Raster model. Raster model. Resolution. Value and data types. Structure and storage. Cell. Values. Data

Transcription

1 Raster model. Resolution. Values and data types 3. Storage. Fitting rasters 5. Map algebra 6. Interpolation 7. Conversion vectorraster 8. Vector vs. raster Raster model Divides the space into a regular grid of cells in a specific order each cell has one assigned value each place is occupied by a single cell Resolution Value and data types spatial Values Integer Real Alphanumeric (coded as numbers) Data Continuous functions Categorical data spectral (number of distinct values that can be stored) Cell Generally a cell has been assigned a single value maybe inadequate: a border can cross a cell rules for deciding the classification Structure and storage n_raster.html

2 Coordinates Structure: Zones and Regions Zones are groups of cells that share the same value Regions are contiguous zones Null image coordinates real coordinates Structure: Associated tables Storage Only to integer-valued rasters Value and Count of zones (not of regions) always available Other attributes may be added Null Row major ABBB ABBB AABB AAAB Column major AAAA BBAA BBBA BBBB For integer grids only: Run Length Encoding (RLE) Row Major A3BA3BAB3AB RLE Column Major ABA3BAB Storage quadtrees Quadtrees nd partition th partition original st partition 3rd partition final tree

3 Storage Fitting rasters The generic model is implemented in diverse computational formats: GRID proprietary format ESRI JPEG, TIFF, MrSid standard format for display but not for analysis; generically need an additional file to get the location (chamado world file) Type Image File World File TIFF image.tif image.tfw Bitmap image.bmp image.bpw BIL image.bil image.blw JPEG image.jpg image.jpw Before the analysis, grids must be made compatible Need for resampling the grid Change in the projection system Change in the width of cells Georeferencing Original image (grid) Fitting rasters georeferencing Reference map Corrected image Original image Fitting rasters Pixel value in the corrected image is the value of the nearest pixel in the original image. Advantages Computationally simple Does not change original values Applies to nominal scales Disadvantages nearest neighbor Objects may displace up to half pixel Structures get a zigzag shape Fitting rasters bilinear interpolation The value of the pixel in the corrected image is a weighted average value of the closest pixels in the original image. Advantages Smoothes the image Disadvantages Smoothes the image Changes pixel values Local functions Focal functions Zonal functions Map algebra Global functions 3

4 _ Local functions combine the values of one or more rasters to produce a new raster using the same cell positions in each one Null Null Null Null Null Null = Local functions Arithmetic operators Basic operators (+,-,*,/) available. Rounding and precedence. Boolean operators Logic operators (AND, OR, NOT) available. Output: =FALSE, =TRUE Input: =FALSE, ~=TRUE Pop Pop 99 Var Pop Local functions Local functions 3 5 Null Null Null Null 3 8 Null 7 Null AND = Null 9 5 Null 3 Null Null Null Null Null Null 3 8 Null 7 Null AND = Null 9 5 Null 3 Null reclassify [,]= ],6]= ]6,9]= Focal functions Focal functions take the value from a cell s neighborhood Focal (normal) Block Nas operações focais existe Focal operations use a mobile uma janela móvel, i.e., as window, i.e., neighbourhoods vizinhanças sobrepõem-se. overlap Nas operações de Bloco as vizinhanças Block operations use non-overlapping são justapostas. neighbourhoods. The output is the same O valor de output é igual em todas as for all cells in a given block células de um dado bloco.

5 Focal functions possible neighborhoods Focal functions Removing noise Errors/outliers Paul Bolstad, GIS Fundamentals Focal functions Zonal functions Roughness index R cel i, j ( X ij X cel ) Zonal functions are very similar to focal functions, except the neighbourhood has not a fixed shape, and can be defined by another grid Taking a raster, they calculate for each cell some function or statistic, using its value and that of all cells belonging to the same zone. Some zonal functions (type I) for which zones are defined by an isolated value, allow statistics or the quantification of geometric characteristics of input zones. Other zonal functions (type II) for which zones are defined through a second grid, allow the statistics or the filling of specific zones with values from the input grid. Zonal functions similar to focal functions, but the neighborhood has no fixed shape, being defined by the distribution of values (type I) or by a second grid (type II) zone layer A G G Zonal functions A Null X X 5 6 G A A X G A A X 3 3 A G G A X A A X X A 5 5 Null type I example: distance to the sea result type II example: zonal sum 5

6 Global functions Position - Buffer - Triangulation - Voronoi diagram Position and value - Visibility maps - Interpolation Global functions: Interpolation Set of methods to estimate unknown values of a function based on measured/known values x f(x) Point data, but a f(a) Phenomena extending to areas b? Transformations c f(c) Point to area d f(d) Polinomial Based on distance (IDW, Kriging, etc) Stochastic functions Linear f^(b) = f(a)(b-a)/(c-a) + f(c)(c-b)/(c-a) Simple polynomials f(x,y) = S S a ik x i y k a ik are the coefficients Polynomial fitted by minimum mean square error method f(x,y) = S S a ik x i y k + e Global functions: interpolation Point-to-area Calculation based on proximity only ex: Voronoi diagrams Global functions: interpolation Distance-based Splines: Based on the nearest points Smooth surfaces Not exact in input points Triangulations: Global functions:interpolation Distance-based IDW f(x,y) = z = ax + by + c z = ax + by + c z = ax + by + c z 3 = ax 3 + by 3 + c A OIJ I J A OIK O All things are related, but nearby things are more related than distant things A OJK K v n i n di v i di i v n i n p di p i di v i 6

7 Global functions: interpolation IDW Normalised weights weights (/di) / x y f(x,y)=zi Dist. à wi= obs. 8 = di / di (S/di) ? S/di =.6. f ^(65,37) = 59. x y z ? (x,y) = z = a + ax + ay Sz = a n + a S x + a S y Sz x = a S x + a S x + a S x y S z y = a S y + a S x y + a S y 75 = a (6) + a (5) + a (5) = a (5) + a (7)+ a (36) 5 = a (5) + a (36)+ a (7) f^(,3) = 9.9 f(x,y) = x -.3y IDW x y f(x,y)=zi Distance to observation 8 = di weights wi= / di (/di) / (S/di) ? S/di =.6. normalized weights Global functions: interpolation IDW: The larger the power, the larger the difference between neighbouring cells Exact interpolator (estimate on sample points gives the point value) As one moves away from the sample points, values will tend to the mean value Needs a good sample distribution f ^(65,37) = 59. Triangulation Quantification of error margins f(x,y) = z = ax + by + c J e = f^(x,y) - f(x,y) estimation error z = ax + by + c z = ax + by + c z 3 = ax 3 + by 3 + c A OIJ I O A OJK K e = /n S f^(x,y) - f(x,y) for n points MAE =e = /n S f^(x,y) - f(x,y) mean error mean abs. error A OIK MSE = /n S [ f^(x,y) - f(x,y) ] mean squared error 7

8 Converting vectorraster Converting vector raster just one value per cell decision rules largest part of the area (for polygons) value at the centre presence in cell (for lines) need to preserve rare features choice of spatial resolution: ½ the smallest lenght, or ¼ of the smallest area of the smallest non-point vector feature Raster advantages Simple data structure Easy analysis Low-tech platforms Remote sensing data Modeling is simple Raster disadvantages Spatial inaccuracy Generalization Implicit data. Each cell must be classified. Large data sets Vector advantages Closest to maps mental model Higher resolution Accuracy in positioning Node-vertex storage Understandable Topology Raster disadvantages Complex data structure Demands geometric processing More complex editing 8