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
  11 open Utils
  12 open Config
  13 open MatchingEllipses
  14 open Const
  15
  16 // This is a ratio of the biggest radius.
  17 let minimumDistanceBetweenDrawnPoints = 0.6
  18
  19 /// <summary>
  20 /// Try to build an ellipse from three points and two tangents passing by the first and the second point.
  21 /// 'Ellipse.A' is always equal or greater than Ellipse.B.
  22 /// 'Ellipse.Alpha' is between 0 and Pi.
  23 /// </summary>
  24 let ellipse (p1x : float) (p1y : float) (m1 : float) (p2x : float) (p2y : float) (m2 : float) (p3x : float) (p3y : float) : Types.Ellipse option =
  25     let p0 = pointFromTwoLines (Types.Line (float32 m1, float32 (p1y - m1 * p1x))) (Types.Line (float32 m2, float32(p2y - m2 * p2x)))
  26     let p0x, p0y = float p0.X, float p0.Y
  27
  28     let s =
  29         matrix
  30             [
  31                 [ 1.;   0.;  0.  ]
  32                 [ 0.;   0.; -0.5 ]
  33                 [ 0.; -0.5;  0.  ]
  34             ]
  35
  36     let v0 = matrix [[ 1.; p0x; p0y ]]
  37     let v1 = matrix [[ 1.; p1x; p1y ]]
  38     let v2 = matrix [[ 1.; p2x; p2y ]]
  39     let v3 = matrix [[ 1.; p3x; p3y ]]
  40
  41     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 ()
  42     let conicMat = p * s.Inverse () * p.Transpose ()
  43     let a = conicMat.[0, 0]
  44     let b = conicMat.[0, 1]
  45     let c = conicMat.[1, 1]
  46     let d = conicMat.[0, 2]
  47     let e = conicMat.[1, 2]
  48     let f = conicMat.[2, 2]
  49
  50     // Center.
  51     let cx = b / a
  52     let cy = d / a
  53
  54     let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
  55     if at = 0. then
  56         None
  57     else
  58         let q = (-1. / at) * (matrix [[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
  59         let eigen = q.Evd ()
  60         let eigenValues = eigen.EigenValues
  61         let lambda = eigenValues.[1].Real
  62         let mu = eigenValues.[0].Real
  63
  64         if lambda <= 0. || mu <= 0. then
  65             None
  66         else
  67             let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu)
  68
  69             let eigenVectors = eigen.EigenVectors
  70             let v_a = eigenVectors.[0, 0]
  71             let v_b = eigenVectors.[1, 0] // [0, 1]
  72
  73             // Angle against the longest axis.
  74             let phi = (if r2 > r1 then atan (v_b / v_a) else atan (v_a / v_b))
  75
  76             let phi' = if phi < 0. then phi + Math.PI else phi
  77             let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
  78
  79             Some (Types.Ellipse (float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
  80
  81 let inline private vectorRotation (px : float32) (py : float32) (vx : float32) (vy : float32) (p0x : float32) (p0y : float32) : float32 =
  82     if py > p0y then
  83         if vx > 0.f then -1.f else 1.f
  84     elif py < p0y then
  85         if vx < 0.f then -1.f else 1.f
  86     elif px > p0x then
  87         if vy < 0.f then -1.f else 1.f
  88     else // p1x < px
  89         if vy > 0.f then -1.f else 1.f
  90
  91 let private areVectorsValid (p1x : float32) (p1y : float32) (p2x : float32) (p2y : float32) (v1x : float32) (v1y : float32) (v2x : float32) (v2y : float32) : (float32 * float32) option =
  92     let m1 = -v1x / v1y
  93     let m2 = -v2x / v2y
  94
  95     let b1 = -m1 * p1x + p1y
  96     let b2 = -m2 * p2x + p2y
  97     let p0x = -(b1 - b2) / (m1 - m2)
  98     let p0y = -(m2 * b1 - m1 * b2) / (m1 - m2)
  99
 100     let rot1 = vectorRotation p1x p1y v1x v1y p0x p0y
 101     let rot2 = vectorRotation p2x p2y v2x v2y p0x p0y
 102
 103     if rot1 = rot2 then
 104         None
 105     else
 106         let alpha1 =
 107             let alpha1' = atan2 (p1y - p0y) (p1x - p0x)
 108             if alpha1' < 0.f then 2.f * PI + alpha1' else alpha1'
 109
 110         let alpha2 =
 111             let alpha2' = atan2 (p2y - p0y) (p2x - p0x)
 112             if alpha2' < 0.f then 2.f * PI + alpha2' else alpha2'
 113
 114         let diff = rot1 * alpha1 + rot2 * alpha2
 115
 116         if diff > PI || (diff < 0.f && diff > -PI) then
 117             Some (m1, m2)
 118         else
 119             None
 120
 121 /// <summary>
 122 /// Build a set of ellipses as a 'MatchingEllipses' object by finding ellipses with the given edges and gradient.
 123 /// </summary>
 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 then
 173                 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 = (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) to (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
 179                 for i = window_i_begin to window_i_end do
 180                     if edgesData.[i, j] = 1uy then
 181                         currentElements.Add (Point (j, i))
 182
 183             if currentElements.Count >= nbPickElementsMin then
 184                 let mutable nbOfPicks = (float currentElements.Count) * factorNbMaxPick |> int
 185                 let mutable nbOfValidPicks = (float currentElements.Count) * factorNbValidPick |> int
 186                 while nbOfPicks > 0 && nbOfValidPicks > 0 do
 187                     let p1 = currentElements.[rng.Next currentElements.Count]
 188                     let p2 = currentElements.[rng.Next currentElements.Count]
 189                     let p3 = currentElements.[rng.Next currentElements.Count]
 190                     if p1 <> p2 && p1 <> p3 && p2 <> p3 then
 191                         nbOfPicks <- nbOfPicks - 1
 192                         let p1yf, p1xf = float p1.Y, float p1.X
 193                         let p2yf, p2xf = float p2.Y, float p2.X
 194                         let p3yf, p3xf = float p3.Y, float p3.X
 195                         if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance &&
 196                            squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
 197                            squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
 198                         then
 199                             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
 200                             | Some (m1, m2) ->
 201                                 match ellipse p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
 202                                 | Some e when e.Cx > 0.f && e.Cx <  w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
 203                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 204                                     nbOfValidPicks <- nbOfValidPicks - 1
 205                                     ellipses.Add e
 206                                 | _ -> ()
 207                             | _ -> ()
 208
 209         currentElements.Clear ()
 210
 211     ellipses
 212