Selection of data in a region of interest in a matrix (with Mathematica)

I am having a (mathematica 8.0.1.0-) problem which I cannot solve by myself. I have measurement data in a matrix, I want to select some of them and then add them up.

To explain my problem better, here an easy example. The data can be produced by a matrix S:

S = Table[ -Sin[i/2] - Sin[j/2], {i,20}, {j,20}];

They can be nicely plotted with:

xmin = N[Min[S]]; 
xmax = N[Max[S]]; 
mycolorfun = Function[ Blend[{Blue,Cyan,Green,Yellow,Red},#] ];

and

MatrixPlot[S, PlotRange -> {All,All,All}, AspectRatio -> 1/1,
   ColorFunction -> (mycolorfun[ Rescale[ #1{xmin,xmax} ] ]&),
   ColorFunctionScaling -> False, MaxPlotPoints -> Automatic,
   FrameLabel -> {y,x} ]

Then one should get a picture similar to this one:

Now I want to select the data which are inside of the brown drawn polygon. These data should be added up at the end.

How can I do this? Ok, I could use rectangles and build a sub-matrix by choosing/guessing good start and end indices. Then I just have to build the sum of this sub-matrix. But I would prefer polygons (more precise if we do not argue about little problems with the matrix values which are crossed by the line of the polygon). And I would love it if I could select my region of interest (ROI) directly by “painting” the polygon into the Matrix (no more time consuming choosing/guessing of matrix indices).
Could somebody here help me with my problem? If it is not solvable with mathematica, is there some other program which I could use?

I would be very happy about some help and hints!