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34 2. Background and Related Work metadata available for the raster, but not to the improvement of the computation of aggregate operations over the values of raster datasets. At present, pre-aggregation support in array databases is limited. Only one comparatively simple pre-aggregation technique has been used, namely image pyramids. The limitation of this technique to two-dimensional datasets and hard-wired interpolation calls for the development of more flexible and efficient techniques. From our study of data modeling, storage techniques, operations in OLAP and remote sensing imaging applications, we have observed the following similarities: • Array databases and OLAP systems typically employ multidimensional data models to organize their data. • Both application domains handle large volumes of multidimensional data. • Operations convey a high degree of similarity, for instance, a roll-up (aggregate) operation in OLAP such as computing the weekly sales per product is very similar to scaling a satellite image by a factor of seven along the X axis. Figure 2.14 illustrates this similarity. (a) Scaling operation (b) Roll-Up operation Figure 2.14. Comparison of Roll-Up and Scaling Operations
2.3 Discussion 35 • Both application domains use pre-aggregation approaches to speed up query processing: OLAP pre-aggregation techniques support a wide range of aggregate operations and speed up query processing by several orders of magnitude (last benchmark reported factors up to 100 times [29, 88]). Scaling of 2D datasets always uses the same scale factor on each dimension to maintain a coherent view, whereas for datasets of higher dimensionality, the scale factor is independent. Scaling resembles a primitive form of pre-aggregation in comparison to existing OLAP pre-aggregation techniques. • While data in OLAP applications are sparsely populated, remote sensing imagery usually are densely populated (100%). There are no guidelines explaining when an OLAP data cube is considered sparse or dense. However, when a data cube contains 30 percent empty cells it is usually treated with sparsity-handling techniques in most OLAP systems. Furthermore, when compared to well-known OLAP pre-aggregation techniques, GIS image pyramids are different in several respects: • Image pyramids are constrained to 2D imagery. To the best of our knowledge there is no generalization of pyramids to n-D. • The x and y axes are always zoomed by the same scalar factor s in the 2D zoom vector (s, s). This is exploited by image pyramids in that they only offer preaggregates along a scalar range. In this respect, image pyramids actually are 1D pre-aggregates. • Several interpolation methods are used for resampling during scaling. Some techniques are standardized [48], they include nearest-neighbor, bi-linear, biquadratic, bi-cubic, and barycentric. The two scaling steps incurred for image pyramids (construction of the pyramid level and rest scaling) must be done using the same interpolation technique to achieve valid results. In OLAP, summation during roll-up corresponds to linear interpolation in imaging. • Scale factors are continuous, as opposed to the discrete hierarchy levels in OLAP. It is, therefore, impossible to materialize all possible pre-aggregates. Based on these observations, this thesis aims to systematically carry over results from OLAP to array databases and provide pre-aggregation support not only for queries using basic aggregate functions, but to more complex operations such as scaling. As a preliminary and fundamental step, it is necessary to have a clear understanding of the various operations performed on remote sensing imagery and to identify those that involve aggregation computation. Next chapter addresses this issue in more detail.
Page 1: Applying OLAP Pre-Aggregation Techn
Page 5 and 6: Acknowledgments I would like to exp
Page 7 and 8: Abstract Large multidimensional arr
Page 9 and 10: Contents 1 Introduction and Problem
Page 11 and 12: List of Figures 2.1 3D Array . . .
Page 13 and 14: List of Tables 3.1 UNO and FAO Suit
Page 15 and 16: Chapter 1 Introduction and Problem
Page 17 and 18: Relevant and complementary question
Page 19 and 20: 1.2 Publications Related to this Th
Page 21 and 22: Chapter 2 Background and Related Wo
Page 23 and 24: 2.1 Array Databases 17 Figure 2.2 s
Page 25 and 26: 2.1 Array Databases 19 toward the s
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Page 29 and 30: 2.1 Array Databases 23 given image
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Page 39: 2.3 Discussion 33 spatial-vector da
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Page 67 and 68: 3.3 Summary 61 Slicing The slicing
Page 69 and 70: Chapter 4 Answering Basic Aggregate
Page 71 and 72: 4.1 Framework 65 pre-aggregated res
Page 73 and 74: 4.2 Cost Model 67 By partitioning t
Page 75 and 76: 4.2 Cost Model 69 Cost of independe
Page 77 and 78: 4.3 Implementation 71 Algorithm 1 Q
Page 79 and 80: 4.4 Experimental Results 73 Query E
Page 81 and 82: 4.5 Summary 75 pre-aggregates: inde
Page 83 and 84: Chapter 5 Pre-Aggregation Support B
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Page 87 and 88: 5.2 Conceptual Framework 81 Benefit
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5.5 Experimental Results 85 Algorit
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5.5 Experimental Results 87 (a) Que
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5.5 Experimental Results 89 (a) Sel
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5.5 Experimental Results 91 vectors
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5.5 Experimental Results 93 root no
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5.5 Experimental Results 95 Figure
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5.6 Summary 101 we considered non-u
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Chapter 6 Conclusion One of the big
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6.1 Future Work 105 more non-spatio
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Bibliography [1] Blakeley J. A., La
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BIBLIOGRAPHY 109 [22] Moon B., Vega
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BIBLIOGRAPHY 111 [47] ESRI Inc. Arc
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BIBLIOGRAPHY 113 [73] Stefanovic N.
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BIBLIOGRAPHY 115 [97] Kotidis Y. an
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