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 =
  30         matrix
  31             [
  32                 [ 1.;   0.;  0.  ]
  33                 [ 0.;   0.; -0.5 ]
  34                 [ 0.; -0.5;  0.  ]
  35             ]
  36
  37     let v0 = matrix [[ 1.; p0x; p0y ]]
  38     let v1 = matrix [[ 1.; p1x; p1y ]]
  39     let v2 = matrix [[ 1.; p2x; p2y ]]
  40     let v3 = matrix [[ 1.; p3x; p3y ]]
  41
  42     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 ()
  43     let conicMat = p * s.Inverse () * p.Transpose ()
  44     let a = conicMat.[0, 0]
  45     let b = conicMat.[0, 1]
  46     let c = conicMat.[1, 1]
  47     let d = conicMat.[0, 2]
  48     let e = conicMat.[1, 2]
  49     let f = conicMat.[2, 2]
  50
  51     // Center.
  52     let cx = b / a
  53     let cy = d / a
  54
  55     let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
  56     if at = 0. then
  57         None
  58     else
  59         let q = (-1. / at) * (matrix [[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
  60         let eigen = q.Evd ()
  61         let eigenValues = eigen.EigenValues
  62         let lambda = eigenValues.[1].Real
  63         let mu = eigenValues.[0].Real
  64
  65         if lambda <= 0. || mu <= 0. then
  66             None
  67         else
  68             let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu)
  69
  70             let eigenVectors = eigen.EigenVectors
  71             let v_a = eigenVectors.[0, 0]
  72             let v_b = eigenVectors.[1, 0] // [0, 1]
  73
  74             // Angle against the longest axis.
  75             let phi = (if r2 > r1 then atan (v_b / v_a) else atan (v_a / v_b))
  76
  77             let phi' = if phi < 0. then phi + Math.PI else phi
  78             let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
  79
  80             Some (Types.Ellipse (float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
  81
  82 let inline private vectorRotation (px : float32) (py : float32) (vx : float32) (vy : float32) (p0x : float32) (p0y : float32) : float32 =
  83     if py > p0y then
  84         if vx > 0.f then -1.f else 1.f
  85     elif py < p0y then
  86         if vx < 0.f then -1.f else 1.f
  87     elif px > p0x then
  88         if vy < 0.f then -1.f else 1.f
  89     else // p1x < px
  90         if vy > 0.f then -1.f else 1.f
  91
  92 let private areVectorsValid (p1x : float32) (p1y : float32) (p2x : float32) (p2y : float32) (v1x : float32) (v1y : float32) (v2x : float32) (v2y : float32) : (float32 * float32) option =
  93     let m1 = -v1x / v1y
  94     let m2 = -v2x / v2y
  95
  96     let b1 = -m1 * p1x + p1y
  97     let b2 = -m2 * p2x + p2y
  98     let p0x = -(b1 - b2) / (m1 - m2)
  99     let p0y = -(m2 * b1 - m1 * b2) / (m1 - m2)
 100
 101     let rot1 = vectorRotation p1x p1y v1x v1y p0x p0y
 102     let rot2 = vectorRotation p2x p2y v2x v2y p0x p0y
 103
 104     if rot1 = rot2 then
 105         None
 106     else
 107         let alpha1 =
 108             let alpha1' = atan2 (p1y - p0y) (p1x - p0x)
 109             if alpha1' < 0.f then 2.f * PI + alpha1' else alpha1'
 110
 111         let alpha2 =
 112             let alpha2' = atan2 (p2y - p0y) (p2x - p0x)
 113             if alpha2' < 0.f then 2.f * PI + alpha2' else alpha2'
 114
 115         let diff = rot1 * alpha1 + rot2 * alpha2
 116
 117         if diff > PI || (diff < 0.f && diff > -PI) then
 118             Some (m1, m2)
 119         else
 120             None
 121
 122 /// <summary>
 123 /// Build a set of ellipses as a 'MatchingEllipses' object by finding ellipses with the given edges and gradient.
 124 /// </summary>
 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 then
 174                 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 = (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) to (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
 180                 for i = window_i_begin to window_i_end do
 181                     if edgesData.[i, j] = 1uy then
 182                         currentElements.Add (Point (j, i))
 183
 184             if currentElements.Count >= nbPickElementsMin 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 then
 192                         nbOfPicks <- nbOfPicks - 1
 193                         let p1yf, p1xf = float p1.Y, float p1.X
 194                         let p2yf, p2xf = float p2.Y, float p2.X
 195                         let p3yf, p3xf = float p3.Y, float p3.X
 196                         if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance &&
 197                            squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
 198                            squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
 199                         then
 200                             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
 201                             | Some (m1, m2) ->
 202                                 match ellipse p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
 203                                 | Some e when e.Cx > 0.f && e.Cx <  w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
 204                                               e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
 205                                     nbOfValidPicks <- nbOfValidPicks - 1
 206                                     ellipses.Add e
 207                                 | _ -> ()
 208                             | _ -> ()
 209
 210         currentElements.Clear ()
 211
 212     ellipses
 213