Parasitemia/ParasitemiaCore/Ellipse.fs

   1 module ParasitemiaCore.Ellipse
   2
   3 open System
   4 open System.Collections.Generic
   5 open System.Drawing
   6
   7 open MathNet.Numerics.LinearAlgebra
   8
   9 open Emgu.CV
  10 open Emgu.CV.Structure
  11
  12 open Utils
  13 open Config
  14 open MatchingEllipses
  15 open Const
  16
  17 type private SearchExtremum = Minimum | Maximum
  18
  19 let private goldenSectionSearch (f: float -> float) (nbIter: int) (xmin: float) (xmax: float) (searchExtremum: SearchExtremum) : (float * float) =
  20     let gr = 1. / 1.6180339887498948482
  21     let mutable a = xmin
  22     let mutable b = xmax
  23     let mutable c = b - gr * (b - a)
  24     let mutable d = a + gr * (b - a)
  25
  26     for i in 1 .. nbIter do
  27         let mutable fc = f c
  28         let mutable fd = f d
  29
  30         if searchExtremum = Maximum
  31         then
  32             let tmp = fc
  33             fc <- fd
  34             fd <- tmp
  35
  36         if fc < fd
  37         then
  38             b <- d
  39             d <- c
  40             c <- b - gr * (b - a)
  41         else
  42             a <- c
  43             c <- d
  44             d <- a + gr * (b - a)
  45
  46     let x = (b + a) / 2.
  47     x, f x
  48
  49 // Ellipse.A is always equal or greater than Ellipse.B.
  50 // Ellipse.Alpha is between 0 and Pi.
  51 let ellipse (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
  52     let accuracy_extremum_search_1 = 10 // 3
  53     let accuracy_extremum_search_2 = 10 // 4
  54
  55     // p3 as the referencial.
  56     let p1x = p1x - p3x
  57     let p1y = p1y - p3y
  58
  59     let p2x = p2x - p3x
  60     let p2y = p2y - p3y
  61
  62     // Convert to polar coordinates.
  63     let alpha1 = atan m1
  64     let alpha2 = atan m2
  65
  66     let r1 = sqrt (p1x ** 2. + p1y ** 2.)
  67     let theta1 = atan2 p1y p1x
  68
  69     let r2 = sqrt (p2x ** 2. + p2y ** 2.)
  70     let theta2 = atan2 p2y p2x
  71
  72     let valid =
  73         4. * sin (alpha1 - theta1) * (-r1 * sin (alpha1 - theta1) + r2 * sin (alpha1 - theta2)) *
  74         sin (alpha2 - theta2) * (-r1 * sin (alpha2 - theta1) + r2 * sin (alpha2 - theta2)) +
  75         r1 * r2 * sin (alpha1 - alpha2) ** 2. * sin (theta1 - theta2) ** 2. < 0.
  76
  77     if valid
  78     then
  79         let r theta =
  80             (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)) /
  81             (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2. - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.)
  82
  83         let rabs = r >> abs
  84
  85         // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
  86         let thetaTan, _ = goldenSectionSearch rabs accuracy_extremum_search_1 0. Math.PI Maximum
  87         let rTan = r thetaTan
  88
  89         let PTanx = rTan * cos thetaTan
  90         let PTany = rTan * sin thetaTan
  91
  92         let d1a = tan alpha1
  93         let d1b = -d1a * p1x + p1y
  94
  95         let d2a = tan alpha2
  96         let d2b = -d2a * p2x + p2y
  97
  98         let d3a = -1. / tan thetaTan
  99         let d3b = -d3a * PTanx + PTany
 100
 101         let Ux = -(d1b - d2b) / (d1a - d2a)
 102         let Uy = -(d2a * d1b - d1a * d2b) / (d1a - d2a)
 103
 104         let Vx = -(d1b - d3b) / (d1a - d3a)
 105         let Vy = -(d3a * d1b - d1a * d3b) / (d1a - d3a)
 106
 107         let Wx = p1x + (p2x - p1x) / 2.
 108         let Wy = p1y + (p2y - p1y) / 2.
 109
 110         let Zx = p1x + (PTanx - p1x) / 2.
 111         let Zy = p1y + (PTany - p1y) / 2.
 112
 113         let va = -(-Vy + Zy) / (Vx - Zx)
 114         let vb = -(Zx * Vy - Vx * Zy) / (Vx - Zx)
 115
 116         let ua = -(-Uy + Wy) / (Ux - Wx)
 117         let ub = -(Wx * Uy - Ux * Wy) / (Ux - Wx)
 118
 119         let cx = -(vb - ub) / (va - ua)
 120         let cy = -(ua * vb - va * ub) / (va - ua)
 121
 122         let rc = sqrt (cx ** 2. + cy ** 2.)
 123         let psi = atan2 cy cx
 124
 125         let rellipse theta =
 126             sqrt (
 127                 rc ** 2. + (r1 ** 2. * r2 ** 2. * (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. * sin (theta1 - theta2) ** 2.) /
 128                 (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2. - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.) ** 2. -
 129                 (2. * 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)) /
 130                 (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2. - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.))
 131
 132         // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
 133         let r1eTheta, r1e = goldenSectionSearch rellipse accuracy_extremum_search_2 0. (Math.PI / 2.) Maximum // Pi/2 and not pi because the period is Pi.
 134         let r2eTheta, r2e = goldenSectionSearch rellipse accuracy_extremum_search_2 0. (Math.PI / 2.) Minimum
 135
 136         let rr1e = r r1eTheta
 137         let r1ex = rr1e * cos r1eTheta
 138         let r1ey = rr1e * sin r1eTheta
 139         let mutable alpha = atan ((r1ey - cy) / (r1ex - cx))
 140         if alpha < 0.
 141         then
 142            alpha <- alpha + Math.PI
 143
 144         // Ride off the p3 referential.
 145         let cx = cx + p3x
 146         let cy = cy + p3y
 147
 148         Some (Types.Ellipse(float32 cx, float32 cy, float32 r1e, float32 r2e, float32 alpha))
 149     else
 150         None
 151
 152 let ellipse2 (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
 153     let p0 = pointFromTwoLines (Types.Line(float32 m1, float32 (p1y - m1 * p1x))) (Types.Line(float32 m2, float32(p2y - m2 * p2x)))
 154     let p0x, p0y = float p0.X, float p0.Y
 155
 156     let s = matrix [[ 1.;   0.;  0.  ]
 157                     [ 0.;   0.; -0.5 ]
 158                     [ 0.; -0.5;  0.  ]]
 159
 160     let v0 = matrix [[ 1.; p0x; p0y ]]
 161     let v1 = matrix [[ 1.; p1x; p1y ]]
 162     let v2 = matrix [[ 1.; p2x; p2y ]]
 163     let v3 = matrix [[ 1.; p3x; p3y ]]
 164
 165     let p = (v3.Stack(v1).Stack(v2).Determinant() * v0).Stack(v0.Stack(v3).Stack(v2).Determinant() * v1).Stack(v0.Stack(v1).Stack(v3).Determinant() * v2).Transpose()
 166     let conicMat = p * s.Inverse() * p.Transpose()
 167     let a = conicMat.[0, 0]
 168     let b = conicMat.[0, 1]
 169     let c = conicMat.[1, 1]
 170     let d = conicMat.[0, 2]
 171     let e = conicMat.[1, 2]
 172     let f = conicMat.[2, 2]
 173
 174     // Center.
 175     let cx = b / a
 176     let cy = d / a
 177
 178     let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
 179     if at = 0.
 180     then
 181         None
 182     else
 183         let q = (-1. / at) * (matrix [[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
 184         let eigen = q.Evd()
 185         let eigenValues = eigen.EigenValues
 186         let lambda = eigenValues.[1].Real
 187         let mu = eigenValues.[0].Real
 188
 189         if lambda <= 0. || mu <= 0.
 190         then
 191             None
 192         else
 193             let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu)
 194
 195             let eigenVectors = eigen.EigenVectors
 196             let v_a = eigenVectors.[0, 0]
 197             let v_b = eigenVectors.[1, 0] // [0, 1]
 198
 199             // Angle against the longest axis.
 200             let phi = (if r2 > r1 then atan (v_b / v_a) else atan (v_a / v_b))
 201
 202             let phi' = if phi < 0. then phi + Math.PI else phi
 203             let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
 204
 205             Some (Types.Ellipse(float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
 206
 207
 208 let private vectorRotation (p1x: float32) (p1y: float32) (v1x: float32) (v1y: float32) (px: float32) (py: float32) : float32 =
 209     let mutable rotation = 1.f
 210     if p1y > py
 211     then
 212         if v1x > 0.f
 213         then
 214             rotation <- -1.f
 215     elif p1y < py
 216     then
 217         if v1x < 0.f
 218         then
 219             rotation <- -1.f
 220     elif p1x > px
 221     then
 222         if v1y < 0.f
 223         then
 224             rotation <- -1.f
 225     elif p1x < px
 226     then
 227         if v1y > 0.f
 228         then
 229             rotation <- -1.f
 230     rotation
 231
 232 let private areVectorsValid (p1x: float32) (p1y: float32) (p2x: float32) (p2y: float32) (v1x: float32) (v1y: float32) (v2x: float32) (v2y: float32) : (float32 * float32) option =
 233     let m1 = -v1x / v1y
 234     let m2 = -v2x / v2y
 235
 236     let b1 = -m1 * p1x + p1y
 237     let b2 = -m2 * p2x + p2y
 238     let px = -((b1 - b2) / (m1 - m2))
 239     let py = -((m2 * b1 - m1 * b2) / (m1 - m2))
 240
 241     let rot1 = vectorRotation p1x p1y v1x v1y px py
 242     let rot2 = vectorRotation p2x p2y v2x v2y px py
 243
 244     if rot1 = rot2
 245     then
 246         None
 247     else
 248         let alpha1 = atan2 (p1y - py) (p1x - px)
 249         let alpha2 = atan2 (p2y - py) (p2x - px)
 250
 251         let alpha1' = if alpha1 < 0.f then 2.f * PI + alpha1 else alpha1
 252         let alpha2' = if alpha2 < 0.f then 2.f * PI + alpha2 else alpha2
 253
 254         let diff = rot1 * alpha1' + rot2 * alpha2'
 255
 256         if diff > PI || (diff < 0.f && diff > -PI)
 257         then
 258             None
 259         else
 260         Some (m1, m2)
 261
 262
 263 let find (edges: Matrix<byte>)
 264          (xGradient: Matrix<float32>)
 265          (yGradient: Matrix<float32>)
 266          (config: Config) : MatchingEllipses =
 267
 268     let r1, r2 = config.RBCRadius.Min, config.RBCRadius.Max
 269     let incrementWindowDivisor = 4.f
 270
 271     // We choose a window size for which the biggest ellipse can always be fitted in.
 272     let windowSize = roundInt (2.f * r2)
 273     let factorNbPick = config.Parameters.factorNbPick
 274
 275     let increment = windowSize / (int incrementWindowDivisor)
 276
 277     let radiusTolerance = (r2 - r1) * 0.2f
 278
 279     let squaredMinimumDistance = (float r2 / 1.5) ** 2.
 280     let inline squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2. + (y1 - y2) ** 2.
 281
 282     let h = edges.Height
 283     let w = edges.Width
 284     let h_f = float32 h
 285     let w_f = float32 w
 286
 287     let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
 288
 289     let currentElements = List<Point>()
 290
 291     let edgesData = edges.Data
 292     let xDirData = xGradient.Data
 293     let yDirData = yGradient.Data
 294
 295     let rng = Random(42)
 296
 297     let ellipses = MatchingEllipses(config.RBCRadius.Pixel)
 298
 299     for window_i in -windowSize + increment .. increment .. h - increment do
 300         for window_j in -windowSize + increment .. increment .. w - increment do
 301
 302             let window_i_begin = if window_i < 0 then 0 else window_i
 303             let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1
 304             let window_j_begin = if window_j < 0 then 0 else window_j
 305             let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
 306
 307             // Remove old elements.
 308             let indexFirstElement = currentElements.FindIndex(fun p -> p.X >= window_j_begin)
 309             if indexFirstElement > 0
 310             then currentElements.RemoveRange(0, indexFirstElement)
 311
 312             // Add the new elements.
 313             let newElemsBegin_j = window_j + windowSize - increment
 314             let newElemsEnd_j = window_j + windowSize - 1
 315             for j in (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) .. (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
 316                 for i in window_i_begin .. window_i_end do
 317                     if edgesData.[i, j] = 1uy
 318                     then currentElements.Add(Point(j, i))
 319
 320             if currentElements.Count >= 10
 321             then
 322                 let mutable nbOfPicks = (float currentElements.Count) * factorNbPick |> int
 323                 while nbOfPicks > 0 do
 324                     let p1 = currentElements.[rng.Next(currentElements.Count)]
 325                     let p2 = currentElements.[rng.Next(currentElements.Count)]
 326                     let p3 = currentElements.[rng.Next(currentElements.Count)]
 327                     if p1 <> p2 && p1 <> p3 && p2 <> p3
 328                     then
 329                         nbOfPicks <- nbOfPicks - 1
 330                         let p1yf, p1xf = float p1.Y, float p1.X
 331                         let p2yf, p2xf = float p2.Y, float p2.X
 332                         let p3yf, p3xf = float p3.Y, float p3.X
 333                         if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance &&
 334                            squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
 335                            squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
 336                         then
 337                             match areVectorsValid (float32 p1xf) (float32 p1yf) (float32 p2xf) (float32 p2yf) -xDirData.[p1.Y, p1.X] -yDirData.[p1.Y, p1.X] -xDirData.[p2.Y, p2.X] -yDirData.[p2.Y, p2.X] with
 338                             | Some (m1, m2) ->
 339                                 match ellipse2 p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
 340                                 | Some e when e.Cx > 0.f && e.Cx < w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
 341                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 342                                      ellipses.Add e
 343                                 | _ -> ()
 344                             | _ -> ()
 345
 346         currentElements.Clear()
 347
 348     ellipses
 349