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 This can also degrade data processing Two issues: 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 They define a total order on the cells of a 2D grid: assign numbers to the cells the cells Also called Space-filling curves Also called Space-filling curves Some methods partially preserve proximity: 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 In our examples, we consider space-filling curves on an underlying N X N array of cells (grid), where N = 2 d (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 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 In other words we embed a 2-dimensional space into a 1-dimensional space Cell numbers should be easy to compute 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: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 Other variants are used too 0145 2367 891213 10111415 NWNE SWSE

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

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)