Canny edge detector: Difference between revisions

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 Edge and non-edge points are represented as zeros and ones respectively. Edges are sets of connected points. Edge points are considered to be connected if within a 3X3 region (or if they are connected to a common third edge point). Edges are represented as points having a common unique identifier.
 <lang J>
-           ... implementation goes here ...
+NB. 2D convolution, filtering, ...
+convolve  =: 4 : 'x apply (($x) partition y)'
+partition =: 4 : '2 0 3 1 |: ((1{x) ([+\]) (2 0 1|: ((0{x) ([+\]) y)))'
+apply     =: 4 : '+/"1 (+/"2 (x *"2 y))'
+addborder =: (0&,@|:@|.)^:4
+normalize =: ]%+/@,
+resample  =: 4 : '|: (1{-x)(+/%#)\ |: (0{-x)(+/%#)\ y'
+crop      =: 4 : 0
+   'h w h0 w0' =: x
+   |: w{. w0}. |: h{. h0}. y
+)
+max3x3 =: 3 : '(1{1{y>0) * (>./,y)'"2
+attach =: 3 : 'max3x3 (3 3 partition (addborder y))'
+unique =: 3 : 'y*i.$y'
+connect =: 4 : 'attach^:x unique y'
+canny =: 3 : 0
+   image0 =: y
+NB. Step 1 - gaussian smoothing
+   NB. Gaussian kernel (from Wikipedia article)
+   <] gaussianKernel =. 5 5$2 4 5 4 2 4 9 12 9 4 5 12 15 12 5 4 9 12 9 4 2 4 5 4 2
+   gaussianKernel =. gaussianKernel % 159
+   image1 =: gaussianKernel convolve image0
+NB. Step 2 - gradient
+   <] gradientKernel =. 3 3$0 _1 0 0j_1 0 0j1 0 1 0
+   image2 =: gradientKernel convolve image1
+NB. Step 3 - edge detection
+   NB. find the octant (eighth of circle) in which the gradient lies
+   octant =: 3 : '4|(>.(_0.5+((4%(o. 1))*(12&o. y))))'
+   <(i:6)(4 : 'octant (x j. y)')"0/(i:6)
+   NB. is this gradient greater than [the projection of] a neighbor?
+   greaterThan   =: 4 : ' (9 o.((x|.y)%y))<1'
+   NB. is this gradient the greatest of immmediate colinear neighbore?
+   greatestOf   =: 4 : '(x greaterThan y) *. ((-x) greaterThan y)'
+   NB. relative address of neighbor relevant to grad direction
+   krnl0 =: _1  0
+   krnl1 =: _1 _1
+   krnl2 =:  0 _1
+   krnl3 =:  1 _1
+   og =: octant image2
+   NB. mask for maximum gradient colinear with gradient
+   ok0 =: (0=og) *. krnl0 greatestOf image2
+   ok1 =: (1=og) *. krnl1 greatestOf image2
+   ok2 =: (2=og) *. krnl2 greatestOf image2
+   ok3 =: (3=og) *. krnl3 greatestOf image2
+   image3 =: image2 *. (ok0 +. ok1 +. ok2 +. ok3)
+NB. Step 4 - Weak edge suppression
+   NB. weak, strong threshholds
+   NB. TODO: parameter picker algorithm or helper
+   threshholds =: 1e14 1e15
+   nearbyKernel =: 3 3 $ 4 1 4 # 1 0 1
+   magnitude =. 10&o. image3
+   weak   =: magnitude > 0{threshholds
+   strong =: magnitude > 1{threshholds
+   strongs =: addborder (nearbyKernel convolve strong) > 0
+   image4 =: strong +. (weak *. strongs)
+)
 }</lang>
 The above implementation solves the 'inner problem' of Canny Edge Detection fully in the J language, with no external dependencies.  Standard libraries provide necessary additional support including interfaces to image file formats and graphic displays.
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 <lang J>
+!:44'D:/rosettacode/canny'
-           ... usage goes  here …
+load'canny.ijs'
+NB. viewers
+require'viewmat plot'
+view =: (16b010101*i.256)&viewmat
+splot =: 'surface;mesh 0'&plot
+NB. image file importers/exporters
+require'png jpeg bmp'
+NB. image =: readjpeg 'camille.jpg'
+NB. image =: readbmp 'chess.bmp'
+NB. image =: readpng 'boat1.png'
+NB. image =: readpng 'valve.png'
+NB. image =: readjpeg 'lena.jpg'
+NB. from http://people.sc.fsu.edu/~jburkardt/data/pgmb/pgmb.html,
+NB>      distributed under the GNU LGPL license.
+    image =: readpng 'bird.png'
+NB. select (or combine) from color channels
+NB. if original image is grayscale, take any color channel
+red   =: <. image % 65538
+green =: 256 | <. image % 256
+blue  =: 256 | image
+image =: blue
+NB. detect the edges
+edges =: canny image
+view 1-edges
+viewmat 1000 connect edges
 </lang>