ac3c041a9d2a7fb5bf3b5769ca65198ea20d22f4
4 open System.Collections.Generic
7 open MathNet.Numerics.LinearAlgebra
10 open Emgu.CV.Structure
17 type private SearchExtremum = Minimum | Maximum
19 let private goldenSectionSearch
(f
: float -> float) (nbIter
: int) (xmin
: float) (xmax
: float) (searchExtremum
: SearchExtremum) : (float * float) =
20 let gr = 1. / 1.6180339887498948482
23 let mutable c = b - gr * (b - a)
24 let mutable d = a + gr * (b - a)
26 for i
in 1 .. nbIter
do
30 if searchExtremum
= Maximum
49 // Ellipse.A is always equal or greater than Ellipse.B.
50 // Ellipse.Alpha is between 0 and Pi.
51 let ellipse (p1x
: float) (p1y
: float) (m1
: float) (p2x
: float) (p2y
: float) (m2
: float) (p3x
: float) (p3y
: float) : Types.Ellipse option =
52 let accuracy_extremum_search_1 = 10 // 3
53 let accuracy_extremum_search_2 = 10 // 4
55 // p3 as the referencial.
62 // Convert to polar coordinates.
66 let r1 = sqrt
(p1x ** 2. + p1y ** 2.)
67 let theta1 = atan2
p1y p1x
69 let r2 = sqrt
(p2x ** 2. + p2y ** 2.)
70 let theta2 = atan2
p2y p2x
73 4. * sin
(alpha1 - theta1) * (-r1 * sin
(alpha1 - theta1) + r2 * sin
(alpha1 - theta2)) *
74 sin
(alpha2 - theta2) * (-r1 * sin
(alpha2 - theta1) + r2 * sin
(alpha2 - theta2)) +
75 r1 * r2 * sin
(alpha1 - alpha2) ** 2. * sin
(theta1 - theta2) ** 2. < 0.
80 (r1 * r2 * (r1 * (cos
(alpha2 + theta
- theta1 - theta2) - cos
(alpha2 - theta
) * cos
(theta1 - theta2)) * sin
(alpha1 - theta1) + r2 * (-cos
(alpha1 + theta
- theta1 - theta2) + cos
(alpha1 - theta
) * cos
(theta1 - theta2)) * sin
(alpha2 - theta2)) * sin
(theta1 - theta2)) /
81 (sin
(alpha1 - theta1) * sin
(alpha2 - theta2) * (r1 * sin
(theta
- theta1) - r2 * sin
(theta
- theta2)) ** 2. - r1 * r2 * sin
(alpha1 - theta
) * sin
(alpha2 - theta
) * sin
(theta1 - theta2) ** 2.)
85 // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
86 let thetaTan, _
= goldenSectionSearch
rabs accuracy_extremum_search_1 0. Math.PI Maximum
89 let PTanx = rTan * cos
thetaTan
90 let PTany = rTan * sin
thetaTan
93 let d1b = -d1a * p1x + p1y
96 let d2b = -d2a * p2x + p2y
98 let d3a = -1. / tan
thetaTan
99 let d3b = -d3a * PTanx + PTany
101 let Ux = -(d1b - d2b) / (d1a - d2a)
102 let Uy = -(d2a * d1b - d1a * d2b) / (d1a - d2a)
104 let Vx = -(d1b - d3b) / (d1a - d3a)
105 let Vy = -(d3a * d1b - d1a * d3b) / (d1a - d3a)
107 let Wx = p1x + (p2x - p1x) / 2.
108 let Wy = p1y + (p2y - p1y) / 2.
110 let Zx = p1x + (PTanx - p1x) / 2.
111 let Zy = p1y + (PTany - p1y) / 2.
113 let va = -(-Vy + Zy) / (Vx - Zx)
114 let vb = -(Zx * Vy - Vx * Zy) / (Vx - Zx)
116 let ua = -(-Uy + Wy) / (Ux - Wx)
117 let ub = -(Wx * Uy - Ux * Wy) / (Ux - Wx)
119 let cx = -(vb - ub) / (va - ua)
120 let cy = -(ua * vb - va * ub) / (va - ua)
122 let rc = sqrt
(cx ** 2. + cy ** 2.)
123 let psi = atan2
cy cx
127 rc ** 2. + (r1 ** 2. * r2 ** 2. * (r1 * (cos
(alpha2 + theta
- theta1 - theta2) - cos
(alpha2 - theta
) * cos
(theta1 - theta2)) * sin
(alpha1 - theta1) + r2 * (-cos
(alpha1 + theta
- theta1 - theta2) + cos
(alpha1 - theta
) * cos
(theta1 - theta2)) * sin
(alpha2 - theta2)) ** 2. * sin
(theta1 - theta2) ** 2.) /
128 (sin
(alpha1 - theta1) * sin
(alpha2 - theta2) * (r1 * sin
(theta
- theta1) - r2 * sin
(theta
- theta2)) ** 2. - r1 * r2 * sin
(alpha1 - theta
) * sin
(alpha2 - theta
) * sin
(theta1 - theta2) ** 2.) ** 2. -
129 (2. * r1 * r2 * rc * cos
(theta
- psi) * (r1 * (cos
(alpha2 + theta
- theta1 - theta2) - cos
(alpha2 - theta
) * cos
(theta1 - theta2)) * sin
(alpha1 - theta1) + r2 * (-cos
(alpha1 + theta
- theta1 - theta2) + cos
(alpha1 - theta
) * cos
(theta1 - theta2)) * sin
(alpha2 - theta2)) * sin
(theta1 - theta2)) /
130 (sin
(alpha1 - theta1) * sin
(alpha2 - theta2) * (r1 * sin
(theta
- theta1) - r2 * sin
(theta
- theta2)) ** 2. - r1 * r2 * sin
(alpha1 - theta
) * sin
(alpha2 - theta
) * sin
(theta1 - theta2) ** 2.))
132 // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
133 let r1eTheta, r1e
= goldenSectionSearch
rellipse accuracy_extremum_search_2 0. (Math.PI / 2.) Maximum // Pi/2 and not pi because the period is Pi.
134 let r2eTheta, r2e
= goldenSectionSearch
rellipse accuracy_extremum_search_2 0. (Math.PI / 2.) Minimum
136 let rr1e = r r1eTheta
137 let r1ex = rr1e * cos
r1eTheta
138 let r1ey = rr1e * sin
r1eTheta
139 let mutable alpha = atan
((r1ey - cy) / (r1ex - cx))
142 alpha <- alpha + Math.PI
144 // Ride off the p3 referential.
148 Some (Types.Ellipse(float32
cx, float32
cy, float32 r1e
, float32 r2e
, float32
alpha))
152 let ellipse2 (p1x: float) (p1y: float) (m1
: float) (p2x: float) (p2y: float) (m2
: float) (p3x
: float) (p3y
: float) : Types.Ellipse option =
153 let p0 = pointFromTwoLines
(Types.Line(float32 m1
, float32
(p1y - m1
* p1x))) (Types.Line(float32 m2
, float32
(p2y - m2
* p2x)))
154 let p0x, p0y
= float p0.X, float p0.Y
156 let s = matrix
[[ 1.; 0.; 0. ]
160 let v0 = matrix
[[ 1.; p0x; p0y
]]
161 let v1 = matrix
[[ 1.; p1x; p1y ]]
162 let v2 = matrix
[[ 1.; p2x; p2y ]]
163 let v3 = matrix
[[ 1.; p3x
; p3y
]]
165 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()
166 let conicMat = p * s.Inverse() * p.Transpose()
167 let a = conicMat.[0, 0]
168 let b = conicMat.[0, 1]
169 let c = conicMat.[1, 1]
170 let d = conicMat.[0, 2]
171 let e = conicMat.[1, 2]
172 let f = conicMat.[2, 2]
178 let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
183 let q = (-1. / at) * (matrix
[[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
185 let eigenValues = eigen.EigenValues
186 let lambda = eigenValues.[1].Real
187 let mu = eigenValues.[0].Real
189 if lambda <= 0. || mu <= 0.
193 let r1, r2 = 1. / (sqrt
lambda), 1. / (sqrt
mu)
195 let eigenVectors = eigen.EigenVectors
196 let v_a = eigenVectors.[0, 0]
197 let v_b = eigenVectors.[1, 0] // [0, 1]
199 // Angle against the longest axis.
200 let phi = (if r2 > r1 then atan
(v_b / v_a) else atan (v_a / v_b))
202 let phi' = if phi < 0. then phi + Math.PI else phi
203 let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
205 Some (Types.Ellipse(float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
208 let private vectorRotation
(p1x: float32
) (p1y: float32
) (v1x
: float32
) (v1y
: float32
) (px
: float32
) (py
: float32
) : float32
=
209 let mutable rotation = 1.f
232 let private areVectorsValid
(p1x: float32
) (p1y: float32
) (p2x: float32
) (p2y: float32
) (v1x
: float32
) (v1y
: float32
) (v2x
: float32
) (v2y
: float32
) : (float32
* float32
) option =
236 let b1 = -m1 * p1x + p1y
237 let b2 = -m2 * p2x + p2y
238 let px = -((b1 - b2) / (m1 - m2))
239 let py = -((m2 * b1 - m1 * b2) / (m1 - m2))
241 let rot1 = vectorRotation
p1x p1y v1x v1y
px py
242 let rot2 = vectorRotation
p2x p2y v2x v2y
px py
248 let alpha1 = atan2
(p1y - py) (p1x - px)
249 let alpha2 = atan2
(p2y - py) (p2x - px)
251 let alpha1' = if alpha1 < 0.f then 2.f * PI + alpha1 else alpha1
252 let alpha2' = if alpha2 < 0.f then 2.f * PI + alpha2 else alpha2
254 let diff = rot1 * alpha1' + rot2 * alpha2'
256 if diff > PI || (diff < 0.f && diff > -PI)
263 let find (edges
: Matrix<byte
>)
264 (xGradient
: Image<Gray, float32
>)
265 (yGradient
: Image<Gray, float32
>)
266 (config
: Config) : MatchingEllipses =
268 let r1, r2 = config
.RBCRadius.Min, config
.RBCRadius.Max
269 let incrementWindowDivisor = 4.f
271 // We choose a window size for which the biggest ellipse can always be fitted in.
272 let windowSize = roundInt
(2.f * r2 / (incrementWindowDivisor - 1.f) * incrementWindowDivisor)
273 let factorNbPick = config
.Parameters.factorNbPick
275 let increment = windowSize / (int incrementWindowDivisor)
277 let radiusTolerance = (r2 - r1) * 0.2f
279 let squaredMinimumDistance = (float r2 / 1.5) ** 2.
280 let inline squaredDistance
x1 y1 x2 y2
= (x1 - x2
) ** 2. + (y1
- y2
) ** 2.
287 let mutable last_i, last_j
= Int32.MaxValue, Int32.MaxValue
289 let currentElements = List<Point>()
291 let edgesData = edges
.Data
292 let xDirData = xGradient
.Data
293 let yDirData = yGradient
.Data
297 let ellipses = MatchingEllipses(config
.RBCRadius.Pixel)
299 for window_i
in -windowSize + increment .. increment .. h - increment do
300 for window_j
in -windowSize + increment .. increment .. w - increment do
302 let window_i_begin = if window_i
< 0 then 0 else window_i
303 let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1
304 let window_j_begin = if window_j
< 0 then 0 else window_j
305 let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
307 // Remove old elements.
308 let indexFirstElement = currentElements.FindIndex(fun p -> p.X >= window_j_begin)
309 if indexFirstElement > 0
310 then currentElements.RemoveRange(0, indexFirstElement)
312 // Add the new elements.
313 let newElemsBegin_j = window_j + windowSize - increment
314 let newElemsEnd_j = window_j + windowSize - 1
315 for j
in (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) .. (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
316 for i
in window_i_begin .. window_i_end do
317 if edgesData.[i
, j
] = 1uy
318 then currentElements.Add(Point(j
, i
))
320 if currentElements.Count >= 10
322 let mutable nbOfPicks = (float currentElements.Count) * factorNbPick |> int
323 while nbOfPicks > 0 do
324 let p1 = currentElements.[rng.Next(currentElements.Count)]
325 let p2 = currentElements.[rng.Next(currentElements.Count)]
326 let p3 = currentElements.[rng.Next(currentElements.Count)]
327 if p1 <> p2 && p1 <> p3 && p2 <> p3
329 nbOfPicks <- nbOfPicks - 1
330 let p1yf, p1xf
= float p1.Y, float p1.X
331 let p2yf, p2xf
= float p2.Y, float p2.X
332 let p3yf, p3xf
= float p3.Y, float p3.X
333 if squaredDistance
p1xf p1yf p2xf
p2yf >= squaredMinimumDistance &&
334 squaredDistance
p1xf p1yf p3xf
p3yf >= squaredMinimumDistance &&
335 squaredDistance
p2xf p2yf p3xf
p3yf >= squaredMinimumDistance
337 match areVectorsValid
(float32
p1xf) (float32
p1yf) (float32
p2xf) (float32
p2yf) -xDirData.[p1.Y, p1.X, 0] -yDirData.[p1.Y, p1.X, 0] -xDirData.[p2.Y, p2.X, 0] -yDirData.[p2.Y, p2.X, 0] with
339 //let pouet = ellipse2 p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf
340 match ellipse2 p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf
p3yf with
341 | Some e when e.Cx > 0.f && e.Cx < w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
342 e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
347 currentElements.Clear()