Spatial Analysis Part 3Analyzing Raster DataNeighborhood FunctionsNeighborhood OperationsSlide 5Slide 6Slide 7Slide 8Neighborhood Operation: Majority FilterNeighborhood Operation - VarianceThe Mean Operation RevisitedEdge EnhancementEdge Enhancement FilterSlide 14Slide 15Density fieldsKernel Function ExampleSlide 18A More Familiar ExampleKernel SizeZonal FunctionsSlide 22Example ZonesZonal StatisticsSpatial AutocorrelationSlide 26Slide 27Slide 28Spatial Autocorrelation ExampleSlide 30Odds and EndsSpatial Analysis Part 3Analyzing Raster Data•Types of functions–Local •These functions happen on a cell-by-cell basis•Example = map algebra –Neighborhood (a.k.a. Focal)•The values for an output cell are derived using neighboring cells•This happens in “window” or “moving window” analyses•Example = filters (e.g., spatial enhancement)–Zonal•The values of output cells are derived using cells in pre-defined zones•Often these zones are vector objects•Example = zonal statistics–Global•The values of the output cells are derived using all cells•Example = cost pathsNeighborhood FunctionsIn neighborhood operations, we look at a neighborhood of cells around the cell of interest to arrive at a new value. We create a new raster layer with these new values.A 3x3 neighborhoodNeighborhood OperationsAn input layerCell ofInterest• Neighborhoods of any size can be used• 3x3 neighborhoods work for all but outer edge cellsNeighborhood Operations•The neighborhood is often called:–A window–A filter–A kernel–They can be applied to:•Raw data (e.g., imagery pixels)•Classified data (nominal landcover classes)A 3x3 neighborhood• The mean for all pixels in the neighborhood is calculated.• The result is placed in the center cell in the new raster layer.2 2 3 4 55 2 1 5 72 6 4 9 73 8 8 3 81 9 1 4 62 2 3 4 55 2 1 5 72 6 4 9 73 8 8 3 81 9 1 4 66419183883794627512554322InputLayerResultLayer3 4 5Neighborhood Operation: Mean FilterLandsat TM 543 False Color Image of Tarboro, NCNormal Image Smoothing FilterSmoothed ImageNeighborhood Operations•Why might we use a filter like this?•Suppose you have a nominal dataset (e.g., a landcover classification)•Sometimes classifications are ‘speckled’.–Usually a few misclassified pixels within a tract of correctly-classified landcover–We want to reclassify those pixels as the surrounding landcover typeNeighborhood Operation: Majority Filter242211338313322723253332224221133831332272325333222422113883133227232533322InputLayerResultLayer2 3 3•The majority value (the value that appears most often, also called a mode filter):Neighborhood Operation - Variance•We may want to know the variability in nearby landcover for each raster pixel–To find cultivated areas - usually less variability than natural area–To find where areas where eco-zones meet•The variance of a 3x3 filter on, for instance, an NIR (near infra red) satellite image band will help find such areas.64191838837946275125543226419183883794627512554322ResultLayer6419183883794627512554322InputLayer2.756 5.751/9 1/9 1/91/9 1/9 1/91/9 1/9 1/9641918388379462751255432264191838837946275125543226419183883794627512554322InputLayerResultLayer3 4 5The Mean Operation Revisited•In the mean operation, each cell in the neighborhood is used in the same way:-1 -1 -1-1 9 -1-1 -1 -1641918388379462751255432264191838837946275125543226419183883794627512554322InputLayerResultLayer-7 -26 5Edge Enhancement•Cells can be treated differently within a kernel:This is an edge enhancement filter (discussed below).Edge Enhancement Filter-1 -1 -1-1 9 -1-1 -1 -1•Why is this an edge enhancement filter? It enhances edges. Let’s look at the kernel’s behavior at and away from edges: Away from edge (in areas with uniform landcover) At edges (between areas with differing landcover)20 19 20 20 19 2120 20 19 20 21 2020 21 20 20 19 205 4 5 4 5 55 5 5 4 6 55 4 4 6 5 4-1 -1 -1-1 9 -1-1 -1 -121 11 22 3076 67 66 56-21 -38 -48 -388 9 -6 16Filter Result:Edge Enhancement FilterEdge EnhancementSharpening FilterNormal ImageEdge enhancement filters sharpen images.Density fields•Neighborhood Operation can create a density surface from discrete point dataA typical kernel functionThe result of applying a 150km-wide kernel to points distributed over CaliforniaKernel Function ExampleKernel Function ExampleKernel width is 16 km instead of 150 km. This shows the S. California part of the database.A More Familiar Example•This is a neighborhood statistic applied to the “Midwest” shapefile from our lab #4•In this case I used a circular kernel (radius 3 cells, cell size = 0.25 degrees) and summed the count value for all pointsKernel Size•The smoothness of the resulting field depends on the width of the kernel•Wide kernels produce smooth surfaces•Narrow kernels produce bumpy surfacesZonal FunctionsZonal Functions•Zonal statistics provide a summary of what is going on in an area (i.e., a zone) by including all the raster cell values that are within that zone•Zones can be defined using raster or vector data•Summary statistics include: –Mean, min, max, range, count, standard deviation, etc.•ArcGIS will also treat lines and points as zonesExample Zones•Raster Zones: –Each state has a different value–All cells in each state have that value•Vector Zones: –Each state has associated attributes–Attributes include name, etc.Zonal Statistics•Example:–How much of each landcover type is in a county?–Zonal attributes will count the pixels of each cover type within the land parcel polygon•Example 2:–What are the average, minimum, and maximum slope values for a hiking trail?–Zonal attributes will include all pixels that intersect the hiking trail line featureSpatial AutocorrelationSpatial Autocorrelation•Tobler’s Law – "Everything is related to everything else, but near things are more related to each other" – Waldo Tobler.•Spatial Autocorrelation is, conceptually as well as empirically, the two-dimensional equivalent of redundancy.•It measures the extent to which the occurrence of an event in an areal unit constrains, or makes more probable, the occurrence of an event in a neighboring areal unit.•We won’t get very deep into this topic, but I want you to at least hear the term.Arthur J. Lembo, Jr., Cornell University www.geography.hunter.cuny.edu/~afrei/gtech702_fall03_webpages/notes_spatial_autocorrelation.htmSpatial