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UNC-Chapel Hill GEOG 070 - LECTURE NOTES

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Neighborhood OperationsSlide 2Slide 3Slide 4Slide 5Slide 6Neighborhood Operation: Majority FilterNeighborhood Operation - VarianceThe Mean Operation RevisitedEdge EnhancementEdge Enhancement FilterSlide 12Slide 13Density fieldsKernel Function ExampleKernel SizeKernel SizeThe CentroidCentroidUSA Population CentroidIn 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 are called convolution operations.Neighborhood Operations•The neighborhood is often called:–A window–A filter–A kernel–They can be applied to:• raw data (BV’s)•classified data (nominal landcover classes)A 3x3 neighborhoodLandsat TM 543 False Color Image of Tarboro, NCNormal Image Smoothing FilterImage Smoothing• The mean for all pixels in the neighborhood is calculated.• The result is placed in the center cell in the new raster layer.•This operation can be done for all cells, or just some cells.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•Suppose you have a nominal dataset: a landuse classification.•Sometimes classifications are ‘speckled’.–Usually a few misclassified pixels within a tract of correctly-classified landcover–How do we correct this? Filter.–We want to reclassify those pixels as the surrounding landcover type.–What kind of filter do we use for this operation?Neighborhood 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 areas•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. Ha! 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 Size•The smoothness of the resulting field depends on the width of the kernel•Wide kernels produce smooth surfaces•Narrow kernels produce bumpy surfacesKernel Size Kernel width is 16 km instead of 150 km. This shows the S. California part of the database.The Centroid•The centroid is the spatial mean. The ‘average’ location of all points.•The centroid can also be thought of as the balance point of a set of points.Centroidxii=1i=nnx =yii=1i=nny =For a set of (x,y) coordinates, the mean center (x,y) is computed using:The spatial mean is called the centroid.USA Population Centroid•Population centroid change over time in


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