1
module ParasitemiaCore.Ellipse
4 open System.Collections.Generic
7 open MathNet.Numerics.LinearAlgebra
16 // This is a ratio of the biggest radius.
17 let minimumDistanceBetweenDrawnPoints = 0.6
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.
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
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
]]
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]
54 let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
58 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 eigenValues = eigen.EigenValues
61 let lambda = eigenValues.[1].Real
62 let mu = eigenValues.[0].Real
64 if lambda <= 0. || mu <= 0. then
67 let r1, r2
= 1. / (sqrt
lambda), 1. / (sqrt
mu)
69 let eigenVectors = eigen.EigenVectors
70 let v_a = eigenVectors.[0, 0]
71 let v_b = eigenVectors.[1, 0] // [0, 1]
73 // Angle against the longest axis.
74 let phi = (if r2
> r1 then atan
(v_b / v_a) else atan (v_a / v_b))
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
79 Some (Types.Ellipse (float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
81 let inline private
vectorRotation (px
: float32
) (py
: float32
) (vx
: float32
) (vy
: float32
) (p0x : float32
) (p0y
: float32
) : float32
=
83 if vx
> 0.f then -1.f else 1.f
85 if vx
< 0.f then -1.f else 1.f
87 if vy
< 0.f then -1.f else 1.f
89 if vy
> 0.f then -1.f else 1.f
91 let private areVectorsValid
(p1x
: float32
) (p1y
: float32
) (p2x
: float32
) (p2y
: float32
) (v1x
: float32
) (v1y
: float32
) (v2x
: float32
) (v2y
: float32
) : (float32
* float32
) option =
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)
100 let rot1 = vectorRotation p1x p1y v1x v1y
p0x p0y
101 let rot2 = vectorRotation p2x p2y v2x v2y
p0x p0y
107 let alpha1' = atan2 (p1y - p0y) (p1x - p0x)
108 if alpha1' < 0.f then 2.f * PI + alpha1' else alpha1'
111 let alpha2' = atan2 (p2y - p0y) (p2x - p0x)
112 if alpha2' < 0.f then 2.f * PI + alpha2' else alpha2'
114 let diff = rot1 * alpha1 + rot2 * alpha2
116 if diff > PI || (diff < 0.f && diff > -PI) then
122 /// Build a set of ellipses as a 'MatchingEllipses' object by finding ellipses with the given edges and gradient.
124 let find (edges
: Matrix<byte
>)
125 (xGradient
: Matrix<float32
>)
126 (yGradient
: Matrix<float32
>)
127 (config
: Config) : MatchingEllipses =
129 let r1, r2 = config
.RBCRadius.Min, config
.RBCRadius.Max
130 let incrementWindowDivisor = 4.f
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
138 let increment = windowSize / (int incrementWindowDivisor)
140 let radiusTolerance = (r2 - r1) * 0.2f
142 let squaredMinimumDistance = (float config.RBCRadius.Pixel * minimumDistanceBetweenDrawnPoints) ** 2.
143 let inline squaredDistance
x1 y1 x2 y2
= (x1 - x2
) ** 2. + (y1
- y2
) ** 2.
150 let mutable last_i, last_j
= Int32.MaxValue, Int32.MaxValue
152 let currentElements = List<Point> ()
154 let edgesData = edges
.Data
155 let xDirData = xGradient
.Data
156 let yDirData = yGradient
.Data
160 let ellipses = MatchingEllipses config.RBCRadius.Pixel
162 for window_i
in -windowSize + increment .. increment .. h - increment do
163 for window_j
in -windowSize + increment .. increment .. w - increment do
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
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)
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
))
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
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
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
209 currentElements.Clear ()