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