With the rapid advances in technologies, strategies for efficiently operating the spatial data are needed. The spatial data consists of points, lines, rectangles, regions, surface, and volumes. In this thesis, we focus on the region data. There are many important and efficient operations for the region data, such as neighbor finding, rotation, and mirroring. The nearest neighbor (NN) finding is frequently used in geographic information system (GIS). We can find the specific point (e.g., a park, a department store, etc.) that is the closest to our position in geographical information systems. In any representation for the region data, it is not instinctive and easy for nearest neighbor finding, since the coordinate information has been lost. Voros, Chen, and Chang have proposed the strategies for the nearest neighbor finding based on the quadtree in eight directions. Chen and Chang have proposed the nearest neighbor finding based on the Peano curves. These strategies for the nearest neighbor finding based on the quadtree and the Peano curve use a looping process, which is time-consuming. On the other hand, in recent years, many researchers have also focused on finding efficient strategies for the rotating and mirroring operations, which is useful when the animation is performed by computers. The boolean function-based encoding is a considerable amount of space-saving with respect to the other binary image representation. The CBLQ representation saves memory space as compared to the other binary image representations that have proposed the strategies of the set operations. However, the processes for obtaining the rotated or mirrored code based on these two representations are time-consuming, since the coordinate information of all pixels has been lost. Therefore, in this thesis, first, for the nearest neighbor finding based on the quadtrees and the Peano curve, we propose the strategy which uses the bitwise and arithmetic operations, and it is more efficient than the strategies based on the looping processes. Next, we propose efficient strategies for rotating and mirroring images based on the boolean function-based encoding and constant bit-length linear quadtrees (CBLQ) representations. From our simulation study, first, we show that our strategies based on the quadtree and the Peano curve require the least CPU-time and our strategy based on the Hilbert curve requires the least total time (the CPU-time + the I/O time) among the strategies for the nearest neighbor finding based on the quadtree and the three space-filling curves. Next, in most of cases, when the black density is no larger than 50%, the CPU-time based on the boolean function-based encoding is less than that based on CBLQ.