical Information System (GIS) and remote sensing techniques, a great deal of data has provided a set of continuous samples of the earth surface from local, regional to global scales. Several multi-scale, multi-resolution, pyramid or hierarchical methods and statistical methods have been developed and used to investigate the scaling property of remotely sensed data: local variance, texture method, scale variance, semivariogram, and fractal analysis. This research introduces the wavelet transform into the realm of scale study in remote sensing and answers three research questions. Three specific objectives corresponding to the three research questions are answered. They include: (1) exploration of wavelets for scale-dependent analysis of remotely sensed imagery; (2) examination of the relationships between wavelet coefficients and classification accuracy for different resolutions and their improvement of classification accuracy; and (3) multiscaling analysis and stochastic down-scaling of an image by using the wavelet transform and multifractals. The significant results obtained are: (1) Haar wavelets can be used to investigate the scale-dependent and spatial structure of an image and provides another method for selection of optimal sampling size; (2) there is a good relationship between classification accuracy and wavelet coefficients. High/low wavelet coefficient reflects low/high classification accuracy in each land cover type. (3) the maximum likelihood classifier with inclusion of wavelet coefficients can improve land cover classification accuracies. (4) the moment-scale analysis of wavelet coefficients can be used to investigate the multifractal properties of an image. Also the stochastic down-scaling model developed based on wavelet and multifractal generates good simulation results of the fine resolution image.