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In this paper, we design fast algorithms for segmenting/classifying 2D images or 2D spatial data. The data is stored in quadtree and Rtree formats, and it may be extracted from spatial databases. The topological and graph-theoretic properties will be used to speed up the segmentation process. The key feature of this paper is to perform a segmentation process without restore data frames. In other words, this segmentation will be done in a virtual or abstracted manner. Based on local connectedness and value-homogeneity, we implemented lambda-connected segmentation and the mean-based region growing segmentation to solve our problem. We will also discuss threshold segmentation. In this paper, we first design the segmentation algorithms for quadtree indexed images, then discuss the algorithms for R-trees indexed data. We will implement Rtree segmentation algorithms in the near future. Our algorithms will make the segmentation process much faster by not decoding the quadtree indexing code before the segmentation. The new algorithm for stream data will modify the boundaries of the segments in previous frames to predict the segments in upcoming frames. This could lead to the widespread use of segmentation technology for computer vision and geo-data processing, medical image processing, object tracking, geometrical simulation, and database application and data-mining as well as multi-dimensional data sets.