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