arcgis desktop - Performing Raster Noise Reduction and Edge Smoothing?

I have a raster image like this

I want to delete the isolated noise point and smooth the edge (say the white single points, and I want the edges of the entity look smooth). How can I do this in ArcGIS or in R?

The cell size is 30*30.

Answer

The morphological operations Expand and Shrink were created for this kind of processing. Use ArcGIS (or GRASS or Mathematica) because R's "raster" library is too slow.

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Often it helps to experiment a little with the parameters: you have to decide how much expanding and shrinking is needed to clean an image; and usually you want to do as little as possible, because each operation tends to smooth out some of the sharp details. Here is a sequence that works well to eliminate much of the apparent "noise" while maintaining most of the detail in the "entities". "Expand" and "shrink" are both with reference to the white cells, so that expanding causes them to grow outwards and shrinking causes the black cells to encroach into white regions.

The "difference" column uses color to highlight differences between the start and end image at each step: blue for black that turned to white, and orange for white that turned to black.

If the larger remaining pieces need to be removed, that might best be done with RegionGroup to identify them, after which they can be obliterated through reclassification. This was an option at the outset, but a little initial cleaning with Expand and Shrink reduces the work and provides the desired smoothing.

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Incidentally, I chose to make the eight images in this illustration with Mathematica commands because they are so simple, easy, and fast to execute:

i = Import["http://i.stack.imgur.com/umDg7.png"];
l = Dilation[k = Erosion[j = Dilation[i, 2], 3], 1];      (* This does all the work *)
delta = ColorCombine /@ {{i, j}, {j, k}, {k, l}, {i, l}}; (* Compares images *)

The workflow in ArcGIS is the same but the syntax will be lengthier. If you really want to use R, load the "raster" library and exploit focalFilter to create functions to do the expanding and shrinking. Then wait about a minute each to execute the operations... .