Hi,

Imagine a detector with square pixels, the pixels arranged in a 256 x 256 matrix. Every pixel has an associated intensity value, normalized in such a way that the biggest value is at the center and it is 1.0. A pixel is characterized with a triplet{i,j,value}, where i is the row, j is the column and value is the intensity. Taking the central {128,128} pixel I draw an annuli with an inner radius and outer radius of {6.89148, 11.4858} pixels. Pixel {0,0}is the lower left corner. This annuli will cover some central area of the detector.
Then starting at the bottom line of the covered pixels, I look a 3x3 matrix at the leftmost pixel of the mentioned pixel line.
Then I look at the center of this 3x3 matrix if it is a maximum intensity or a minimum among the nine in the 3x3 matrix, and if it is, then I collect that value with its pixel coordinates.
Then I slide this 3x3 matrix till I get to the last such position where I still have a full 3x3 matrix. If I cannot get a full 3x3 matrix, - let say hit the inner radius somewhere -, then I just slide further. If no more such position is attainable on the given pixel line then I slide up one pixel, look for the leftmost starting position and repeat the above process. I do this till I cover all the pixels under the annuli.

Here is the code below that does this. For small annuli it runs relatively fast, but for bigger annuli - {43.6461, 48.2404} - it is not so fast, even on a 4 core MacPro. So I am interested to see which ways can I still speed it up. Oh, and at once I do it with 67 different configurations. Annuli200[[k]] is one such annuli where k goes from 1 to 67. Annuli[[k]] contains a bunch of triplets, the first one for the bottom left pixel and the last one for the upper right pixel in the given annuli. Thanks ahead, János

pixelScale = 21.766; (* mas/pixel *)
masdelta = 50/pixelScale;
mas200 = 200/pixelScale;


rr = ParallelTable[Reap[
   firsti = First[First[annuli200[[k]] ] ];                                       (* Bottom pixel line in the annuli *)
    lasti = First[Last[annuli200[[k]] ] ];                                           (* Top pixel line in the annuli *)
    firstj = 
     First[Rest[
       First[Select[annuli200[[k]] , #[[1]] == firsti &] ] ] ];       (* The starting column on the bottom pixel line *)
    delta = 2;
    While[firsti + delta <= lasti,
     firstinline = First[Select[annuli200[[k]], #[[1]] == firsti &]];  (* the per moment starting triplet on the per moment pixel line *)
     firstj = 
      First[Rest[
        First[Select[annuli200[[k]] , #[[1]] == firsti &] ] ] ];    (* the per moment column on the per moment pixel line *)
     lastinline = Last[Select[annuli200[[k]], #[[1]] == firsti &]];   (* the per moment end triplet on the per moment pixel line *)
     lastj = First[Rest[lastinline]];                                  (* the last column on the per moment pixel line *)
     While[firstj <= lastj - delta,
      dd = 
       Select[annuli200[[k]], 
        firsti <= #[[1]] <= firsti + delta && 
          firstj <= #[[2]] <= firstj + delta &];
      If [Length[dd] == 9,
       If[! MemberQ[Union[Map[dd[[5, 3]] >= #[[3]] &, dd]], False],
        Sow[Select[dd, #[[3]] == Max[dd[[All, 3]] ] &], maxn];
        ];
       If[! MemberQ[Union[Map[dd[[5, 3]] <= #[[3]] &, dd]], False],
        Sow[Select[dd, #[[3]] == Min[dd[[All, 3]] ] &], minn];
        ];
       ];
      firstj++
      ];
     firsti++;
     ], {maxn, minn}], {k, 1, Length[annuli200]}];