cf94be28df77826f391d6ad84d8e051c233b23b8
[master-thesis.git] / 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 >= 10
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