how to simplify connected blobs

Hi, i have a binary image. I can find the boundaries with the bwboundaries and get point list of boundary of a each blobs and pass to some line simplification algorith e.g. Douglas Peucker algorithm (see fig in http://stackoverflow.com/questions/1849928/how-to-intelligently-degrade-or-smooth-gis-data-simplifying-polygons).

The Douglas peucker give back points that need to be retained after simplification, my problem is how to connect retained points to form a closed polygon.

Anybody has a hint, how it should be done.

THanks

Answer 1

[Sven]

Hi Sukuchha,

I think that you just need to do this:

XY = [0 0; 1 0; 1 1; 0 1]; % unclosed XY points
XY_closed = XY([1:end 1],:); % closed XY points

The Douglas Peucker algorithm (at least, the one used by reducem in the Mapping Toolbox) takes account of the shape as a polygon, so its result should be closed (or at least closeable via the code I gave above).

Furthermore, the output from bwboundaries supplies each boundary as closed (ie, the first XY boundary point is coincident with the last XY boundary point), so I think you can simply pass the results of bwboundary to a Douglas Peucker function, and then use that result directly.

BW = false(9)
BW(3:6,3:6) = true
bb = bwboundaries(BW)
bb{1}
ans =

     2     2
     2     3
     2     4
     3     4
     4     4
     4     3
     4     2
     3     2
     2     2  % Note that this last coordinate is the same as the first

[newX, newY] = reducem(bb{1}(:,2),bb{1}(:,1));
[newX, newY]
ans =

     2     2
     4     2
     4     3
     4     4
     2     4
     2     2 % In the reduced result the first/last coords also match

If you want to turn this reduced polygon back into a mask that was the same size as the original BW, you can just use poly2mask() as follows:

newBW = poly2mask(newX,newY,size(BW,1),size(BW,2)) - BW

[Sukuchha]

Hi Sven, Thank you very much for taking time to answer in an elaborate manner. The points list returned by reducem is a close one. My problem is how to fill points inside the returned list as 1's to produce another binary image to represent as a blob.

What i am doing is trying to smoothen the boundary of buildings that i detected in Remote sensing images. After line simplication with Douglas-pecker algorithm, i want to have another image in which buildings lines are smoothen with closed polygon, the points inside polygon as 1's and the points outside polygon as 0's.

[Sven]

Ok, I've updated the answer with a call to poly2mask. Note that the end result ( newBW ) may have tiny pieces near the corners different (from your input) by up to 1 pixel as explained here.

[Sukuchha]

Hi sven, Thank you very much your kind help, Poly2mask function is what i am missing. One last questions, can poly2msk can handle blobs with the holes as well. Some of my buildings have a rectangualar shape with a hole (courtyard), in this case how poly2mask works with reduced number of points given by douglas pecker algo. I will try and see if this works in the case i mentioned, and let you know tommorrow.

Thanks a heap.

Answer 2

[Sven]

Hi Sukuchha, please see this blog post or this file exchange entry. It does exactly what you're looking for.

[Image Analyst]

Sukuchha, why do you want to simply the boundary, or represent it with fewer vertices, anyway? For what purpose do you want to do that? Why not just use the full resolution data?