#@cli chough : radius>0,_BackgroundNoiseElim(15)>0,_precision(2)>=1,0<=_decimate(0.875)<=1,0.1<=_sensitivity(0.9)<1,_verbose(False)
#@cli : Select image(s) to be scanned for circular-like artifacts, via
#@cli : Circular Hough. 'radius' sets the scan target pixel radius
#@cli : (required). Replace selected images with 1xN vector array lists of the
#@cli : N discovered center points of matching circles, along with the
#@cli : specified target radius parameter, these data are for the benefit of
#@cli : downstream mask plotters. Increasing 'BackgroundNoiseElim' favors
#@cli : edges, but faint edges may be taken as noise and
#@cli : eliminated. Increasing 'precision' sizes an internal 'parameter space'
#@cli : image. It is a multiplier that scales parameter space upward from the
#@cli : selected input image. Multipliers of 2-4 are less susceptible noise
#@cli : but consumes memory. 'decimate' reduces an internally generated
#@cli : pointcloud of candidate center points.  Unity decimates the entire
#@cli : pointcloud (including solutions); zero leaves it intact, resulting in
#@cli : excessive plotting that can obscure solutions. The pointcloud tends to
#@cli : be highly redundant; decimations of 0.7 -> 0.9 are typical. Use
#@cli : smaller values (getting more points) for faint or noisy
#@cli : images. 'sensitivity' cuts all but the most likely solutions of
#@cli : clusters around potential center points; 0.9 is typical. Use lower (less
#@cli : sensitive) values to capture less likely center points, increase to
#@cli : reduce false solutions. Try to get 'radius' correct before adjusting
#@cli : 'sensitivity'. 'verbose' turns on intermediary displays of internal
#@cli : images and dumps of trial lists of center points.
#@cli : $ chough[imagetocheck] 55 -if h repeat {h} a='{I(0,$>)}' echo \$a done -fi
chough : check "${1}>0 &&                   \
                ${2=15}>0 &&                \
                ${3=2}>=1.0 &&              \
                ${4=0.875}>=0 && ${4}<=1 && \
                ${5=0.9}>=0.1 && ${5}<=1 && \
                isbool(${6=0})"
   rad,nsmooth,pr,decim,sensitivity,verb=${1-6}
   -echo[^-1] "Search for circles of radius"$1" in selected images and report centers in 1xN image vectors."
   -foreach {
      nm={-1,n}
      -name. inputimage
      ow={w#$inputimage}
      oh={h#$inputimage}

      # Sprite radius
      sd={_round($pr*$rad+1,1)}

      -edges[inputimage] $nsmooth%
      -oneminus[inputimage]
      -if $verb
          -display[inputimage] ,
      -fi
      # Trimming the data
      # has little effect on solution
      -fill[inputimage] 'i>0?(u(1)>($decim)?1:0):0'
      -input {$ow*$pr},{$oh*$pr},1,1
      -name. sprite

      # Draw circular sprite for shift/adding paramspace
      # edgepoints. Draw just one circle, then rubber-
      # stamp with shift/add
      stat={ellipse(#$sprite,{w/2},{h/2},-$sd,-$sd,0,1,0xffffffff,1.0);1.0}
      -pointcloud[inputimage] 3
      -if w#$inputimage
         -channels[inputimage] 0,1
         -fill[inputimage] "$pr*I"
         ox,oy={I(#$inputimage,0,0)}

         # Shift sprite image by way of deltas
         # from point-to-point. Get those deltas
         # by subtracting the pointcloud from a
         # one-plot-point-shifted copy of itself,
         # i.e., foreach p(n)-p(n-1)

         +shift[inputimage] -1,0,0,0,2,0
         -move. 0
         -sub[-3,-2]
         -name.. diffs
         -input {$ow*$pr},{$oh*$pr},1,1
         -name. paramspace
         -shift[sprite] {$ox-w/2},{$oy-h/2},0,0,2,0
         -repeat {w#$diffs}
            -add[paramspace] [sprite]
            -shift[sprite] {I(#$diffs,$>,0)},0,0,2,0
         -done
         -keep[paramspace]
         -if $verb
            -display ,
         -fi
         -fill[paramspace] i>=$sensitivity*iM?1:0
         -if $verb
            -display ,
         -fi
         -if im==iM
            -echo[^-1] "No\ detected\ coins\ @\ "$rad"\ radius."
         -else
            # Find means of the noisy patches.
            -medianofclusters[paramspace] 32,$verb
            +fill[paramspace] "V=I(x,y);V=V/$pr;V[2]=$rad;V"
               -keep.
               -name. $nm
         -fi
      -else # Seems that w#$inputimage == 0 ...
         echo[^-1] $nm"\ seems to have no features. No points found."
      -fi
    }

#@cli medianofclusters: errorball(32)>0,_verbose(False)
#@cli : Find clusters in pointclouds; compute their
#@cli : medians. Package these in a column vector of
#@cli : centers. 'errorball' defines cluster radius. Points
#@cli : farther apart than this distance are not in the
#@cli : same cluster. 'verbose', when true, emits debug
#@cli : data to G'MIC shell log.
#@cli : $ medianofclusters[pointcloudimage] 64
medianofclusters: -skip ${1=32},${2=0}
   ed={$1^2}
   verb=$2
   echo[^-1] "Extract from selected images of impulse pixels \
   point cluster median locations with radius "$ed" or less."
   -foreach {
      -pointcloud. 3
      -channels. 0,2
      -if w>1 # Takes at least two points to cluster
         # Consolidate clusters: find
         # their average centers.
         nm={-1,n}
         -name. cloud
         -input 0
         -name. cstack
         -shift[cloud] 0,0,0,1,2
         -permute[cloud] cxzy
         -eval ">P=crop(#$cloud);
                 psz=size(P)/3;
                 erb=$ed;
                 vrb=$verb;
                 cc=0;
                 ACC=vector2(0);
                 if(vrb,print(P));
                 for(
# --------------- INIT
                     t=1;
                     k=1;
                     Q=P[1,2];
                     ACC+=Q;
                     if(vrb, print(ACC));
                     chk=P[0];
                     P[0]=t;
                     cc=1,
# --------------- CONDITION
                     chk==0,
# --------------- PROCEDURE
                     if(
                          chk==0,
                          t=t+1;
                          k=1;
                          P[0]=t;
                          cc=1;
                          Q=P[1,2];
                          ACC=Q
                       ),
# --------------- BODY
                     do(
                          if(vrb,
                               print(Q);
                               print(P[3*k,3])
                            );
                          if(
                               P[3*k]==0,
                               err = mse(Q,P[3*k+1,2]);
                               if(vrb, print(err,erb));
                               if(
                                   err<erb,
                                   P[3*k]=t;
                                   cc+=1;
                                   ACC+=P[3*k+1,2];
                                   if(vrb,
                                        print(P[3*k,3]);
                                        print(ACC);
                                        print(cc)
                                     )
                                 ),
                               _(DO BREAK: Remaining points in P already clustered);
                               break()
                             );
                          k=k+1;
                          if(vrb, print(k)),
                          k<psz
                       ); _(Do clustering);
                       da_push(#$cstack,[ACC/cc,t]);
                       _(P sort: Shuffle unclustered points to front);
                       P=sort(P,1,psz,3);
                       chk=P[0];
                       if(vrb,
                            print(t);
                            print(chk);
                            print(P)
                         )
# --------------- END FOR FINDING CLUSTER CENTERS
                    ); _(for: Find median points of clusters);
                 if(vrb, print(P));
                 da_freeze(#$cstack)
               " # eval math expression argument
         -remove[cloud]
         -name. $nm
      -fi # w>1 - Takes at least two points to cluster
   } # foreach image in command's selection

#@cli circlefix : radius>0,_preblur(0)>=0,_outer(2)>0,_nsmooth(15)>=0,_medianf(10)>0,_medians(10)>0,_decimate(0.125)>=0&&<=1,senverbose=0
#@cli : Replace circular features with given 'radius' with an inpaint-generated
#@cli : synthesized patch.
#@cli : 'preblur' Optional pre-blurring to reduce false identification of
#@cli :           circular features. Default to no blurring (0).
#@cli : 'outer'   Optionally extend synthesized path boundary by outer number
#@cli :           of pixels. Default to two pixels.
#@cli : 'nsmooth' Edge-detection smoothing. Default to 15, Larger to further
#@cli :           smooth edges; smaller to detect faint circular features.
#@cli : 'medianf/medians' Blur/sharpen parameters for edge detection. Default
#@cli :           to 10/10. Adjust blur down and sharpen up for greater edge
#@cli :           detection, but also susceptibility to false detection.
#@cli : 'decimate' Decimate pointcloud by this factor. Default to
#@cli :           0.125; limit to 1 (no decimation). Smaller arguments yield
#@cli :           greater decimation and faster results, but a greater
#@cli :           liklihood of missed circular features.
#@cli : 'sensitivity' Reduces all but the most likely solutions of pointcloud
#@cli :           clusters around potential center points; 0.9 is typical.
#@cli :           Use lower (less sensitive) values to capture less likely
#@cli :           center points, increase to reduce false solutions.
#@cli :           Try to get 'radius' correct before adjusting 'sensitivity'.
#@cli : 'verbose' Set to enable display of intermediary analytic images.
#@cli : $ circlefix[0] 32
circlefix :    check "${1}>0    &&                \
                      ${2=0}>=0 &&                \
                      ${3=2}>0  &&                \
                      ${4=15}>0 &&                \
                      ${5=10}>0 &&                \
                      ${6=10}>0 &&                \
                      ${7=0.125}>0 && ${7}<=1 &&  \
                      ${8=0.9}>=0.1 && ${8}<=1 && \
                      isbool(${9=0})"
    rad,preblur,outer,nsmooth,medianf,medians,decimate,sensitivity,verbose=${1-9}
    -echo[^-1] "Seek "$1" pixel radius circles in selected images; perform inpaint removal of same."
    -foreach {
       nm={-1,n}
       -name. coinpic
       +blur[coinpic] {$preblur},2
       -median. {$medianf},{$medians}
       -name. medianpic
       -if $verbose -v + -fi
       +chough[medianpic] $rad,$nsmooth,1,$decimate,$sensitivity,$verbose
       -name. clist
       +fill[medianpic] 0
       -name. mask
       xmin,ymin=1e06
       xmax,ymax=-1e06
       -repeat {h#$clist}
          cx,cy,r={I(#$clist,0,$>)}
          ofs={$r+$outer}
          -if isnum($sprite)==0
             -input {2*$ofs+1},{2*$ofs+1},{d#$medianpic},{s#$medianpic},1
             -name. sprite
          -fi
          -image[mask] [sprite],{$cx-$ofs},{$cy-$ofs}
          -if $xmin>$cx-$ofs xmin={$cx-$ofs} -fi
          -if $xmax<$cx+$ofs xmax={$cx+$ofs} -fi
          -if $ymin>$cy-$ofs ymin={$cy-$ofs} -fi
          -if $ymax<$cy+$ofs ymax={$cy+$ofs} -fi
       -done
       -remove[^coinpic,mask]
       -if $verbose
          -display ,
       -fi
       -inpaint[coinpic] [mask],15,45,1.5,1,1.5,0,0.05,50,{$outer>0}
       +luminance[coinpic]
       -name. varpix
       +crop[varpix] $xmin,$ymin,$xmax,$ymax,2
       -if $verbose
          -echo {iv}","{iv#$varpix}
          -display ,
       -fi
       -if (iv/iv#$varpix)<=0.25
          -inpaint_matchpatch[coinpic] [mask],0,15,13,45,1,1
       -fi
       -keep[coinpic]
       -name. $nm
    }