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 /// <summary>
  18 /// Try to build an ellipse from three points and two tangents passing by the first and the second point.
  19 /// 'Ellipse.A' is always equal or greater than Ellipse.B.
  20 /// 'Ellipse.Alpha' is between 0 and Pi.
  21 /// </summary>
  22 let ellipse (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
  23     let p0 = pointFromTwoLines (Types.Line(float32 m1, float32 (p1y - m1 * p1x))) (Types.Line(float32 m2, float32(p2y - m2 * p2x)))
  24     let p0x, p0y = float p0.X, float p0.Y
  25
  26     let s = matrix [[ 1.;   0.;  0.  ]
  27                     [ 0.;   0.; -0.5 ]
  28                     [ 0.; -0.5;  0.  ]]
  29
  30     let v0 = matrix [[ 1.; p0x; p0y ]]
  31     let v1 = matrix [[ 1.; p1x; p1y ]]
  32     let v2 = matrix [[ 1.; p2x; p2y ]]
  33     let v3 = matrix [[ 1.; p3x; p3y ]]
  34
  35     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()
  36     let conicMat = p * s.Inverse() * p.Transpose()
  37     let a = conicMat.[0, 0]
  38     let b = conicMat.[0, 1]
  39     let c = conicMat.[1, 1]
  40     let d = conicMat.[0, 2]
  41     let e = conicMat.[1, 2]
  42     let f = conicMat.[2, 2]
  43
  44     // Center.
  45     let cx = b / a
  46     let cy = d / a
  47
  48     let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
  49     if at = 0.
  50     then
  51         None
  52     else
  53         let q = (-1. / at) * (matrix [[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
  54         let eigen = q.Evd()
  55         let eigenValues = eigen.EigenValues
  56         let lambda = eigenValues.[1].Real
  57         let mu = eigenValues.[0].Real
  58
  59         if lambda <= 0. || mu <= 0.
  60         then
  61             None
  62         else
  63             let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu)
  64
  65             let eigenVectors = eigen.EigenVectors
  66             let v_a = eigenVectors.[0, 0]
  67             let v_b = eigenVectors.[1, 0] // [0, 1]
  68
  69             // Angle against the longest axis.
  70             let phi = (if r2 > r1 then atan (v_b / v_a) else atan (v_a / v_b))
  71
  72             let phi' = if phi < 0. then phi + Math.PI else phi
  73             let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
  74
  75             Some (Types.Ellipse(float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
  76
  77
  78 let private vectorRotation (p1x: float32) (p1y: float32) (v1x: float32) (v1y: float32) (px: float32) (py: float32) : float32 =
  79     let mutable rotation = 1.f
  80     if p1y > py
  81     then
  82         if v1x > 0.f
  83         then
  84             rotation <- -1.f
  85     elif p1y < py
  86     then
  87         if v1x < 0.f
  88         then
  89             rotation <- -1.f
  90     elif p1x > px
  91     then
  92         if v1y < 0.f
  93         then
  94             rotation <- -1.f
  95     elif p1x < px
  96     then
  97         if v1y > 0.f
  98         then
  99             rotation <- -1.f
 100     rotation
 101
 102 let private areVectorsValid (p1x: float32) (p1y: float32) (p2x: float32) (p2y: float32) (v1x: float32) (v1y: float32) (v2x: float32) (v2y: float32) : (float32 * float32) option =
 103     let m1 = -v1x / v1y
 104     let m2 = -v2x / v2y
 105
 106     let b1 = -m1 * p1x + p1y
 107     let b2 = -m2 * p2x + p2y
 108     let px = -((b1 - b2) / (m1 - m2))
 109     let py = -((m2 * b1 - m1 * b2) / (m1 - m2))
 110
 111     let rot1 = vectorRotation p1x p1y v1x v1y px py
 112     let rot2 = vectorRotation p2x p2y v2x v2y px py
 113
 114     if rot1 = rot2
 115     then
 116         None
 117     else
 118         let alpha1 = atan2 (p1y - py) (p1x - px)
 119         let alpha2 = atan2 (p2y - py) (p2x - px)
 120
 121         let alpha1' = if alpha1 < 0.f then 2.f * PI + alpha1 else alpha1
 122         let alpha2' = if alpha2 < 0.f then 2.f * PI + alpha2 else alpha2
 123
 124         let diff = rot1 * alpha1' + rot2 * alpha2'
 125
 126         if diff > PI || (diff < 0.f && diff > -PI)
 127         then
 128             None
 129         else
 130         Some (m1, m2)
 131
 132 let find (edges: Matrix<byte>)
 133          (xGradient: Matrix<float32>)
 134          (yGradient: Matrix<float32>)
 135          (config: Config) : MatchingEllipses =
 136
 137     let r1, r2 = config.RBCRadius.Min, config.RBCRadius.Max
 138     let incrementWindowDivisor = 4.f
 139
 140     // We choose a window size for which the biggest ellipse can always be fitted in.
 141     let windowSize = roundInt (2.f * r2)
 142     let factorNbPick = config.Parameters.factorNbPick
 143
 144     let increment = windowSize / (int incrementWindowDivisor)
 145
 146     let radiusTolerance = (r2 - r1) * 0.2f
 147
 148     let squaredMinimumDistance = (float r2 / 1.5) ** 2.
 149     let inline squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2. + (y1 - y2) ** 2.
 150
 151     let h = edges.Height
 152     let w = edges.Width
 153     let h_f = float32 h
 154     let w_f = float32 w
 155
 156     let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
 157
 158     let currentElements = List<Point>()
 159
 160     let edgesData = edges.Data
 161     let xDirData = xGradient.Data
 162     let yDirData = yGradient.Data
 163
 164     let rng = Random(42)
 165
 166     let ellipses = MatchingEllipses(config.RBCRadius.Pixel)
 167
 168     for window_i in -windowSize + increment .. increment .. h - increment do
 169         for window_j in -windowSize + increment .. increment .. w - increment do
 170
 171             let window_i_begin = if window_i < 0 then 0 else window_i
 172             let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1
 173             let window_j_begin = if window_j < 0 then 0 else window_j
 174             let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
 175
 176             // Remove old elements.
 177             let indexFirstElement = currentElements.FindIndex(fun p -> p.X >= window_j_begin)
 178             if indexFirstElement > 0
 179             then currentElements.RemoveRange(0, indexFirstElement)
 180
 181             // Add the new elements.
 182             let newElemsBegin_j = window_j + windowSize - increment
 183             let newElemsEnd_j = window_j + windowSize - 1
 184             for j in (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) .. (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
 185                 for i in window_i_begin .. window_i_end do
 186                     if edgesData.[i, j] = 1uy
 187                     then currentElements.Add(Point(j, i))
 188
 189             if currentElements.Count >= 10
 190             then
 191                 let mutable nbOfPicks = (float currentElements.Count) * factorNbPick |> int
 192                 while nbOfPicks > 0 do
 193                     let p1 = currentElements.[rng.Next(currentElements.Count)]
 194                     let p2 = currentElements.[rng.Next(currentElements.Count)]
 195                     let p3 = currentElements.[rng.Next(currentElements.Count)]
 196                     if p1 <> p2 && p1 <> p3 && p2 <> p3
 197                     then
 198                         nbOfPicks <- nbOfPicks - 1
 199                         let p1yf, p1xf = float p1.Y, float p1.X
 200                         let p2yf, p2xf = float p2.Y, float p2.X
 201                         let p3yf, p3xf = float p3.Y, float p3.X
 202                         if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance &&
 203                            squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
 204                            squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
 205                         then
 206                             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
 207                             | Some (m1, m2) ->
 208                                 match ellipse p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
 209                                 | Some e when e.Cx > 0.f && e.Cx < w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
 210                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 211                                      ellipses.Add e
 212                                 | _ -> ()
 213                             | _ -> ()
 214
 215         currentElements.Clear()
 216
 217     ellipses
 218