Parasitemia/Parasitemia/ImgTools.fs

   1 module ImgTools
   2
   3 open System
   4 open System.Drawing
   5 open System.Collections.Generic
   6 open System.Linq
   7
   8 open Emgu.CV
   9 open Emgu.CV.Structure
  10
  11 open Heap
  12 open Const
  13 open Utils
  14
  15 // Normalize image values between 0uy and 255uy.
  16 let normalizeAndConvert (img: Image<Gray, 'TDepth>) : Image<Gray, byte> =
  17     let min = ref [| 0.0 |]
  18     let minLocation = ref <| [| Point() |]
  19     let max = ref [| 0.0 |]
  20     let maxLocation = ref <| [| Point() |]
  21     img.MinMax(min, max, minLocation, maxLocation)
  22     ((img.Convert<Gray, float32>() - (!min).[0]) / ((!max).[0] - (!min).[0]) * 255.0).Convert<Gray, byte>()
  23
  24
  25 let saveImg (img: Image<'TColor, 'TDepth>) (filepath: string) =
  26     img.Save(filepath)
  27
  28
  29 let saveMat (mat: Matrix<'TDepth>) (filepath: string) =
  30     use img = new Image<Gray, 'TDeph>(mat.Size)
  31     mat.CopyTo(img)
  32     saveImg img filepath
  33
  34 type Histogram = { data: int[]; total: int; sum: int; min: float32; max: float32 }
  35
  36 let histogramImg (img: Image<Gray, float32>) (nbSamples: int) : Histogram =
  37     let imgData = img.Data
  38
  39     let min, max =
  40         let min = ref [| 0.0 |]
  41         let minLocation = ref <| [| Point() |]
  42         let max = ref [| 0.0 |]
  43         let maxLocation = ref <| [| Point() |]
  44         img.MinMax(min, max, minLocation, maxLocation)
  45         float32 (!min).[0], float32 (!max).[0]
  46
  47     let bin (x: float32) : int =
  48         let p = int ((x - min) / (max - min) * float32 nbSamples)
  49         if p >= nbSamples then nbSamples - 1 else p
  50
  51     let data = Array.zeroCreate nbSamples
  52
  53     for i in 0 .. img.Height - 1 do
  54         for j in 0 .. img.Width - 1 do
  55             let p = bin imgData.[i, j, 0]
  56             data.[p] <- data.[p] + 1
  57
  58     { data = data; total = img.Height * img.Width; sum = Array.sum data; min = min; max = max }
  59
  60 let histogramMat (mat: Matrix<float32>) (nbSamples: int) : Histogram =
  61     let matData = mat.Data
  62
  63     let min, max =
  64         let min = ref 0.0
  65         let minLocation = ref <| Point()
  66         let max = ref 0.0
  67         let maxLocation = ref <| Point()
  68         mat.MinMax(min, max, minLocation, maxLocation)
  69         float32 !min, float32 !max
  70
  71     let bin (x: float32) : int =
  72         let p = int ((x - min) / (max - min) * float32 nbSamples)
  73         if p >= nbSamples then nbSamples - 1 else p
  74
  75     let data = Array.zeroCreate nbSamples
  76
  77     for i in 0 .. mat.Height - 1 do
  78         for j in 0 .. mat.Width - 1 do
  79             let p = bin matData.[i, j]
  80             data.[p] <- data.[p] + 1
  81
  82     { data = data; total = mat.Height * mat.Width; sum = Array.sum data; min = min; max = max }
  83
  84 let histogram (values: float32 seq) (nbSamples: int) : Histogram =
  85     let mutable min = Single.MaxValue
  86     let mutable max = Single.MinValue
  87     let mutable n = 0
  88
  89     for v in values do
  90         n <- n + 1
  91         if v < min then min <- v
  92         if v > max then max <- v
  93
  94     let bin (x: float32) : int =
  95         let p = int ((x - min) / (max - min) * float32 nbSamples)
  96         if p >= nbSamples then nbSamples - 1 else p
  97
  98     let data = Array.zeroCreate nbSamples
  99
 100     for v in values do
 101         let p = bin v
 102         data.[p] <- data.[p] + 1
 103
 104     { data = data; total = n; sum = Array.sum data; min = min; max = max }
 105
 106 let otsu (hist: Histogram) : float32 * float32 * float32 =
 107     let mutable sumB = 0
 108     let mutable wB = 0
 109     let mutable maximum = 0.0
 110     let mutable level = 0
 111     let sum = hist.data |> Array.mapi (fun i v -> i * v) |> Array.sum |> float
 112
 113     for i in 0 .. hist.data.Length - 1 do
 114         wB <- wB + hist.data.[i]
 115         if wB <> 0
 116         then
 117             let wF = hist.total - wB
 118             if wF <> 0
 119             then
 120                 sumB <- sumB + i * hist.data.[i]
 121                 let mB = (float sumB) / (float wB)
 122                 let mF = (sum - float sumB) / (float wF)
 123                 let between = (float wB) * (float wF) * (mB - mF) ** 2.;
 124                 if between >= maximum
 125                 then
 126                     level <- i
 127                     maximum <- between
 128
 129     let mean1 =
 130         let mutable sum = 0
 131         let mutable nb = 0
 132         for i in 0 .. level - 1 do
 133             sum <- sum + i * hist.data.[i]
 134             nb <- nb + hist.data.[i]
 135         (sum + level * hist.data.[level] / 2) / (nb + hist.data.[level] / 2)
 136
 137     let mean2 =
 138         let mutable sum = 0
 139         let mutable nb = 0
 140         for i in level + 1 .. hist.data.Length - 1 do
 141             sum <- sum + i * hist.data.[i]
 142             nb <- nb + hist.data.[i]
 143         (sum + level * hist.data.[level] / 2) / (nb + hist.data.[level] / 2)
 144
 145     let toFloat l =
 146         float32 l / float32 hist.data.Length * (hist.max - hist.min) + hist.min
 147
 148     toFloat level, toFloat mean1, toFloat mean2
 149
 150 let suppressMConnections (img: Matrix<byte>) =
 151     let w = img.Width
 152     let h = img.Height
 153     for i in 1 .. h - 2 do
 154         for j in 1 .. w - 2 do
 155             if img.[i, j] > 0uy && img.Data.[i + 1, j] > 0uy && (img.Data.[i, j - 1] > 0uy && img.Data.[i - 1, j + 1] = 0uy || img.Data.[i, j + 1] > 0uy && img.Data.[i - 1, j - 1] = 0uy)
 156             then
 157                 img.[i, j] <- 0uy
 158     for i in 1 .. h - 2 do
 159         for j in 1 .. w - 2 do
 160             if img.[i, j] > 0uy && img.Data.[i - 1, j] > 0uy && (img.Data.[i, j - 1] > 0uy && img.Data.[i + 1, j + 1] = 0uy || img.Data.[i, j + 1] > 0uy && img.Data.[i + 1, j - 1] = 0uy)
 161             then
 162                 img.[i, j] <- 0uy
 163
 164 let findEdges (img: Image<Gray, float32>) : Matrix<byte> * Image<Gray, float32> * Image<Gray, float32> =
 165     let w = img.Width
 166     let h = img.Height
 167
 168     use sobelKernel =
 169         new ConvolutionKernelF(array2D [[ 1.0f; 0.0f; -1.0f ]
 170                                         [ 2.0f; 0.0f; -2.0f ]
 171                                         [ 1.0f; 0.0f; -1.0f ]], Point(1, 1))
 172
 173     let xGradient = img.Convolution(sobelKernel)
 174     let yGradient = img.Convolution(sobelKernel.Transpose())
 175
 176     let xGradientData = xGradient.Data
 177     let yGradientData = yGradient.Data
 178     for r in 0 .. h - 1 do
 179         xGradientData.[r, 0, 0] <- 0.f
 180         xGradientData.[r, w - 1, 0] <- 0.f
 181         yGradientData.[r, 0, 0] <- 0.f
 182         yGradientData.[r, w - 1, 0] <- 0.f
 183
 184     for c in 0 .. w - 1 do
 185         xGradientData.[0, c, 0] <- 0.f
 186         xGradientData.[h - 1, c, 0] <- 0.f
 187         yGradientData.[0, c, 0] <- 0.f
 188         yGradientData.[h - 1, c, 0] <- 0.f
 189
 190     use magnitudes = new Matrix<float32>(xGradient.Size)
 191     use angles = new Matrix<float32>(xGradient.Size)
 192     CvInvoke.CartToPolar(xGradient, yGradient, magnitudes, angles) // Compute the magnitudes (without angles).
 193
 194     let thresholdHigh, thresholdLow =
 195         let sensibilityHigh = 0.1f
 196         let sensibilityLow = 0.0f
 197         use magnitudesByte = magnitudes.Convert<byte>()
 198         let threshold, _, _ = otsu (histogramMat magnitudes 300)
 199         threshold + (sensibilityHigh * threshold), threshold - (sensibilityLow * threshold)
 200
 201     // Non-maximum suppression.
 202     use nms = new Matrix<byte>(xGradient.Size)
 203
 204     let nmsData = nms.Data
 205     let anglesData = angles.Data
 206     let magnitudesData = magnitudes.Data
 207     let xGradientData = xGradient.Data
 208     let yGradientData = yGradient.Data
 209
 210     let PI = float32 Math.PI
 211
 212     for i in 0 .. h - 1 do
 213         nmsData.[i, 0] <- 0uy
 214         nmsData.[i, w - 1] <- 0uy
 215
 216     for j in 0 .. w - 1 do
 217         nmsData.[0, j] <- 0uy
 218         nmsData.[h - 1, j] <- 0uy
 219
 220     for i in 1 .. h - 2 do
 221         for j in 1 .. w - 2 do
 222             let vx = xGradientData.[i, j, 0]
 223             let vy = yGradientData.[i, j, 0]
 224             if vx <> 0.f || vy <> 0.f
 225             then
 226                 let angle = anglesData.[i, j]
 227
 228                 let vx', vy' = abs vx, abs vy
 229                 let ratio2 = if vx' > vy' then vy' / vx' else vx' / vy'
 230                 let ratio1 = 1.f - ratio2
 231
 232                 let mNeigbors (sign: int) : float32 =
 233                     if angle < PI / 4.f
 234                     then ratio1 * magnitudesData.[i, j + sign] + ratio2 * magnitudesData.[i + sign, j + sign]
 235                     elif angle < PI / 2.f
 236                     then ratio2 * magnitudesData.[i + sign, j + sign] + ratio1 * magnitudesData.[i + sign, j]
 237                     elif angle < 3.f * PI / 4.f
 238                     then ratio1 * magnitudesData.[i + sign, j] + ratio2 * magnitudesData.[i + sign, j - sign]
 239                     elif angle < PI
 240                     then ratio2 * magnitudesData.[i + sign, j - sign] + ratio1 * magnitudesData.[i, j - sign]
 241                     elif angle < 5.f * PI / 4.f
 242                     then ratio1 * magnitudesData.[i, j - sign] + ratio2 * magnitudesData.[i - sign, j - sign]
 243                     elif angle < 3.f * PI / 2.f
 244                     then ratio2 * magnitudesData.[i - sign, j - sign] + ratio1 * magnitudesData.[i - sign, j]
 245                     elif angle < 7.f * PI / 4.f
 246                     then ratio1 * magnitudesData.[i - sign, j] + ratio2 * magnitudesData.[i - sign, j + sign]
 247                     else ratio2 * magnitudesData.[i - sign, j + sign] + ratio1 * magnitudesData.[i, j + sign]
 248
 249                 let m = magnitudesData.[i, j]
 250                 if m >= thresholdLow && m > mNeigbors 1 && m > mNeigbors -1
 251                 then
 252                     nmsData.[i, j] <- 1uy
 253
 254     // suppressMConnections nms // It's not helpful for the rest of the process (ellipse detection).
 255
 256     let edges = new Matrix<byte>(xGradient.Size)
 257     let edgesData = edges.Data
 258
 259     // Hysteresis thresholding.
 260     let toVisit = Stack<Point>()
 261     for i in 0 .. h - 1 do
 262         for j in 0 .. w - 1 do
 263             if nmsData.[i, j] = 1uy && magnitudesData.[i, j] >= thresholdHigh
 264             then
 265                 nmsData.[i, j] <- 0uy
 266                 toVisit.Push(Point(j, i))
 267                 while toVisit.Count > 0 do
 268                     let p = toVisit.Pop()
 269                     edgesData.[p.Y, p.X] <- 1uy
 270                     for i' in -1 .. 1  do
 271                         for j' in -1 .. 1 do
 272                             if i' <> 0 || j' <> 0
 273                             then
 274                                 let ni = p.Y + i'
 275                                 let nj = p.X + j'
 276                                 if ni >= 0 && ni < h && nj >= 0 && nj < w && nmsData.[ni, nj] = 1uy
 277                                 then
 278                                     nmsData.[ni, nj] <- 0uy
 279                                     toVisit.Push(Point(nj, ni))
 280
 281     edges, xGradient, yGradient
 282
 283 let gaussianFilter (img : Image<'TColor, 'TDepth>) (standardDeviation : float) : Image<'TColor, 'TDepth> =
 284     let size = 2 * int (ceil (4.0 * standardDeviation)) + 1
 285     img.SmoothGaussian(size, size, standardDeviation, standardDeviation)
 286
 287 type Points = HashSet<Point>
 288
 289 let drawPoints (img: Image<Gray, 'TDepth>) (points: Points) (intensity: 'TDepth) =
 290     for p in points do
 291         img.Data.[p.Y, p.X, 0] <- intensity
 292
 293 type ExtremumType =
 294     | Maxima = 1
 295     | Minima = 2
 296
 297 let findExtremum (img: Image<Gray, 'TDepth>) (extremumType: ExtremumType) : IEnumerable<Points> =
 298     let w = img.Width
 299     let h = img.Height
 300     let se = [| -1, 0; 0, -1; 1, 0; 0, 1 |]
 301
 302     let imgData = img.Data
 303     let suppress: bool[,] = Array2D.zeroCreate h w
 304
 305     let result = List<List<Point>>()
 306
 307     let flood (start: Point) : List<List<Point>> =
 308         let sameLevelToCheck = Stack<Point>()
 309         let betterLevelToCheck = Stack<Point>()
 310         betterLevelToCheck.Push(start)
 311
 312         let result' = List<List<Point>>()
 313
 314         while betterLevelToCheck.Count > 0 do
 315             let p = betterLevelToCheck.Pop()
 316             if not suppress.[p.Y, p.X]
 317             then
 318                 suppress.[p.Y, p.X] <- true
 319                 sameLevelToCheck.Push(p)
 320                 let current = List<Point>()
 321
 322                 let mutable betterExists = false
 323
 324                 while sameLevelToCheck.Count > 0 do
 325                     let p' = sameLevelToCheck.Pop()
 326                     let currentLevel = imgData.[p'.Y, p'.X, 0]
 327                     current.Add(p') |> ignore
 328                     for i, j in se do
 329                         let ni = i + p'.Y
 330                         let nj = j + p'.X
 331                         if ni >= 0 && ni < h && nj >= 0 && nj < w
 332                         then
 333                             let level = imgData.[ni, nj, 0]
 334                             let notSuppressed = not suppress.[ni, nj]
 335
 336                             if level = currentLevel && notSuppressed
 337                             then
 338                                 suppress.[ni, nj] <- true
 339                                 sameLevelToCheck.Push(Point(nj, ni))
 340                             elif if extremumType = ExtremumType.Maxima then level > currentLevel else level < currentLevel
 341                             then
 342                                 betterExists <- true
 343                                 if notSuppressed
 344                                 then
 345                                     betterLevelToCheck.Push(Point(nj, ni))
 346
 347                 if not betterExists
 348                 then
 349                     result'.Add(current)
 350         result'
 351
 352     for i in 0 .. h - 1 do
 353         for j in 0 .. w - 1 do
 354             let maxima = flood (Point(j, i))
 355             if maxima.Count > 0
 356             then
 357                 result.AddRange(maxima)
 358
 359     result.Select(fun l -> Points(l))
 360
 361 let findMaxima (img: Image<Gray, 'TDepth>) : IEnumerable<Points> =
 362     findExtremum img ExtremumType.Maxima
 363
 364 let findMinima (img: Image<Gray, 'TDepth>) : IEnumerable<Points> =
 365     findExtremum img ExtremumType.Minima
 366
 367 type PriorityQueue () =
 368     let size = 256
 369     let q: Points[] = Array.init size (fun i -> Points())
 370     let mutable highest = -1 // Value of the first elements of 'q'.
 371     let mutable lowest = size
 372
 373     member this.NextMax () : byte * Point =
 374         if this.IsEmpty
 375         then
 376             invalidOp "Queue is empty"
 377         else
 378             let l = q.[highest]
 379             let next = l.First()
 380             l.Remove(next) |> ignore
 381             let value = byte highest
 382
 383             if l.Count = 0
 384             then
 385                 highest <- highest - 1
 386                 while highest > lowest && q.[highest].Count = 0 do
 387                     highest <- highest - 1
 388                 if highest = lowest
 389                 then
 390                     highest <- -1
 391                     lowest <- size
 392
 393             value, next
 394
 395     member this.NextMin () : byte * Point =
 396         if this.IsEmpty
 397         then
 398             invalidOp "Queue is empty"
 399         else
 400             let l = q.[lowest + 1]
 401             let next = l.First()
 402             l.Remove(next) |> ignore
 403             let value = byte (lowest + 1)
 404
 405             if l.Count = 0
 406             then
 407                 lowest <- lowest + 1
 408                 while lowest < highest && q.[lowest + 1].Count = 0 do
 409                     lowest <- lowest + 1
 410                 if highest = lowest
 411                 then
 412                     highest <- -1
 413                     lowest <- size
 414
 415             value, next
 416
 417     member this.Max =
 418         highest |> byte
 419
 420     member this.Min =
 421         lowest + 1 |> byte
 422
 423     member this.Add (value: byte) (p: Point) =
 424         let vi = int value
 425
 426         if vi > highest
 427         then
 428             highest <- vi
 429         if vi <= lowest
 430         then
 431             lowest <- vi - 1
 432
 433         q.[vi].Add(p) |> ignore
 434
 435     member this.Remove (value: byte) (p: Point) =
 436         let vi = int value
 437         if q.[vi].Remove(p) && q.[vi].Count = 0
 438         then
 439             if vi = highest
 440             then
 441                 highest <- highest - 1
 442                 while highest > lowest && q.[highest].Count = 0 do
 443                     highest <- highest - 1
 444             elif vi - 1 = lowest
 445             then
 446                 lowest <- lowest + 1
 447                 while lowest < highest && q.[lowest + 1].Count = 0 do
 448                     lowest <- lowest + 1
 449
 450             if highest = lowest // The queue is now empty.
 451             then
 452                 highest <- -1
 453                 lowest <- size
 454
 455     member this.IsEmpty =
 456         highest = -1
 457
 458     member this.Clear () =
 459         while highest > lowest  do
 460             q.[highest].Clear()
 461             highest <- highest - 1
 462         highest <- -1
 463         lowest <- size
 464
 465 type private AreaState =
 466     | Removed = 1
 467     | Unprocessed = 2
 468     | Validated = 3
 469
 470 type private AreaOperation =
 471     | Opening = 1
 472     | Closing = 2
 473
 474 [<AllowNullLiteral>]
 475 type private Area (elements: Points) =
 476     member this.Elements = elements
 477     member val Intensity = None with get, set
 478     member val State = AreaState.Unprocessed with get, set
 479
 480 let private areaOperation (img: Image<Gray, byte>) (area: int) (op: AreaOperation) =
 481     let w = img.Width
 482     let h = img.Height
 483     let imgData = img.Data
 484     let se = [| -1, 0; 0, -1; 1, 0; 0, 1 |]
 485
 486     let areas = List<Area>((if op = AreaOperation.Opening then findMaxima img else findMinima img) |> Seq.map Area)
 487
 488     let pixels: Area[,] = Array2D.create h w null
 489     for m in areas do
 490         for e in m.Elements do
 491             pixels.[e.Y, e.X] <- m
 492
 493     let queue = PriorityQueue()
 494
 495     let addEdgeToQueue (elements: Points) =
 496         for p in elements do
 497             for i, j in se do
 498                 let ni = i + p.Y
 499                 let nj = j + p.X
 500                 let p' = Point(nj, ni)
 501                 if ni >= 0 && ni < h && nj >= 0 && nj < w && not (elements.Contains(p'))
 502                 then
 503                     queue.Add (imgData.[ni, nj, 0]) p'
 504
 505     // Reverse order is quicker.
 506     for i in areas.Count - 1 .. -1 .. 0 do
 507         let m = areas.[i]
 508         if m.Elements.Count <= area && m.State <> AreaState.Removed
 509         then
 510             queue.Clear()
 511             addEdgeToQueue m.Elements
 512
 513             let mutable intensity = if op = AreaOperation.Opening then queue.Max else queue.Min
 514             let nextElements = Points()
 515
 516             let mutable stop = false
 517             while not stop do
 518                 let intensity', p = if op = AreaOperation.Opening then queue.NextMax () else queue.NextMin ()
 519                 let mutable merged = false
 520
 521                 if intensity' = intensity // The intensity doesn't change.
 522                 then
 523                     if m.Elements.Count + nextElements.Count + 1 > area
 524                     then
 525                         m.State <- AreaState.Validated
 526                         m.Intensity <- Some intensity
 527                         stop <- true
 528                     else
 529                         nextElements.Add(p) |> ignore
 530
 531                 elif if op = AreaOperation.Opening then intensity' < intensity else intensity' > intensity
 532                 then
 533                     m.Elements.UnionWith(nextElements)
 534                     for e in nextElements do
 535                         pixels.[e.Y, e.X] <- m
 536
 537                     if m.Elements.Count = area
 538                     then
 539                         m.State <- AreaState.Validated
 540                         m.Intensity <- Some (intensity')
 541                         stop <- true
 542                     else
 543                         intensity <- intensity'
 544                         nextElements.Clear()
 545                         nextElements.Add(p) |> ignore
 546
 547                 else
 548                     match pixels.[p.Y, p.X] with
 549                     | null -> ()
 550                     | m' ->
 551                         if m'.Elements.Count + m.Elements.Count <= area
 552                         then
 553                             m'.State <- AreaState.Removed
 554                             for e in m'.Elements do
 555                                 pixels.[e.Y, e.X] <- m
 556                                 queue.Remove imgData.[e.Y, e.X, 0] e
 557                             addEdgeToQueue m'.Elements
 558                             m.Elements.UnionWith(m'.Elements)
 559                             let intensityMax = if op = AreaOperation.Opening then queue.Max else queue.Min
 560                             if intensityMax <> intensity
 561                             then
 562                                 intensity <- intensityMax
 563                                 nextElements.Clear()
 564                             merged <- true
 565
 566                     if not merged
 567                     then
 568                         m.State <- AreaState.Validated
 569                         m.Intensity <- Some (intensity)
 570                         stop <- true
 571
 572                 if not stop && not merged
 573                 then
 574                     for i, j in se do
 575                         let ni = i + p.Y
 576                         let nj = j + p.X
 577                         let p' = Point(nj, ni)
 578                         if ni < 0 || ni >= h || nj < 0 || nj >= w
 579                         then
 580                             m.State <- AreaState.Validated
 581                             m.Intensity <- Some (intensity)
 582                             stop <- true
 583                         elif not (m.Elements.Contains(p')) && not (nextElements.Contains(p'))
 584                         then
 585                             queue.Add (imgData.[ni, nj, 0]) p'
 586
 587                 if queue.IsEmpty
 588                 then
 589                     if m.Elements.Count + nextElements.Count <= area
 590                     then
 591                         m.State <- AreaState.Validated
 592                         m.Intensity <- Some intensity'
 593                         m.Elements.UnionWith(nextElements)
 594                     stop <- true
 595
 596     for m in areas do
 597         if m.State = AreaState.Validated
 598         then
 599             match m.Intensity with
 600             | Some i ->
 601                 for p in m.Elements do
 602                     imgData.[p.Y, p.X, 0] <- i
 603             | _ -> ()
 604     ()
 605
 606 let areaOpen (img: Image<Gray, byte>) (area: int) =
 607     areaOperation img area AreaOperation.Opening
 608
 609 let areaClose (img: Image<Gray, byte>) (area: int) =
 610     areaOperation img area AreaOperation.Closing
 611
 612 [<AllowNullLiteral>]
 613 type Island (cmp: IComparer<float32>) =
 614     member val Shore = Heap.Heap<float32, Point>(cmp) with get
 615     member val Level = 0.f with get, set
 616     member val Surface = 0 with get, set
 617
 618 let private areaOperationF (img: Image<Gray, float32>) (areas: (int * 'a) list) (f: ('a -> float32 -> unit) option) (op: AreaOperation) =
 619     let w = img.Width
 620     let h = img.Height
 621     let earth = img.Data
 622     let se = [| -1, 0; 0, -1; 1, 0; 0, 1 |]
 623
 624     let comparer = if op = AreaOperation.Opening
 625                    then { new IComparer<float32> with member this.Compare(v1, v2) = v1.CompareTo(v2) }
 626                    else { new IComparer<float32> with member this.Compare(v1, v2) = v2.CompareTo(v1) }
 627
 628     let ownership: Island[,] = Array2D.create h w null
 629
 630     // Initialize islands with their shore.
 631     let islands = List<Island>()
 632     let extremum = img |> if op = AreaOperation.Opening then findMaxima else findMinima
 633     for e in extremum do
 634         let island =
 635             let p = e.First()
 636             Island(comparer, Level = earth.[p.Y, p.X, 0], Surface = e.Count)
 637         islands.Add(island)
 638         let shorePoints = Points()
 639         for p in e do
 640             ownership.[p.Y, p.X] <- island
 641             for i, j in se do
 642                 let ni = i + p.Y
 643                 let nj = j + p.X
 644                 let neighbor = Point(nj, ni)
 645                 if ni >= 0 && ni < h && nj >= 0 && nj < w && Object.ReferenceEquals(ownership.[ni, nj], null) && not (shorePoints.Contains(neighbor))
 646                 then
 647                     shorePoints.Add(neighbor) |> ignore
 648                     island.Shore.Add earth.[ni, nj, 0] neighbor
 649
 650     for area, obj in areas do
 651         for island in islands do
 652             let mutable stop = island.Shore.IsEmpty
 653
 654             // 'true' if 'p' is owned or adjacent to 'island'.
 655             let inline ownedOrAdjacent (p: Point) : bool =
 656                 ownership.[p.Y, p.X] = island ||
 657                 (p.Y > 0 && ownership.[p.Y - 1, p.X] = island) ||
 658                 (p.Y < h - 1 && ownership.[p.Y + 1, p.X] = island) ||
 659                 (p.X > 0 && ownership.[p.Y, p.X - 1] = island) ||
 660                 (p.X < w - 1 && ownership.[p.Y, p.X + 1] = island)
 661
 662             while not stop && island.Surface < area do
 663                 let level, next = island.Shore.Max
 664                 let other = ownership.[next.Y, next.X]
 665                 if other = island // During merging, some points on the shore may be owned by the island itself -> ignored.
 666                 then
 667                     island.Shore.RemoveNext ()
 668                 else
 669                     if not <| Object.ReferenceEquals(other, null)
 670                     then // We touching another island.
 671                         if island.Surface + other.Surface >= area
 672                         then
 673                             stop <- true
 674                         else // We can merge 'other' into 'surface'.
 675                             island.Surface <- island.Surface + other.Surface
 676                             island.Level <- if comparer.Compare(island.Level, other.Level) > 0 then island.Level else other.Level
 677                             for l, p in other.Shore do
 678                                 let mutable currentY = p.Y + 1
 679                                 while currentY < h && ownership.[currentY, p.X] = other do
 680                                     ownership.[currentY, p.X] <- island
 681                                     currentY <- currentY + 1
 682                                 island.Shore.Add l p
 683                             other.Shore.Clear()
 684
 685                     elif comparer.Compare(level, island.Level) > 0
 686                     then
 687                         stop <- true
 688                     else
 689                         island.Shore.RemoveNext ()
 690                         for i, j in se do
 691                             let ni = i + next.Y
 692                             let nj = j + next.X
 693                             if ni < 0 || ni >= h || nj < 0 || nj >= w
 694                             then
 695                                 island.Surface <- Int32.MaxValue
 696                                 stop <- true
 697                             else
 698                                 let neighbor = Point(nj, ni)
 699                                 if not <| ownedOrAdjacent neighbor
 700                                 then
 701                                     island.Shore.Add earth.[ni, nj, 0] neighbor
 702                         if not stop
 703                         then
 704                             ownership.[next.Y, next.X] <- island
 705                             island.Level <- level
 706                             island.Surface <- island.Surface + 1
 707
 708         let mutable diff = 0.f
 709
 710         for i in 0 .. h - 1 do
 711             for j in 0 .. w - 1 do
 712                 match ownership.[i, j] with
 713                 | null -> ()
 714                 | island ->
 715                     let l = island.Level
 716                     diff <- diff + l - earth.[i, j, 0]
 717                     earth.[i, j, 0] <- l
 718
 719         match f with
 720         | Some f' -> f' obj diff
 721         | _ -> ()
 722     ()
 723
 724 let areaOpenF (img: Image<Gray, float32>) (area: int) =
 725     areaOperationF img [ area, () ] None AreaOperation.Opening
 726
 727 let areaCloseF (img: Image<Gray, float32>) (area: int) =
 728     areaOperationF img [ area, () ] None AreaOperation.Closing
 729
 730 let areaOpenFWithFun (img: Image<Gray, float32>) (areas: (int * 'a) list) (f: 'a -> float32 -> unit) =
 731     areaOperationF img areas (Some f) AreaOperation.Opening
 732
 733 let areaCloseFWithFun (img: Image<Gray, float32>) (areas: (int * 'a) list) (f: 'a -> float32 -> unit) =
 734     areaOperationF img areas (Some f) AreaOperation.Closing
 735
 736 // A simpler algorithm than 'areaOpen' but slower.
 737 let areaOpen2 (img: Image<Gray, byte>) (area: int) =
 738     let w = img.Width
 739     let h = img.Height
 740     let imgData = img.Data
 741     let se = [| -1, 0; 0, -1; 1, 0; 0, 1 |]
 742
 743     let histogram = Array.zeroCreate 256
 744     for i in 0 .. h - 1 do
 745         for j in 0 .. w - 1 do
 746             let v = imgData.[i, j, 0] |> int
 747             histogram.[v] <- histogram.[v] + 1
 748
 749     let flooded : bool[,] = Array2D.zeroCreate h w
 750
 751     let pointsChecked = HashSet<Point>()
 752     let pointsToCheck = Stack<Point>()
 753
 754     for level in 255 .. -1 .. 0 do
 755         let mutable n = histogram.[level]
 756         if n > 0
 757         then
 758             for i in 0 .. h - 1 do
 759                 for j in 0 .. w - 1 do
 760                     if not flooded.[i, j] && imgData.[i, j, 0] = byte level
 761                     then
 762                         let mutable maxNeighborValue = 0uy
 763                         pointsChecked.Clear()
 764                         pointsToCheck.Clear()
 765                         pointsToCheck.Push(Point(j, i))
 766
 767                         while pointsToCheck.Count > 0 do
 768                             let next = pointsToCheck.Pop()
 769                             pointsChecked.Add(next) |> ignore
 770                             flooded.[next.Y, next.X] <- true
 771
 772                             for nx, ny in se do
 773                                 let p = Point(next.X + nx, next.Y + ny)
 774                                 if p.X >= 0 && p.X < w && p.Y >= 0 && p.Y < h
 775                                 then
 776                                     let v = imgData.[p.Y, p.X, 0]
 777                                     if v = byte level
 778                                     then
 779                                         if not (pointsChecked.Contains(p))
 780                                         then
 781                                             pointsToCheck.Push(p)
 782                                     elif v > maxNeighborValue
 783                                     then
 784                                         maxNeighborValue <- v
 785
 786                         if int maxNeighborValue < level && pointsChecked.Count <= area
 787                         then
 788                             for p in pointsChecked do
 789                                 imgData.[p.Y, p.X, 0] <- maxNeighborValue
 790
 791 // Zhang and Suen algorithm.
 792 // Modify 'mat' in place.
 793 let thin (mat: Matrix<byte>) =
 794     let w = mat.Width
 795     let h = mat.Height
 796     let mutable data1 = mat.Data
 797     let mutable data2 = Array2D.copy data1
 798
 799     let mutable pixelChanged = true
 800     let mutable oddIteration = true
 801
 802     while pixelChanged do
 803         pixelChanged <- false
 804         for i in 0..h-1 do
 805             for j in 0..w-1 do
 806                 if data1.[i, j] = 1uy
 807                 then
 808                     let p2 = if i = 0 then 0uy else data1.[i-1, j]
 809                     let p3 = if i = 0 || j = w-1 then 0uy else data1.[i-1, j+1]
 810                     let p4 = if j = w-1 then 0uy else data1.[i, j+1]
 811                     let p5 = if i = h-1 || j = w-1 then 0uy else data1.[i+1, j+1]
 812                     let p6 = if i = h-1 then 0uy else data1.[i+1, j]
 813                     let p7 = if i = h-1 || j = 0 then 0uy else data1.[i+1, j-1]
 814                     let p8 = if j = 0 then 0uy else data1.[i, j-1]
 815                     let p9 = if i = 0 || j = 0 then 0uy else data1.[i-1, j-1]
 816
 817                     let sumNeighbors = p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9
 818                     if sumNeighbors >= 2uy && sumNeighbors <= 6uy &&
 819                         (if p2 = 0uy && p3 = 1uy then 1 else 0) +
 820                         (if p3 = 0uy && p4 = 1uy then 1 else 0) +
 821                         (if p4 = 0uy && p5 = 1uy then 1 else 0) +
 822                         (if p5 = 0uy && p6 = 1uy then 1 else 0) +
 823                         (if p6 = 0uy && p7 = 1uy then 1 else 0) +
 824                         (if p7 = 0uy && p8 = 1uy then 1 else 0) +
 825                         (if p8 = 0uy && p9 = 1uy then 1 else 0) +
 826                         (if p9 = 0uy && p2 = 1uy then 1 else 0) = 1 &&
 827                         if oddIteration
 828                         then p2 * p4 * p6 = 0uy && p4 * p6 * p8 = 0uy
 829                         else p2 * p4 * p8 = 0uy && p2 * p6 * p8 = 0uy
 830                     then
 831                         data2.[i, j] <- 0uy
 832                         pixelChanged <- true
 833                 else
 834                     data2.[i, j] <- 0uy
 835
 836         oddIteration <- not oddIteration
 837         let tmp = data1
 838         data1 <- data2
 839         data2 <- tmp
 840
 841 // Remove all 8-connected pixels with an area equal or greater than 'areaSize'.
 842 // Modify 'mat' in place.
 843 let removeArea (mat: Matrix<byte>) (areaSize: int) =
 844     let neighbors = [|
 845         (-1,  0) // p2
 846         (-1,  1) // p3
 847         ( 0,  1) // p4
 848         ( 1,  1) // p5
 849         ( 1,  0) // p6
 850         ( 1, -1) // p7
 851         ( 0, -1) // p8
 852         (-1, -1) |] // p9
 853
 854     use mat' = new Matrix<byte>(mat.Size)
 855     let w = mat'.Width
 856     let h = mat'.Height
 857     mat.CopyTo(mat')
 858
 859     let data = mat.Data
 860     let data' = mat'.Data
 861
 862     for i in 0..h-1 do
 863         for j in 0..w-1 do
 864             if data'.[i, j] = 1uy
 865             then
 866                 let neighborhood = List<Point>()
 867                 let neighborsToCheck = Stack<Point>()
 868                 neighborsToCheck.Push(Point(j, i))
 869                 data'.[i, j] <- 0uy
 870
 871                 while neighborsToCheck.Count > 0 do
 872                     let n = neighborsToCheck.Pop()
 873                     neighborhood.Add(n)
 874                     for (ni, nj) in neighbors do
 875                         let pi = n.Y + ni
 876                         let pj = n.X + nj
 877                         if pi >= 0 && pi < h && pj >= 0 && pj < w && data'.[pi, pj] = 1uy
 878                         then
 879                             neighborsToCheck.Push(Point(pj, pi))
 880                             data'.[pi, pj] <- 0uy
 881                 if neighborhood.Count <= areaSize
 882                 then
 883                     for n in neighborhood do
 884                         data.[n.Y, n.X] <- 0uy
 885
 886 let connectedComponents (img: Image<Gray, byte>) (startPoints: List<Point>) : List<Point> =
 887     let w = img.Width
 888     let h = img.Height
 889
 890     let pointChecked = Points()
 891     let pointToCheck = Stack<Point>(startPoints);
 892
 893     let data = img.Data
 894
 895     while pointToCheck.Count > 0 do
 896         let next = pointToCheck.Pop()
 897         pointChecked.Add(next) |> ignore
 898         for ny in -1 .. 1 do
 899             for nx in -1 .. 1 do
 900                 if ny <> 0 && nx <> 0
 901                 then
 902                     let p = Point(next.X + nx, next.Y + ny)
 903                     if p.X >= 0 && p.X < w && p.Y >= 0 && p.Y < h && data.[p.Y, p.X, 0] > 0uy && not (pointChecked.Contains p)
 904                     then
 905                         pointToCheck.Push(p)
 906
 907     List<Point>(pointChecked)
 908
 909 let drawLine (img: Image<'TColor, 'TDepth>) (color: 'TColor) (x0: int) (y0: int) (x1: int) (y1: int) (thickness: int) =
 910     img.Draw(LineSegment2D(Point(x0, y0), Point(x1, y1)), color, thickness);
 911
 912 let drawLineF (img: Image<'TColor, 'TDepth>) (color: 'TColor) (x0: float) (y0: float) (x1: float) (y1: float) (thickness: int) =
 913     img.Draw(LineSegment2DF(PointF(float32 x0, float32 y0), PointF(float32 x1, float32 y1)), color, thickness, CvEnum.LineType.AntiAlias);
 914
 915 let drawEllipse (img: Image<'TColor, 'TDepth>) (e: Types.Ellipse) (color: 'TColor) (alpha: float) =
 916     if alpha >= 1.0
 917     then
 918         img.Draw(Ellipse(PointF(float32 e.Cx, float32 e.Cy), SizeF(2.f * e.B, 2.f * e.A), e.Alpha / PI * 180.f), color, 1, CvEnum.LineType.AntiAlias)
 919     else
 920         let windowPosX = e.Cx - e.A - 5.f
 921         let gapX = windowPosX - (float32 (int windowPosX))
 922
 923         let windowPosY = e.Cy - e.A - 5.f
 924         let gapY = windowPosY - (float32 (int windowPosY))
 925
 926         let roi = Rectangle(int windowPosX, int windowPosY, 2.f * (e.A + 5.f) |> int, 2.f * (e.A + 5.f) |> int)
 927
 928         img.ROI <- roi
 929         if roi = img.ROI // We do not display ellipses touching the edges (FIXME)
 930         then
 931             use i = new Image<'TColor, 'TDepth>(img.ROI.Size)
 932             i.Draw(Ellipse(PointF(float32 <| (e.A + 5.f + gapX) , float32 <| (e.A + 5.f + gapY)), SizeF(2.f * e.B, 2.f * e.A), e.Alpha / PI * 180.f), color, 1, CvEnum.LineType.AntiAlias)
 933             CvInvoke.AddWeighted(img, 1.0, i, alpha, 0.0, img)
 934         img.ROI <- Rectangle.Empty
 935
 936 let drawEllipses (img: Image<'TColor, 'TDepth>) (ellipses: Types.Ellipse list) (color: 'TColor) (alpha: float) =
 937     List.iter (fun e -> drawEllipse img e color alpha) ellipses
 938
 939 let rngCell =  System.Random()
 940 let drawCell (img: Image<Bgr, byte>) (drawCellContent: bool) (c: Types.Cell) =
 941     if drawCellContent
 942     then
 943         let colorB = rngCell.Next(20, 70)
 944         let colorG = rngCell.Next(20, 70)
 945         let colorR = rngCell.Next(20, 70)
 946
 947         for y in 0 .. c.elements.Height - 1 do
 948             for x in 0 .. c.elements.Width - 1 do
 949                 if c.elements.[y, x] > 0uy
 950                 then
 951                     let dx, dy = c.center.X - c.elements.Width / 2, c.center.Y - c.elements.Height / 2
 952                     let b = img.Data.[y + dy, x + dx, 0] |> int
 953                     let g = img.Data.[y + dy, x + dx, 1] |> int
 954                     let r = img.Data.[y + dy, x + dx, 2] |> int
 955                     img.Data.[y + dy, x + dx, 0] <- if b + colorB > 255 then 255uy else byte (b + colorB)
 956                     img.Data.[y + dy, x + dx, 1] <- if g + colorG > 255 then 255uy else byte (g + colorG)
 957                     img.Data.[y + dy, x + dx, 2] <- if r + colorR > 255 then 255uy else byte (r + colorR)
 958
 959     let crossColor, crossColor2 =
 960         match c.cellClass with
 961         | Types.HealthyRBC -> Bgr(255., 0., 0.), Bgr(255., 255., 255.)
 962         | Types.InfectedRBC -> Bgr(0., 0., 255.), Bgr(120., 120., 255.)
 963         | Types.Peculiar -> Bgr(0., 0., 0.), Bgr(80., 80., 80.)
 964
 965     drawLine img crossColor2 (c.center.X - 3) c.center.Y (c.center.X + 3) c.center.Y 2
 966     drawLine img crossColor2 c.center.X (c.center.Y - 3) c.center.X (c.center.Y + 3) 2
 967
 968     drawLine img crossColor (c.center.X - 3) c.center.Y (c.center.X + 3) c.center.Y 1
 969     drawLine img crossColor c.center.X (c.center.Y - 3) c.center.X (c.center.Y + 3) 1
 970
 971
 972 let drawCells (img: Image<Bgr, byte>) (drawCellContent: bool) (cells: Types.Cell list) =
 973     List.iter (fun c -> drawCell img drawCellContent c) cells