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.
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
Incidentally, I chose to make the eight images in this illustration with Mathematica commands because they are so simple, easy, and fast to execute:
The workflow in ArcGIS is the same but the syntax will be lengthier. If you really want to use
Using the Spatial Analyst Extension, you can use some of the Generalization tools. Some of them perform similar tasks, so you might need to play around with a few to get the results to be how you want them. But, I would have a look at the Majority Filter tool and the Boundary Clean tool.
Here is a page on the concepts of these two tools.
I'm not sure how to perform these tasks in R, but here is a post on how to perform a Majority Filter using GRASS GIS.