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u36-HIERARCHICAL DATA STRUCTURES

# u36-HIERARCHICAL DATA STRUCTURES - UNIT 36 HIERARCHICAL...

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Sheet1 Page 1 UNIT 36 - HIERARCHICAL DATA STRUCTURES <toc.html#UNIT36> UNIT 36 - HIERARCHICAL DATA STRUCTURES # A. INTRODUCTION <#SEC36.1> # B. INDEXING PIXELS <#SEC36.2> * Procedure <#SEC36.2.1> * Decoding locations <#SEC36.2.2> # C. THE QUADTREE <#SEC36.3> * Coding quadtrees <#SEC36.3.1> * Accessing data through a quadtree <#SEC36.3.2> * Comparison of different data structures <#SEC36.3.3> # D. VARIANTS OF QUADTREES <#SEC36.4> # E. ADVANTAGES OF HIERARCHICAL DATA STRUCTURES <#SEC36.5> # REFERENCES <#SEC36.6> # DISCUSSION AND EXAM QUESTIONS <#SEC36.7> # NOTES <#SEC36.8> UNIT 36 - HIERARCHICAL DATA STRUCTURES A. INTRODUCTION <#OUT36.1> * different scan orders produce only small differences in compression o the major reason for interest in Morton and other hierarchical scan orders is for faster data access * the amount of information shown on a map varies enormously from area to area, depending on the local variability o it would make sense then to use rasters of different sizes depending on the density of information + large cells in smooth or unvarying areas, small cells in rugged or rapidly varying areas o unfortunately unequal-sized squares won't fit together ("tile the plane") except under unusual circumstances + one such circumstance is when small squares nest within large ones * there are, however, some methods for compressing raster data that do allow for varying information densities B. INDEXING PIXELS <#OUT36.2>

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Page 2 overhead - Raster to quadtree I and II handout - Raster to quadtree * consider the 16 by 16 array in which just one cell is different o notation: row and column numbering starts at 0 + thus the odd cell is at row 4, column 7 Procedure <#OUT36.2.1> * begin by dividing the array into four 8x8 quadrants, and numbering them 0, 1, 2 and 3 as in the Morton order o quads 1, 2 and 3 are homogeneous (all A) o quad 0 is not homogeneous, so we divide only it into four 4x4 quads + these are numbered 00, 01, 02 and 03 because they are partitions of the 8x8 quad 0 + of these, 00, 01 and 02 are homogeneous, but 03 is divided again into 030, 031, 032 and 033 + now only 031 is not homogeneous, so it is divided again into 0310, 0311, 0312 and 0313 * what we have done is to recursively subdivide using a rule of 4 until either: o a square is homogeneous or o we reach the highest level of resolution (the pixel size) * this allows for discretely adaptable resolution where each resolution step is fixed * this concept is related to the use of Morton order for run encoding o if we had coded the raster using Morton order, each homogeneous square would have been a run + 8x8 squares are runs of 64 in Morton order, 4x4 are runs of 16, etc o the run encoded Morton order would have been: 16A 16A 16A 4A 1A 1B 1A 1A 4A 4A 64A 64A 64A o if we allow runs to continue between blocks we could reduce this to: 53A 1B 202A o i.e. a homogeneous block of 2m by 2m pixels is equivalent to a Morton run of 22m pixels Decoding locations <#OUT36.2.2>
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u36-HIERARCHICAL DATA STRUCTURES - UNIT 36 HIERARCHICAL...

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