Geographic Window Fixing and Its Application Based on Spatial Statistics

Fixing the size and shape of geographic window is vitally important in geo-spatial data processing, especially in the field of remotely sensed data processing. Conventionally, geographic window(both the size and the shape)will be fixed before the image processing task is carried out and this fixed window will be moved within the whole image while operators such as Sobel filter are being calculated within it. Such is the case commonly encountered in spatial filtering. Though commonly used neighborhood processing operators have their fixed shapes and sizes, and weights in their corresponding position in the window, there is no existing methodology for fixing the geographic window self-adaptedly, that is, determining the shape and size of a window according to the image data themselves, other than arbitrarily chosen by the analysts. This paper presents the strategy for implementing the objectives mentioned above in the con-text of two practical examples, by employing theories and approaches from spatial statistics. The first case is to enhance the ground resolution of TM6 by em ploying regression model, which requires some statistical parameters before the regression analysis and all these parameters should be calculated within small image blocks. The second case is to correct the non-uniform illumination effect appearing in pictures of deep sea-floor. The non-uniform illumination effect could be easily removed according to the algorithm proposed in this paper, however, the w hole im age is also needed to be divided into small image blocks before the algorithm can be used. The sizes of all the small image blocks in both cases can not be determined arbitrarily, otherwise, the resultant w ill not be optimal in the first case or the non-uniform illumination effect w ill not be removed completely in the second one. A concise introduction of spatial statistics is presented in the paper in order to help those who are not familiar with this subject. The range, an important parameter from variogram, reflects the area within which the autocorrelation of a regionarized variable between two separated spatial points, say x and x +h, is significant or not. This property is actually the embodiment of the homogeneity in the given area. Once this area is sensed by satellite sensors or by other means and digitized to be digital images, this homogeneity will be inherited. So it is obvious that the size of a geographic window within which geo-spatial data analysis will be carried out should be determined according to the homogeneity of the corresponding area. With this conclusion in mind, the horizontal and vertical variogram can be calculated and the corresponding ranges can be obtained. Assign the values of the horizontal and vertical range to be the width and height of a geographic window respectively, the window is then determined. The main steps implementing the suggested strategy are listed and some attentions that should be paid when using this method are also expounded in the paper. Finally, the two problems presented at the beginning of the paper are successfully solved using the method described here. Besides, the method proposed in this paper of non-uniform illumination correction for deep sea floor pictures is a simple but successful one. Borrowing the idea of linearization and planarization from calculus, a stretching formula proposed in this paper removes the non-uniform illumination effect completely. This method has been widely adopted in practice.