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
  81 let private vectorRotation (p1x: float32) (p1y: float32) (v1x: float32) (v1y: float32) (px: float32) (py: float32) : float32 =
  82     if p1y > py
  83     then
  84         if v1x > 0.f then -1.f else 1.f
  85     elif p1y < py
  86     then
  87         if v1x < 0.f then -1.f else 1.f
  88     elif p1x > px
  89     then
  90         if v1y < 0.f then -1.f else 1.f
  91     else // p1x < px
  92         if v1y > 0.f then -1.f else 1.f
  93
  94 let private areVectorsValid (p1x: float32) (p1y: float32) (p2x: float32) (p2y: float32) (v1x: float32) (v1y: float32) (v2x: float32) (v2y: float32) : (float32 * float32) option =
  95     let m1 = -v1x / v1y
  96     let m2 = -v2x / v2y
  97
  98     let b1 = -m1 * p1x + p1y
  99     let b2 = -m2 * p2x + p2y
 100     let px = -((b1 - b2) / (m1 - m2))
 101     let py = -((m2 * b1 - m1 * b2) / (m1 - m2))
 102
 103     let rot1 = vectorRotation p1x p1y v1x v1y px py
 104     let rot2 = vectorRotation p2x p2y v2x v2y px py
 105
 106     if rot1 = rot2
 107     then
 108         None
 109     else
 110         let alpha1 = atan2 (p1y - py) (p1x - px)
 111         let alpha2 = atan2 (p2y - py) (p2x - px)
 112
 113         let alpha1' = if alpha1 < 0.f then 2.f * PI + alpha1 else alpha1
 114         let alpha2' = if alpha2 < 0.f then 2.f * PI + alpha2 else alpha2
 115
 116         let diff = rot1 * alpha1' + rot2 * alpha2'
 117
 118         if diff > PI || (diff < 0.f && diff > -PI)
 119         then
 120             Some (m1, m2)
 121         else
 122             None
 123
 124 let find (edges: Matrix<byte>)
 125          (xGradient: Matrix<float32>)
 126          (yGradient: Matrix<float32>)
 127          (config: Config) : MatchingEllipses =
 128
 129     let r1, r2 = config.RBCRadius.Min, config.RBCRadius.Max
 130     let incrementWindowDivisor = 4.f
 131
 132     // We choose a window size for which the biggest ellipse can always be fitted in.
 133     let windowSize = roundInt (2.f * r2)
 134     let factorNbValidPick = config.Parameters.factorNbValidPick
 135     let factorNbMaxPick = config.Parameters.factorNbMaxPick
 136     let nbPickElementsMin = config.Parameters.nbPickElementsMin
 137
 138     let increment = windowSize / (int incrementWindowDivisor)
 139
 140     let radiusTolerance = (r2 - r1) * 0.2f
 141
 142     let squaredMinimumDistance = (float config.RBCRadius.Pixel * minimumDistanceBetweenDrawnPoints) ** 2.
 143     let inline squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2. + (y1 - y2) ** 2.
 144
 145     let h = edges.Height
 146     let w = edges.Width
 147     let h_f = float32 h
 148     let w_f = float32 w
 149
 150     let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
 151
 152     let currentElements = List<Point>()
 153
 154     let edgesData = edges.Data
 155     let xDirData = xGradient.Data
 156     let yDirData = yGradient.Data
 157
 158     let rng = Random(42)
 159
 160     let ellipses = MatchingEllipses(config.RBCRadius.Pixel)
 161
 162     for window_i in -windowSize + increment .. increment .. h - increment do
 163         for window_j in -windowSize + increment .. increment .. w - increment do
 164
 165             let window_i_begin = if window_i < 0 then 0 else window_i
 166             let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1
 167             let window_j_begin = if window_j < 0 then 0 else window_j
 168             let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
 169
 170             // Remove old elements.
 171             let indexFirstElement = currentElements.FindIndex(fun p -> p.X >= window_j_begin)
 172             if indexFirstElement > 0
 173             then currentElements.RemoveRange(0, indexFirstElement)
 174
 175             // Add the new elements.
 176             let newElemsBegin_j = window_j + windowSize - increment
 177             let newElemsEnd_j = window_j + windowSize - 1
 178             for j in (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) .. (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
 179                 for i in window_i_begin .. window_i_end do
 180                     if edgesData.[i, j] = 1uy
 181                     then currentElements.Add(Point(j, i))
 182
 183             if currentElements.Count >= 10
 184             then
 185                 let mutable nbOfPicks = (float currentElements.Count) * factorNbMaxPick |> int
 186                 let mutable nbOfValidPicks = (float currentElements.Count) * factorNbValidPick |> int
 187                 while nbOfPicks > 0 && nbOfValidPicks > 0 do
 188                     let p1 = currentElements.[rng.Next(currentElements.Count)]
 189                     let p2 = currentElements.[rng.Next(currentElements.Count)]
 190                     let p3 = currentElements.[rng.Next(currentElements.Count)]
 191                     if p1 <> p2 && p1 <> p3 && p2 <> p3
 192                     then
 193                         nbOfPicks <- nbOfPicks - 1
 194                         let p1yf, p1xf = float p1.Y, float p1.X
 195                         let p2yf, p2xf = float p2.Y, float p2.X
 196                         let p3yf, p3xf = float p3.Y, float p3.X
 197                         if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance &&
 198                            squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
 199                            squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
 200                         then
 201                             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
 202                             | Some (m1, m2) ->
 203                                 match ellipse p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
 204                                 | Some e when e.Cx > 0.f && e.Cx < w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
 205                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 206                                     nbOfValidPicks <- nbOfValidPicks - 1
 207                                     ellipses.Add e
 208                                 | _ -> ()
 209                             | _ -> ()
 210
 211         currentElements.Clear()
 212
 213     ellipses
 214