Parasitemia/Parasitemia/Ellipse.fs

   1 module Ellipse
   2
   3 open System
   4 open System.Collections.Generic
   5
   6 open Emgu.CV
   7 open Emgu.CV.Structure
   8
   9 open Utils
  10 open Config
  11 open MatchingEllipses
  12
  13
  14 type private SearchExtremum = Minimum | Maximum
  15
  16 let private goldenSectionSearch (f: float -> float) (nbIter: int) (xmin: float) (xmax: float) (searchExtremum: SearchExtremum) : (float * float) =
  17     let gr = 1.0 / 1.6180339887498948482
  18     let mutable a = xmin
  19     let mutable b = xmax
  20     let mutable c = b - gr * (b - a)
  21     let mutable d = a + gr * (b - a)
  22
  23     for i in 1 .. nbIter do
  24         let mutable fc = f c
  25         let mutable fd = f d
  26
  27         if searchExtremum = Maximum
  28         then
  29             let tmp = fc
  30             fc <- fd
  31             fd <- tmp
  32
  33         if fc < fd
  34         then
  35             b <- d
  36             d <- c
  37             c <- b - gr * (b - a)
  38         else
  39             a <- c
  40             c <- d
  41             d <- a + gr * (b - a)
  42
  43     let x = (b + a) / 2.0
  44     x, f x
  45
  46 // Ellipse.A is always equal or greater than Ellipse.B.
  47 // Ellipse.Alpha is between 0 and Pi.
  48 let ellipse (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
  49     let accuracy_extremum_search_1 = 8 // 3
  50     let accuracy_extremum_search_2 = 8 // 4
  51
  52     // p3 as the referencial.
  53     let p1x = p1x - p3x
  54     let p1y = p1y - p3y
  55
  56     let p2x = p2x - p3x
  57     let p2y = p2y - p3y
  58
  59     // Convert to polar coordinates.
  60     let alpha1 = atan m1
  61     let alpha2 = atan m2
  62
  63     let r1 = sqrt (p1x ** 2.0 + p1y ** 2.0)
  64     let theta1 = atan2 p1y p1x
  65
  66     let r2 = sqrt (p2x**2.0 + p2y**2.0)
  67     let theta2 = atan2 p2y p2x
  68
  69     let valid =
  70         4.0 * sin (alpha1 - theta1) * (-r1 * sin (alpha1 - theta1) + r2 * sin (alpha1 - theta2)) *
  71         sin (alpha2 - theta2) * (-r1 * sin (alpha2 - theta1) + r2 * sin (alpha2 - theta2)) +
  72         r1 * r2 * sin (alpha1 - alpha2) ** 2.0 * sin (theta1 - theta2) ** 2.0 < 0.0
  73
  74     if valid
  75     then
  76         let r theta =
  77             (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)) /
  78             (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.0)
  79
  80         let rabs = r >> abs
  81
  82         // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
  83         let thetaTan, _ = goldenSectionSearch rabs accuracy_extremum_search_1 0.0 Math.PI Maximum
  84         let rTan = r thetaTan
  85
  86         let PTanx = rTan * cos thetaTan
  87         let PTany = rTan * sin thetaTan
  88
  89         let d1a = tan alpha1
  90         let d1b = -d1a * p1x + p1y
  91
  92         let d2a = tan alpha2
  93         let d2b = -d2a * p2x + p2y
  94
  95         let d3a = -1.0 / tan thetaTan
  96         let d3b = -d3a * PTanx + PTany
  97
  98         let Ux = -(d1b - d2b) / (d1a - d2a)
  99         let Uy = -(d2a * d1b - d1a * d2b) / (d1a - d2a)
 100
 101         let Vx = -(d1b - d3b) / (d1a - d3a)
 102         let Vy = -(d3a * d1b - d1a * d3b) / (d1a - d3a)
 103
 104         let Wx = p1x + (p2x - p1x) / 2.0
 105         let Wy = p1y + (p2y - p1y) / 2.0
 106
 107         let Zx = p1x + (PTanx - p1x) / 2.0
 108         let Zy = p1y + (PTany - p1y) / 2.0
 109
 110         let va = -(-Vy + Zy) / (Vx - Zx)
 111         let vb = -(Zx * Vy - Vx * Zy) / (Vx - Zx)
 112
 113         let ua = -(-Uy + Wy) / (Ux - Wx)
 114         let ub = -(Wx * Uy - Ux * Wy) / (Ux - Wx)
 115
 116         let cx = -(vb - ub) / (va - ua)
 117         let cy = -(ua * vb - va * ub) / (va - ua)
 118
 119         let rc = sqrt (cx**2.0 + cy**2.0)
 120         let psi = atan2 cy cx
 121
 122         let rellipse theta =
 123             sqrt (
 124                 rc ** 2.0 + (r1 ** 2.0 * r2 ** 2.0 * (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)) ** 2.0 * sin (theta1 - theta2) ** 2.0) /
 125                 (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.0) ** 2.0 -
 126                 (2.0 * 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)) /
 127                 (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.0))
 128
 129         // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
 130         let r1eTheta, r1e = goldenSectionSearch rellipse accuracy_extremum_search_2 0.0 (Math.PI / 2.0) Maximum // Pi/2 and not pi because the period is Pi.
 131         let r2eTheta, r2e = goldenSectionSearch rellipse accuracy_extremum_search_2 0.0 (Math.PI / 2.0) Minimum
 132
 133         let rr1e = r r1eTheta
 134         let r1ex = rr1e * cos r1eTheta
 135         let r1ey = rr1e * sin r1eTheta
 136         let mutable alpha = atan ((r1ey - cy) / (r1ex - cx))
 137         if alpha < 0.0
 138         then
 139            alpha <- alpha + Math.PI
 140
 141         // Ride off the p3 referential.
 142         let cx = cx + p3x
 143         let cy = cy + p3y
 144
 145         Some (Types.Ellipse(cx, cy, r1e, r2e, alpha))
 146     else
 147         None
 148
 149
 150 let private vectorRotation (p1x: float) (p1y: float) (v1x: float) (v1y: float) (px: float) (py: float) : float =
 151     let mutable rotation = 1.0
 152     if p1y > py
 153     then
 154         if v1x > 0.0
 155         then
 156             rotation <- -1.0
 157     elif p1y < py
 158     then
 159         if v1x < 0.0
 160         then
 161             rotation <- -1.0
 162     elif p1x > px
 163     then
 164         if v1y < 0.0
 165         then
 166             rotation <- -1.0
 167     elif p1x < px
 168     then
 169         if v1y > 0.0
 170         then
 171             rotation <- -1.0
 172     rotation
 173
 174
 175 let private areVectorsValid (p1x: float) (p1y: float) (p2x: float) (p2y: float) (v1x: float) (v1y: float) (v2x: float) (v2y: float) : (float * float) option =
 176     let m1 = -v1x / v1y
 177     let m2 = -v2x / v2y
 178
 179     let b1 = -m1 * p1x + p1y
 180     let b2 = -m2 * p2x + p2y
 181     let px = -((b1 - b2) / (m1 - m2))
 182     let py = -((m2 * b1 - m1 * b2) / (m1 - m2))
 183
 184     let rot1 = vectorRotation p1x p1y v1x v1y px py
 185     let rot2 = vectorRotation p2x p2y v2x v2y px py
 186
 187     if rot1 = rot2
 188     then
 189         None
 190     else
 191         let alpha1 = atan2 (p1y - py) (p1x - px)
 192         let alpha2 = atan2 (p2y - py) (p2x - px)
 193
 194         let alpha1' = if alpha1 < 0.0 then 2.0 * Math.PI + alpha1 else alpha1
 195         let alpha2' = if alpha2 < 0.0 then 2.0 * Math.PI + alpha2 else alpha2
 196
 197         let diff = rot1 * alpha1' + rot2 * alpha2'
 198
 199         if diff > Math.PI || (diff < 0.0 && diff > -Math.PI)
 200         then
 201             None
 202         else
 203         Some (m1, m2)
 204
 205
 206 let find (edges: Matrix<byte>)
 207          (xGradient: Image<Gray, float>)
 208          (yGradient: Image<Gray, float>)
 209          (config: Config) : MatchingEllipses =
 210
 211     let r1, r2 = config.RBCMinRadius, config.RBCMaxRadius
 212     let windowSize = roundInt (config.Parameters.factorWindowSize * r2)
 213     let factorNbPick = config.Parameters.factorNbPick
 214
 215     let increment = windowSize / 4
 216
 217     let radiusTolerance = (r2 - r1) * 0.2
 218
 219     let minimumDistance = (r2 / 1.5) ** 2.0
 220     let squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2.0 + (y1 - y2) ** 2.0
 221
 222     let h = edges.Height
 223     let w = edges.Width
 224
 225     let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
 226
 227     let currentElements = List<(int * int)>()
 228
 229     let edgesData = edges.Data
 230     let xDirData = xGradient.Data
 231     let yDirData = yGradient.Data
 232
 233     let rng = Random(42)
 234
 235     let ellipses = MatchingEllipses(r1)
 236
 237     for window_i in -windowSize + increment .. increment .. h - increment do
 238         for window_j in -windowSize + increment .. increment .. w - increment do
 239
 240             let window_i_begin = if window_i < 0 then 0 else window_i
 241             let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1
 242             let window_j_begin = if window_j < 0 then 0 else window_j
 243             let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
 244
 245             // Remove old elements.
 246             let indexFirstElement = currentElements.FindIndex(fun (_, pj) -> pj >= window_j)
 247             if indexFirstElement > 0
 248             then currentElements.RemoveRange(0, indexFirstElement)
 249
 250             // Add the new elements.
 251             for j in window_j + windowSize - increment .. window_j + windowSize - 1  do
 252                 for i in window_i_begin .. window_i_end do
 253                     if j >= 0 && j < w && edgesData.[i, j] = 1uy
 254                     then currentElements.Add((i, j))
 255
 256             if currentElements.Count >= 10
 257             then
 258                 let mutable nbOfPicks = (float currentElements.Count) * factorNbPick |> int
 259                 while nbOfPicks > 0 do
 260                     let (p1y, p1x) as p1 = currentElements.[rng.Next(currentElements.Count)]
 261                     let (p2y, p2x) as p2 = currentElements.[rng.Next(currentElements.Count)]
 262                     let (p3y, p3x) as p3 = currentElements.[rng.Next(currentElements.Count)]
 263                     if p1 <> p2 && p1 <> p3 && p2 <> p3
 264                     then
 265                         nbOfPicks <- nbOfPicks - 1
 266                         let p1yf, p1xf = float p1y, float p1x
 267                         let p2yf, p2xf = float p2y, float p2x
 268                         let p3yf, p3xf = float p3y, float p3x
 269                         if squaredDistance p1xf p1yf p2xf p2yf >= minimumDistance &&
 270                            squaredDistance p1xf p1yf p3xf p3yf >= minimumDistance &&
 271                            squaredDistance p2xf p2yf p3xf p3yf >= minimumDistance
 272                         then
 273                             match areVectorsValid p1xf p1yf p2xf p2yf -xDirData.[p1y, p1x, 0] -yDirData.[p1y, p1x, 0] -xDirData.[p2y, p2x, 0] -yDirData.[p2y, p2x, 0] with
 274                             | Some (m1, m2) ->
 275                                 match ellipse p1xf p1yf m1 p2xf p2yf m2 p3xf p3yf with
 276                                 | Some e when e.Cx > 0.0 && e.Cx < (float w) - 1.0 && e.Cy > 0.0 && e.Cy < (float h) - 1.0 &&
 277                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 278
 279                                      let prout = areVectorsValid p1xf p1yf p2xf p2yf -xDirData.[p1y, p1x, 0] -yDirData.[p1y, p1x, 0] -xDirData.[p2y, p2x, 0] -yDirData.[p2y, p2x, 0]
 280                                      ellipses.Add e
 281                                 | _ -> ()
 282                             | _ -> ()
 283
 284         currentElements.Clear()
 285
 286     ellipses
 287