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 // This is a ratio of the biggest radius.
  18 let minimumDistanceBetweenDrawnPoints = 0.6
  19
  20 /// <summary>
  21 /// Try to build an ellipse from three points and two tangents passing by the first and the second point.
  22 /// 'Ellipse.A' is always equal or greater than Ellipse.B.
  23 /// 'Ellipse.Alpha' is between 0 and Pi.
  24 /// </summary>
  25 let ellipse (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
  26     let p0 = pointFromTwoLines (Types.Line(float32 m1, float32 (p1y - m1 * p1x))) (Types.Line(float32 m2, float32(p2y - m2 * p2x)))
  27     let p0x, p0y = float p0.X, float p0.Y
  28
  29     let s = matrix [[ 1.;   0.;  0.  ]
  30                     [ 0.;   0.; -0.5 ]
  31                     [ 0.; -0.5;  0.  ]]
  32
  33     let v0 = matrix [[ 1.; p0x; p0y ]]
  34     let v1 = matrix [[ 1.; p1x; p1y ]]
  35     let v2 = matrix [[ 1.; p2x; p2y ]]
  36     let v3 = matrix [[ 1.; p3x; p3y ]]
  37
  38     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()
  39     let conicMat = p * s.Inverse() * p.Transpose()
  40     let a = conicMat.[0, 0]
  41     let b = conicMat.[0, 1]
  42     let c = conicMat.[1, 1]
  43     let d = conicMat.[0, 2]
  44     let e = conicMat.[1, 2]
  45     let f = conicMat.[2, 2]
  46
  47     // Center.
  48     let cx = b / a
  49     let cy = d / a
  50
  51     let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
  52     if at = 0.
  53     then
  54         None
  55     else
  56         let q = (-1. / at) * (matrix [[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
  57         let eigen = q.Evd()
  58         let eigenValues = eigen.EigenValues
  59         let lambda = eigenValues.[1].Real
  60         let mu = eigenValues.[0].Real
  61
  62         if lambda <= 0. || mu <= 0.
  63         then
  64             None
  65         else
  66             let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu)
  67
  68             let eigenVectors = eigen.EigenVectors
  69             let v_a = eigenVectors.[0, 0]
  70             let v_b = eigenVectors.[1, 0] // [0, 1]
  71
  72             // Angle against the longest axis.
  73             let phi = (if r2 > r1 then atan (v_b / v_a) else atan (v_a / v_b))
  74
  75             let phi' = if phi < 0. then phi + Math.PI else phi
  76             let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
  77
  78             Some (Types.Ellipse(float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
  79
  80 let inline private vectorRotation (px: float32) (py: float32) (vx: float32) (vy: float32) (p0x: float32) (p0y: float32) : float32 =
  81     if py > p0y
  82     then
  83         if vx > 0.f then -1.f else 1.f
  84     elif py < p0y
  85     then
  86         if vx < 0.f then -1.f else 1.f
  87     elif px > p0x
  88     then
  89         if vy < 0.f then -1.f else 1.f
  90     else // p1x < px
  91         if vy > 0.f then -1.f else 1.f
  92
  93 let private areVectorsValid (p1x: float32) (p1y: float32) (p2x: float32) (p2y: float32) (v1x: float32) (v1y: float32) (v2x: float32) (v2y: float32) : (float32 * float32) option =
  94     let m1 = -v1x / v1y
  95     let m2 = -v2x / v2y
  96
  97     let b1 = -m1 * p1x + p1y
  98     let b2 = -m2 * p2x + p2y
  99     let p0x = -(b1 - b2) / (m1 - m2)
 100     let p0y = -(m2 * b1 - m1 * b2) / (m1 - m2)
 101
 102     let rot1 = vectorRotation p1x p1y v1x v1y p0x p0y
 103     let rot2 = vectorRotation p2x p2y v2x v2y p0x p0y
 104
 105     if rot1 = rot2
 106     then
 107         None
 108     else
 109         let alpha1 =
 110             let alpha1' = atan2 (p1y - p0y) (p1x - p0x)
 111             if alpha1' < 0.f then 2.f * PI + alpha1' else alpha1'
 112
 113         let alpha2 =
 114             let alpha2' = atan2 (p2y - p0y) (p2x - p0x)
 115             if alpha2' < 0.f then 2.f * PI + alpha2' else alpha2'
 116
 117         let diff = rot1 * alpha1 + rot2 * alpha2
 118
 119         if diff > PI || (diff < 0.f && diff > -PI)
 120         then
 121             Some (m1, m2)
 122         else
 123             None
 124
 125 let find (edges: Matrix<byte>)
 126          (xGradient: Matrix<float32>)
 127          (yGradient: Matrix<float32>)
 128          (config: Config) : MatchingEllipses =
 129
 130     let r1, r2 = config.RBCRadius.Min, config.RBCRadius.Max
 131     let incrementWindowDivisor = 4.f
 132
 133     // We choose a window size for which the biggest ellipse can always be fitted in.
 134     let windowSize = roundInt (2.f * r2)
 135     let factorNbValidPick = config.Parameters.factorNbValidPick
 136     let factorNbMaxPick = config.Parameters.factorNbMaxPick
 137     let nbPickElementsMin = config.Parameters.nbPickElementsMin
 138
 139     let increment = windowSize / (int incrementWindowDivisor)
 140
 141     let radiusTolerance = (r2 - r1) * 0.2f
 142
 143     let squaredMinimumDistance = (float config.RBCRadius.Pixel * minimumDistanceBetweenDrawnPoints) ** 2.
 144     let inline squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2. + (y1 - y2) ** 2.
 145
 146     let h = edges.Height
 147     let w = edges.Width
 148     let h_f = float32 h
 149     let w_f = float32 w
 150
 151     let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
 152
 153     let currentElements = List<Point>()
 154
 155     let edgesData = edges.Data
 156     let xDirData = xGradient.Data
 157     let yDirData = yGradient.Data
 158
 159     let rng = Random(42)
 160
 161     let ellipses = MatchingEllipses(config.RBCRadius.Pixel)
 162
 163     for window_i in -windowSize + increment .. increment .. h - increment do
 164         for window_j in -windowSize + increment .. increment .. w - increment do
 165
 166             let window_i_begin = if window_i < 0 then 0 else window_i
 167             let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1
 168             let window_j_begin = if window_j < 0 then 0 else window_j
 169             let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
 170
 171             // Remove old elements.
 172             let indexFirstElement = currentElements.FindIndex(fun p -> p.X >= window_j_begin)
 173             if indexFirstElement > 0
 174             then currentElements.RemoveRange(0, indexFirstElement)
 175
 176             // Add the new elements.
 177             let newElemsBegin_j = window_j + windowSize - increment
 178             let newElemsEnd_j = window_j + windowSize - 1
 179             for j in (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) .. (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
 180                 for i in window_i_begin .. window_i_end do
 181                     if edgesData.[i, j] = 1uy
 182                     then currentElements.Add(Point(j, i))
 183
 184             if currentElements.Count >= nbPickElementsMin
 185             then
 186                 let mutable nbOfPicks = (float currentElements.Count) * factorNbMaxPick |> int
 187                 let mutable nbOfValidPicks = (float currentElements.Count) * factorNbValidPick |> int
 188                 while nbOfPicks > 0 && nbOfValidPicks > 0 do
 189                     let p1 = currentElements.[rng.Next(currentElements.Count)]
 190                     let p2 = currentElements.[rng.Next(currentElements.Count)]
 191                     let p3 = currentElements.[rng.Next(currentElements.Count)]
 192                     if p1 <> p2 && p1 <> p3 && p2 <> p3
 193                     then
 194                         nbOfPicks <- nbOfPicks - 1
 195                         let p1yf, p1xf = float p1.Y, float p1.X
 196                         let p2yf, p2xf = float p2.Y, float p2.X
 197                         let p3yf, p3xf = float p3.Y, float p3.X
 198                         if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance &&
 199                            squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
 200                            squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
 201                         then
 202                             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
 203                             | Some (m1, m2) ->
 204                                 match ellipse p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
 205                                 | Some e when e.Cx > 0.f && e.Cx <  w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
 206                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 207                                     nbOfValidPicks <- nbOfValidPicks - 1
 208                                     ellipses.Add e
 209                                 | _ -> ()
 210                             | _ -> ()
 211
 212         currentElements.Clear()
 213
 214     ellipses
 215