open MatchingEllipses
open Const
-type private SearchExtremum = Minimum | Maximum
-
-let private goldenSectionSearch (f: float -> float) (nbIter: int) (xmin: float) (xmax: float) (searchExtremum: SearchExtremum) : (float * float) =
- let gr = 1. / 1.6180339887498948482
- let mutable a = xmin
- let mutable b = xmax
- let mutable c = b - gr * (b - a)
- let mutable d = a + gr * (b - a)
-
- for i in 1 .. nbIter do
- let mutable fc = f c
- let mutable fd = f d
-
- if searchExtremum = Maximum
- then
- let tmp = fc
- fc <- fd
- fd <- tmp
-
- if fc < fd
- then
- b <- d
- d <- c
- c <- b - gr * (b - a)
- else
- a <- c
- c <- d
- d <- a + gr * (b - a)
-
- let x = (b + a) / 2.
- x, f x
-
-// Ellipse.A is always equal or greater than Ellipse.B.
-// Ellipse.Alpha is between 0 and Pi.
-let ellipse (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
- let accuracy_extremum_search_1 = 10 // 3
- let accuracy_extremum_search_2 = 10 // 4
-
- // p3 as the referencial.
- let p1x = p1x - p3x
- let p1y = p1y - p3y
-
- let p2x = p2x - p3x
- let p2y = p2y - p3y
-
- // Convert to polar coordinates.
- let alpha1 = atan m1
- let alpha2 = atan m2
-
- let r1 = sqrt (p1x ** 2. + p1y ** 2.)
- let theta1 = atan2 p1y p1x
-
- let r2 = sqrt (p2x ** 2. + p2y ** 2.)
- let theta2 = atan2 p2y p2x
-
- let valid =
- 4. * sin (alpha1 - theta1) * (-r1 * sin (alpha1 - theta1) + r2 * sin (alpha1 - theta2)) *
- sin (alpha2 - theta2) * (-r1 * sin (alpha2 - theta1) + r2 * sin (alpha2 - theta2)) +
- r1 * r2 * sin (alpha1 - alpha2) ** 2. * sin (theta1 - theta2) ** 2. < 0.
-
- if valid
- then
- let r theta =
- (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)) /
- (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.)
-
- let rabs = r >> abs
-
- // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
- let thetaTan, _ = goldenSectionSearch rabs accuracy_extremum_search_1 0. Math.PI Maximum
- let rTan = r thetaTan
-
- let PTanx = rTan * cos thetaTan
- let PTany = rTan * sin thetaTan
-
- let d1a = tan alpha1
- let d1b = -d1a * p1x + p1y
-
- let d2a = tan alpha2
- let d2b = -d2a * p2x + p2y
-
- let d3a = -1. / tan thetaTan
- let d3b = -d3a * PTanx + PTany
-
- let Ux = -(d1b - d2b) / (d1a - d2a)
- let Uy = -(d2a * d1b - d1a * d2b) / (d1a - d2a)
-
- let Vx = -(d1b - d3b) / (d1a - d3a)
- let Vy = -(d3a * d1b - d1a * d3b) / (d1a - d3a)
-
- let Wx = p1x + (p2x - p1x) / 2.
- let Wy = p1y + (p2y - p1y) / 2.
-
- let Zx = p1x + (PTanx - p1x) / 2.
- let Zy = p1y + (PTany - p1y) / 2.
-
- let va = -(-Vy + Zy) / (Vx - Zx)
- let vb = -(Zx * Vy - Vx * Zy) / (Vx - Zx)
-
- let ua = -(-Uy + Wy) / (Ux - Wx)
- let ub = -(Wx * Uy - Ux * Wy) / (Ux - Wx)
-
- let cx = -(vb - ub) / (va - ua)
- let cy = -(ua * vb - va * ub) / (va - ua)
-
- let rc = sqrt (cx ** 2. + cy ** 2.)
- let psi = atan2 cy cx
-
- let rellipse theta =
- sqrt (
- 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.) /
- (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. -
- (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)) /
- (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.))
-
- // We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
- let r1eTheta, r1e = goldenSectionSearch rellipse accuracy_extremum_search_2 0. (Math.PI / 2.) Maximum // Pi/2 and not pi because the period is Pi.
- let r2eTheta, r2e = goldenSectionSearch rellipse accuracy_extremum_search_2 0. (Math.PI / 2.) Minimum
-
- let rr1e = r r1eTheta
- let r1ex = rr1e * cos r1eTheta
- let r1ey = rr1e * sin r1eTheta
- let mutable alpha = atan ((r1ey - cy) / (r1ex - cx))
- if alpha < 0.
- then
- alpha <- alpha + Math.PI
-
- // Ride off the p3 referential.
- let cx = cx + p3x
- let cy = cy + p3y
-
- Some (Types.Ellipse(float32 cx, float32 cy, float32 r1e, float32 r2e, float32 alpha))
- else
- None
-
-let ellipse2 (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
- let p0 = pointFromTwoLines (Types.Line(float32 m1, float32 (p1y - m1 * p1x))) (Types.Line(float32 m2, float32(p2y - m2 * p2x)))
+// This is a ratio of the biggest radius.
+let minimumDistanceBetweenDrawnPoints = 0.6
+
+/// <summary>
+/// Try to build an ellipse from three points and two tangents passing by the first and the second point.
+/// 'Ellipse.A' is always equal or greater than Ellipse.B.
+/// 'Ellipse.Alpha' is between 0 and Pi.
+/// </summary>
+let ellipse (p1x : float) (p1y : float) (m1 : float) (p2x : float) (p2y : float) (m2 : float) (p3x : float) (p3y : float) : Types.Ellipse option =
+ let p0 = pointFromTwoLines (Types.Line (float32 m1, float32 (p1y - m1 * p1x))) (Types.Line (float32 m2, float32(p2y - m2 * p2x)))
let p0x, p0y = float p0.X, float p0.Y
- let s = matrix [[ 1.; 0.; 0. ]
- [ 0.; 0.; -0.5 ]
- [ 0.; -0.5; 0. ]]
+ let s =
+ matrix
+ [
+ [ 1.; 0.; 0. ]
+ [ 0.; 0.; -0.5 ]
+ [ 0.; -0.5; 0. ]
+ ]
let v0 = matrix [[ 1.; p0x; p0y ]]
let v1 = matrix [[ 1.; p1x; p1y ]]
let v2 = matrix [[ 1.; p2x; p2y ]]
let v3 = matrix [[ 1.; p3x; p3y ]]
- 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()
- let conicMat = p * s.Inverse() * p.Transpose()
+ 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 ()
+ let conicMat = p * s.Inverse () * p.Transpose ()
let a = conicMat.[0, 0]
let b = conicMat.[0, 1]
let c = conicMat.[1, 1]
let cy = d / a
let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
- if at = 0.
- then
+ if at = 0. then
None
else
let q = (-1. / at) * (matrix [[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
- let eigen = q.Evd()
+ let eigen = q.Evd ()
let eigenValues = eigen.EigenValues
let lambda = eigenValues.[1].Real
let mu = eigenValues.[0].Real
- if lambda <= 0. || mu <= 0.
- then
+ if lambda <= 0. || mu <= 0. then
None
else
let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu)
let phi' = if phi < 0. then phi + Math.PI else phi
let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
- Some (Types.Ellipse(float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
-
-
-let private vectorRotation (p1x: float32) (p1y: float32) (v1x: float32) (v1y: float32) (px: float32) (py: float32) : float32 =
- let mutable rotation = 1.f
- if p1y > py
- then
- if v1x > 0.f
- then
- rotation <- -1.f
- elif p1y < py
- then
- if v1x < 0.f
- then
- rotation <- -1.f
- elif p1x > px
- then
- if v1y < 0.f
- then
- rotation <- -1.f
- elif p1x < px
- then
- if v1y > 0.f
- then
- rotation <- -1.f
- rotation
-
-let private areVectorsValid (p1x: float32) (p1y: float32) (p2x: float32) (p2y: float32) (v1x: float32) (v1y: float32) (v2x: float32) (v2y: float32) : (float32 * float32) option =
+ Some (Types.Ellipse (float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
+
+let inline private vectorRotation (px : float32) (py : float32) (vx : float32) (vy : float32) (p0x : float32) (p0y : float32) : float32 =
+ if py > p0y then
+ if vx > 0.f then -1.f else 1.f
+ elif py < p0y then
+ if vx < 0.f then -1.f else 1.f
+ elif px > p0x then
+ if vy < 0.f then -1.f else 1.f
+ else // p1x < px
+ if vy > 0.f then -1.f else 1.f
+
+let private areVectorsValid (p1x : float32) (p1y : float32) (p2x : float32) (p2y : float32) (v1x : float32) (v1y : float32) (v2x : float32) (v2y : float32) : (float32 * float32) option =
let m1 = -v1x / v1y
let m2 = -v2x / v2y
let b1 = -m1 * p1x + p1y
let b2 = -m2 * p2x + p2y
- let px = -((b1 - b2) / (m1 - m2))
- let py = -((m2 * b1 - m1 * b2) / (m1 - m2))
+ let p0x = -(b1 - b2) / (m1 - m2)
+ let p0y = -(m2 * b1 - m1 * b2) / (m1 - m2)
- let rot1 = vectorRotation p1x p1y v1x v1y px py
- let rot2 = vectorRotation p2x p2y v2x v2y px py
+ let rot1 = vectorRotation p1x p1y v1x v1y p0x p0y
+ let rot2 = vectorRotation p2x p2y v2x v2y p0x p0y
- if rot1 = rot2
- then
+ if rot1 = rot2 then
None
else
- let alpha1 = atan2 (p1y - py) (p1x - px)
- let alpha2 = atan2 (p2y - py) (p2x - px)
+ let alpha1 =
+ let alpha1' = atan2 (p1y - p0y) (p1x - p0x)
+ if alpha1' < 0.f then 2.f * PI + alpha1' else alpha1'
- let alpha1' = if alpha1 < 0.f then 2.f * PI + alpha1 else alpha1
- let alpha2' = if alpha2 < 0.f then 2.f * PI + alpha2 else alpha2
+ let alpha2 =
+ let alpha2' = atan2 (p2y - p0y) (p2x - p0x)
+ if alpha2' < 0.f then 2.f * PI + alpha2' else alpha2'
- let diff = rot1 * alpha1' + rot2 * alpha2'
+ let diff = rot1 * alpha1 + rot2 * alpha2
- if diff > PI || (diff < 0.f && diff > -PI)
- then
- None
+ if diff > PI || (diff < 0.f && diff > -PI) then
+ Some (m1, m2)
else
- Some (m1, m2)
-
+ None
-let find (edges: Matrix<byte>)
- (xGradient: Image<Gray, float32>)
- (yGradient: Image<Gray, float32>)
- (config: Config) : MatchingEllipses =
+/// <summary>
+/// Build a set of ellipses as a 'MatchingEllipses' object by finding ellipses with the given edges and gradient.
+/// </summary>
+let find (edges : Matrix<byte>)
+ (xGradient : Matrix<float32>)
+ (yGradient : Matrix<float32>)
+ (config : Config) : MatchingEllipses =
let r1, r2 = config.RBCRadius.Min, config.RBCRadius.Max
let incrementWindowDivisor = 4.f
// We choose a window size for which the biggest ellipse can always be fitted in.
- let windowSize = roundInt (2.f * r2 / (incrementWindowDivisor - 1.f) * incrementWindowDivisor)
- let factorNbPick = config.Parameters.factorNbPick
+ let windowSize = roundInt (2.f * r2)
+ let factorNbValidPick = config.Parameters.factorNbValidPick
+ let factorNbMaxPick = config.Parameters.factorNbMaxPick
+ let nbPickElementsMin = config.Parameters.nbPickElementsMin
let increment = windowSize / (int incrementWindowDivisor)
let radiusTolerance = (r2 - r1) * 0.2f
- let squaredMinimumDistance = (float r2 / 1.5) ** 2.
+ let squaredMinimumDistance = (float config.RBCRadius.Pixel * minimumDistanceBetweenDrawnPoints) ** 2.
let inline squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2. + (y1 - y2) ** 2.
let h = edges.Height
let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
- let currentElements = List<Point>()
+ let currentElements = List<Point> ()
let edgesData = edges.Data
let xDirData = xGradient.Data
let yDirData = yGradient.Data
- let rng = Random(42)
+ let rng = Random 42
- let ellipses = MatchingEllipses(config.RBCRadius.Pixel)
+ let ellipses = MatchingEllipses config.RBCRadius.Pixel
for window_i in -windowSize + increment .. increment .. h - increment do
for window_j in -windowSize + increment .. increment .. w - increment do
let window_j_end = if window_j + windowSize - 1 >= w then w - 1 else window_j + windowSize - 1
// Remove old elements.
- let indexFirstElement = currentElements.FindIndex(fun p -> p.X >= window_j_begin)
- if indexFirstElement > 0
- then currentElements.RemoveRange(0, indexFirstElement)
+ let indexFirstElement = currentElements.FindIndex (fun p -> p.X >= window_j_begin)
+ if indexFirstElement > 0 then
+ currentElements.RemoveRange (0, indexFirstElement)
// Add the new elements.
let newElemsBegin_j = window_j + windowSize - increment
let newElemsEnd_j = window_j + windowSize - 1
- for j in (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) .. (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
- for i in window_i_begin .. window_i_end do
- if edgesData.[i, j] = 1uy
- then currentElements.Add(Point(j, i))
-
- if currentElements.Count >= 10
- then
- let mutable nbOfPicks = (float currentElements.Count) * factorNbPick |> int
- while nbOfPicks > 0 do
- let p1 = currentElements.[rng.Next(currentElements.Count)]
- let p2 = currentElements.[rng.Next(currentElements.Count)]
- let p3 = currentElements.[rng.Next(currentElements.Count)]
- if p1 <> p2 && p1 <> p3 && p2 <> p3
- then
+ for j = (if newElemsBegin_j < 0 then 0 else newElemsBegin_j) to (if newElemsEnd_j >= w then w - 1 else newElemsEnd_j) do
+ for i = window_i_begin to window_i_end do
+ if edgesData.[i, j] = 1uy then
+ currentElements.Add (Point (j, i))
+
+ if currentElements.Count >= nbPickElementsMin then
+ let mutable nbOfPicks = (float currentElements.Count) * factorNbMaxPick |> int
+ let mutable nbOfValidPicks = (float currentElements.Count) * factorNbValidPick |> int
+ while nbOfPicks > 0 && nbOfValidPicks > 0 do
+ let p1 = currentElements.[rng.Next currentElements.Count]
+ let p2 = currentElements.[rng.Next currentElements.Count]
+ let p3 = currentElements.[rng.Next currentElements.Count]
+ if p1 <> p2 && p1 <> p3 && p2 <> p3 then
nbOfPicks <- nbOfPicks - 1
let p1yf, p1xf = float p1.Y, float p1.X
let p2yf, p2xf = float p2.Y, float p2.X
squaredDistance p1xf p1yf p3xf p3yf >= squaredMinimumDistance &&
squaredDistance p2xf p2yf p3xf p3yf >= squaredMinimumDistance
then
- 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
+ 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
| Some (m1, m2) ->
- //let pouet = ellipse2 p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf
- match ellipse2 p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
- | Some e when e.Cx > 0.f && e.Cx < w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
+ match ellipse p1xf p1yf (float m1) p2xf p2yf (float m2) p3xf p3yf with
+ | Some e when e.Cx > 0.f && e.Cx < w_f - 1.f && e.Cy > 0.f && e.Cy < h_f - 1.f &&
e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance ->
- ellipses.Add e
+ nbOfValidPicks <- nbOfValidPicks - 1
+ ellipses.Add e
| _ -> ()
| _ -> ()
- currentElements.Clear()
+ currentElements.Clear ()
ellipses
projects / master-thesis.git / blobdiff