Spatial Information Systems (SIS) COMP 30110 Raster-based structures (2) Data conversion

1. Spatial Information Systems (SIS) COMP 30110 Raster-based structures (2) Data conversion

2. Efficiency issues The simple raster-based structure of the example is inefficient in terms of data storage: regardless of the data distribution it uses the same amount of disk space This can also degrade data processing Two issues: compression methods (efficiently store data) scan order (how to scan the data in the array)

3. Scan-order methods Mainly concerned with performance in terms of data processing They define a total order on the cells of a 2D grid: assign numbers to the cells Also called Space-filling curves Some methods partially preserve proximity: two cells that are close in space are likely to be close in the total order In our examples, we consider space-filling curves on an underlying NXN array of cells (grid), where N = 2d (i.e., a complete quadtree with depth d)

4. Space-filling curves They define a total order (i.e., a linear order) on the cells of a 2D grid: assign numbers to the cells In other words we embed a 2-dimensional space into a 1-dimensional space Cell numbers should be easy to compute

5. Row method Scans one row at a time

6. Row-prime method Scans one row at a time but reverses every second row

7. Morton scan method Morton curve (it orders the quadrants of a quadtree as SW, SE, NW, NE) This method preserves spatial proximity relatively well

8. Morton scan method (cont.d) Also called Z-buffering: when the reverse order NW,NE, SW, SE is considered this method repeats a Z-like shape with four neighboring cells as a unit and repeats the shape at all levels Other variants are used too

9. Z-order and Z-values Coding of cells: Partition the space recursively into two halves (alternating X and Y dimension) Left and bottom parts are assigned code 0 Right and top parts are assigned code 1

10. 1 0 1 0111 (7) 1 1 0 010000(16) 0 1 0 0 10(2) 1 0 Z-order and Z-values (cont.d) Example: Z-value: (n,l) n = decimal value of the bit code l = level, i.e., number of bits

11. Peano-Hilbert curve Use of a U-like shape that repeats at all levels

12. Remarks Vector data: focus on spatial objects Raster data: focus on the underlying space Vector data: objects are explicitly stored Raster data: objects must be “extracted”

13. Remarks (cont.d) We have seen data structures for vector data and raster data In vector data structures, topology is explicit: a subset of the topological/connectivity relations is explicitly stored In raster data structures, topology is implicit: topological relations must be calculated (generally, use of MBRs)

14. Data conversion Intra-format conversion: raster-to-raster vector-to-vector Inter-format conversion: raster-to-vector vector-to-raster

15. Raster-to-raster Raster formats differ in the way they are stored: different layers in different files with same resolution pixels stored sequentially with all data values (corresponding to different layers) stored after each pixel etc. Conversion between raster formats requires reorganisation of the raster cells and their corresponding data values (relatively simple operation)

16. Vector-to-vector Different vector formats are based on different data structures Converting from one format to another requires converting from one data structure to another (more tricky)

17. Raster-to-vector This type of conversion must start with assumptions about the raster and vector representation of data For example, in a binary image, if a point occurs inside a cell, the cell value is 1, otherwise is 0 (interior black, exterior white) Connectivity: two different ways to connect adjoining pixels only orthogonally (4-connected) orthogonally and diagonally (8-connected)

18. Raster-to-vector (cont.d) 4-connected neighborhood: only pixels located in one of the four positions with respect to a given pixel are considered connected to it: immediately above, below, left, right

19. Raster-to-vector (cont.d) 8-connected neighborhood: adjoining cells that are diagonally located are also considered connected to the pixel

20. Raster-to-vector (cont.d) Other assumptions must be made in relation to the orientation of the resulting vector and its thickness An orthogonal vector (vector parallel to either x or y axis) with unit width can be converted from its raster structure using the 4-connected approach simply by joining adjacent pixels by unit vectors Orthogonal polygons can similarly be constructed

21. Raster-to-vector (cont.d) To extract a non-orthogonal vector with unit width from the corresponding raster structure, the 4-connected approach results in distortion because such a vector can only be represented by horizontal and vertical line segments, which lie in the general direction of the vector as fragmented segments

22. Raster-to-vector (cont.d) Consequently a polygon with several non-orthogonal vectors results in a high degree of distortion 8-connected approach results in a less distorted image Extracting correctly polygons and lines from a raster images is still a semi-automatic process

23. Vector-to-raster Converting a vector to a raster representation involves overlaying the vector to a raster array and identifying the pixels that the vector intersects This approach often produces a stair-step distortion (aliasing) Antialiasing: gray scale pixels according to coverage measures of the pixel by the vector (e.g., length of the intersection)