Parasitemia/Parasitemia/Ellipse.fs

   1 module Ellipse
   2
   3 open System
   4 open System.Collections.Generic
   5 open System.Drawing
   6
   7 open Emgu.CV
   8 open Emgu.CV.Structure
   9
  10 open Utils
  11 open Config
  12 open MatchingEllipses
  13 open Const
  14
  15 type private SearchExtremum = Minimum | Maximum
  16
  17 let private goldenSectionSearch (f: float32 -> float32) (nbIter: int) (xmin: float32) (xmax: float32) (searchExtremum: SearchExtremum) : (float32 * float32) =
  18     let gr = 1.f / 1.6180339887498948482f
  19     let mutable a = xmin
  20     let mutable b = xmax
  21     let mutable c = b - gr * (b - a)
  22     let mutable d = a + gr * (b - a)
  23
  24     for i in 1 .. nbIter do
  25         let mutable fc = f c
  26         let mutable fd = f d
  27
  28         if searchExtremum = Maximum
  29         then
  30             let tmp = fc
  31             fc <- fd
  32             fd <- tmp
  33
  34         if fc < fd
  35         then
  36             b <- d
  37             d <- c
  38             c <- b - gr * (b - a)
  39         else
  40             a <- c
  41             c <- d
  42             d <- a + gr * (b - a)
  43
  44     let x = (b + a) / 2.f
  45     x, f x
  46
  47 // Ellipse.A is always equal or greater than Ellipse.B.
  48 // Ellipse.Alpha is between 0 and Pi.
  49 let ellipse (p1x: float32) (p1y: float32) (m1: float32) (p2x: float32) (p2y: float32) (m2: float32) (p3x: float32) (p3y: float32) : Types.Ellipse option =
  50     let accuracy_extremum_search_1 = 8 // 3
  51     let accuracy_extremum_search_2 = 8 // 4
  52
  53     // p3 as the referencial.
  54     let p1x = p1x - p3x
  55     let p1y = p1y - p3y
  56
  57     let p2x = p2x - p3x
  58     let p2y = p2y - p3y
  59
  60     // Convert to polar coordinates.
  61     let alpha1 = atan m1
  62     let alpha2 = atan m2
  63
  64     let r1 = sqrt (p1x ** 2.f + p1y ** 2.f)
  65     let theta1 = atan2 p1y p1x
  66
  67     let r2 = sqrt (p2x ** 2.f + p2y ** 2.f)
  68     let theta2 = atan2 p2y p2x
  69
  70     let valid =
  71         4.f * sin (alpha1 - theta1) * (-r1 * sin (alpha1 - theta1) + r2 * sin (alpha1 - theta2)) *
  72         sin (alpha2 - theta2) * (-r1 * sin (alpha2 - theta1) + r2 * sin (alpha2 - theta2)) +
  73         r1 * r2 * sin (alpha1 - alpha2) ** 2.f * sin (theta1 - theta2) ** 2.f < 0.f
  74
  75     if valid
  76     then
  77         let r theta =
  78             (r1 * r2 * (r1 * (cos (alpha2 + theta - theta1 - theta2) - cos (alpha2 - theta) * cos (theta1 - theta2)) * sin (alpha1 - theta1) + r2 * (-cos (alpha1 + theta - theta1 - theta2) + cos (alpha1 - theta) * cos (theta1 - theta2)) * sin (alpha2 - theta2)) * sin (theta1 - theta2)) /
  79             (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.f - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.f)
  80
  81         let rabs = r >> abs
  82
  83         // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
  84         let thetaTan, _ = goldenSectionSearch rabs accuracy_extremum_search_1 0.f PI Maximum
  85         let rTan = r thetaTan
  86
  87         let PTanx = rTan * cos thetaTan
  88         let PTany = rTan * sin thetaTan
  89
  90         let d1a = tan alpha1
  91         let d1b = -d1a * p1x + p1y
  92
  93         let d2a = tan alpha2
  94         let d2b = -d2a * p2x + p2y
  95
  96         let d3a = -1.f / tan thetaTan
  97         let d3b = -d3a * PTanx + PTany
  98
  99         let Ux = -(d1b - d2b) / (d1a - d2a)
 100         let Uy = -(d2a * d1b - d1a * d2b) / (d1a - d2a)
 101
 102         let Vx = -(d1b - d3b) / (d1a - d3a)
 103         let Vy = -(d3a * d1b - d1a * d3b) / (d1a - d3a)
 104
 105         let Wx = p1x + (p2x - p1x) / 2.f
 106         let Wy = p1y + (p2y - p1y) / 2.f
 107
 108         let Zx = p1x + (PTanx - p1x) / 2.f
 109         let Zy = p1y + (PTany - p1y) / 2.f
 110
 111         let va = -(-Vy + Zy) / (Vx - Zx)
 112         let vb = -(Zx * Vy - Vx * Zy) / (Vx - Zx)
 113
 114         let ua = -(-Uy + Wy) / (Ux - Wx)
 115         let ub = -(Wx * Uy - Ux * Wy) / (Ux - Wx)
 116
 117         let cx = -(vb - ub) / (va - ua)
 118         let cy = -(ua * vb - va * ub) / (va - ua)
 119
 120         let rc = sqrt (cx ** 2.f + cy ** 2.f)
 121         let psi = atan2 cy cx
 122
 123         let rellipse theta =
 124             sqrt (
 125                 rc ** 2.f + (r1 ** 2.f * r2 ** 2.f * (r1 * (cos (alpha2 + theta - theta1 - theta2) - cos (alpha2 - theta) * cos (theta1 - theta2)) * sin (alpha1 - theta1) + r2 * (-cos (alpha1 + theta - theta1 - theta2) + cos (alpha1 - theta) * cos (theta1 - theta2)) * sin (alpha2 - theta2)) ** 2.f * sin (theta1 - theta2) ** 2.f) /
 126                 (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.f - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.f) ** 2.f -
 127                 (2.f * r1 * r2 * rc * cos (theta - psi) * (r1 * (cos (alpha2 + theta - theta1 - theta2) - cos (alpha2 - theta) * cos (theta1 - theta2)) * sin (alpha1 - theta1) + r2 * (-cos (alpha1 + theta - theta1 - theta2) + cos (alpha1 - theta) * cos (theta1 - theta2)) * sin (alpha2 - theta2)) * sin (theta1 - theta2)) /
 128                 (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.f - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.f))
 129
 130         // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
 131         let r1eTheta, r1e = goldenSectionSearch rellipse accuracy_extremum_search_2 0.f (PI / 2.f) Maximum // Pi/2 and not pi because the period is Pi.
 132         let r2eTheta, r2e = goldenSectionSearch rellipse accuracy_extremum_search_2 0.f (PI / 2.f) Minimum
 133
 134         let rr1e = r r1eTheta
 135         let r1ex = rr1e * cos r1eTheta
 136         let r1ey = rr1e * sin r1eTheta
 137         let mutable alpha = atan ((r1ey - cy) / (r1ex - cx))
 138         if alpha < 0.f
 139         then
 140            alpha <- alpha + PI
 141
 142         // Ride off the p3 referential.
 143         let cx = cx + p3x
 144         let cy = cy + p3y
 145
 146         Some (Types.Ellipse(cx, cy, r1e, r2e, alpha))
 147     else
 148         None
 149
 150
 151 let private vectorRotation (p1x: float32) (p1y: float32) (v1x: float32) (v1y: float32) (px: float32) (py: float32) : float32 =
 152     let mutable rotation = 1.f
 153     if p1y > py
 154     then
 155         if v1x > 0.f
 156         then
 157             rotation <- -1.f
 158     elif p1y < py
 159     then
 160         if v1x < 0.f
 161         then
 162             rotation <- -1.f
 163     elif p1x > px
 164     then
 165         if v1y < 0.f
 166         then
 167             rotation <- -1.f
 168     elif p1x < px
 169     then
 170         if v1y > 0.f
 171         then
 172             rotation <- -1.f
 173     rotation
 174
 175
 176 let private areVectorsValid (p1x: float32) (p1y: float32) (p2x: float32) (p2y: float32) (v1x: float32) (v1y: float32) (v2x: float32) (v2y: float32) : (float32 * float32) option =
 177     let m1 = -v1x / v1y
 178     let m2 = -v2x / v2y
 179
 180     let b1 = -m1 * p1x + p1y
 181     let b2 = -m2 * p2x + p2y
 182     let px = -((b1 - b2) / (m1 - m2))
 183     let py = -((m2 * b1 - m1 * b2) / (m1 - m2))
 184
 185     let rot1 = vectorRotation p1x p1y v1x v1y px py
 186     let rot2 = vectorRotation p2x p2y v2x v2y px py
 187
 188     if rot1 = rot2
 189     then
 190         None
 191     else
 192         let alpha1 = atan2 (p1y - py) (p1x - px)
 193         let alpha2 = atan2 (p2y - py) (p2x - px)
 194
 195         let alpha1' = if alpha1 < 0.f then 2.f * PI + alpha1 else alpha1
 196         let alpha2' = if alpha2 < 0.f then 2.f * PI + alpha2 else alpha2
 197
 198         let diff = rot1 * alpha1' + rot2 * alpha2'
 199
 200         if diff > PI || (diff < 0.f && diff > -PI)
 201         then
 202             None
 203         else
 204         Some (m1, m2)
 205
 206
 207 let find (edges: Matrix<byte>)
 208          (xGradient: Image<Gray, float32>)
 209          (yGradient: Image<Gray, float32>)
 210          (config: Config) : MatchingEllipses =
 211
 212     let r1, r2 = config.RBCMinRadius, config.RBCMaxRadius
 213     let incrementWindowDivisor = 4.f
 214
 215     // We choose a window size for which the biggest ellipse can always be fitted in.
 216     let windowSize = roundInt (2.f * r2 / (incrementWindowDivisor - 1.f) * incrementWindowDivisor)
 217     let factorNbPick = config.Parameters.factorNbPick
 218
 219     let increment = windowSize / (int incrementWindowDivisor)
 220
 221     let radiusTolerance = (r2 - r1) * 0.2f
 222
 223     let squaredMinimumDistance = (r2 / 1.5f) ** 2.f
 224     let squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2.f + (y1 - y2) ** 2.f
 225
 226     let h = edges.Height
 227     let w = edges.Width
 228     let h_f = float32 h
 229     let w_f = float32 w
 230
 231     let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
 232
 233     let currentElements = List<Point>()
 234
 235     let edgesData = edges.Data
 236     let xDirData = xGradient.Data
 237     let yDirData = yGradient.Data
 238
 239     let rng = Random(42)
 240
 241     let ellipses = MatchingEllipses(r1)
 242
 243     for window_i in -windowSize + increment .. increment .. h - increment do
 244         for window_j in -windowSize + increment .. increment .. w - increment do
 245
 246             let window_i_begin = if window_i < 0 then 0 else window_i
 247             let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1
 248             let window_j_begin = if window_j < 0 then 0 else window_j
 249             let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
 250
 251             // Remove old elements.
 252             let indexFirstElement = currentElements.FindIndex(fun p -> p.X >= window_j_begin)
 253             if indexFirstElement > 0
 254             then currentElements.RemoveRange(0, indexFirstElement)
 255
 256             // Add the new elements.
 257             let newElemsBegin_j = window_j + windowSize - increment
 258             let newElemsEnd_j = window_j + windowSize - 1
 259             for j in (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) .. (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
 260                 for i in window_i_begin .. window_i_end do
 261                     if edgesData.[i, j] = 1uy
 262                     then currentElements.Add(Point(j, i))
 263
 264             if currentElements.Count >= 10
 265             then
 266                 let mutable nbOfPicks = (float currentElements.Count) * factorNbPick |> int
 267                 while nbOfPicks > 0 do
 268                     let p1 = currentElements.[rng.Next(currentElements.Count)]
 269                     let p2 = currentElements.[rng.Next(currentElements.Count)]
 270                     let p3 = currentElements.[rng.Next(currentElements.Count)]
 271                     if p1 <> p2 && p1 <> p3 && p2 <> p3
 272                     then
 273                         nbOfPicks <- nbOfPicks - 1
 274                         let p1yf, p1xf = float32 p1.Y, float32 p1.X
 275                         let p2yf, p2xf = float32 p2.Y, float32 p2.X
 276                         let p3yf, p3xf = float32 p3.Y, float32 p3.X
 277                         if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance &&
 278                            squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
 279                            squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
 280                         then
 281                             match areVectorsValid p1xf p1yf p2xf p2yf -xDirData.[p1.Y, p1.X, 0] -yDirData.[p1.Y, p1.X, 0] -xDirData.[p2.Y, p2.X, 0] -yDirData.[p2.Y, p2.X, 0] with
 282                             | Some (m1, m2) ->
 283                                 match ellipse p1xf p1yf m1 p2xf p2yf m2 p3xf p3yf with
 284                                 | Some e when e.Cx > 0.f && e.Cx < w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
 285                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 286                                      ellipses.Add e
 287                                 | _ -> ()
 288                             | _ -> ()
 289
 290         currentElements.Clear()
 291
 292     ellipses
 293