X-Git-Url: http://git.euphorik.ch/?a=blobdiff_plain;f=Parasitemia%2FParasitemiaCore%2FEllipse.fs;fp=Parasitemia%2FParasitemiaCore%2FEllipse.fs;h=520d29d83a9e2d005963a4a9874deef924d099b6;hb=4bfa3cbdc6145e6944f02e24829ab2ef3a851ac1;hp=0000000000000000000000000000000000000000;hpb=48ecdfc43001c444eff6ad442986049384674af2;p=master-thesis.git diff --git a/Parasitemia/ParasitemiaCore/Ellipse.fs b/Parasitemia/ParasitemiaCore/Ellipse.fs new file mode 100644 index 0000000..520d29d --- /dev/null +++ b/Parasitemia/ParasitemiaCore/Ellipse.fs @@ -0,0 +1,350 @@ +module ParasitemiaCore.Ellipse + +open System +open System.Collections.Generic +open System.Drawing + +open MathNet.Numerics.LinearAlgebra + +open Emgu.CV +open Emgu.CV.Structure + +open Utils +open Config +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))) + let p0x, p0y = float p0.X, float p0.Y + + 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 a = conicMat.[0, 0] + let b = conicMat.[0, 1] + let c = conicMat.[1, 1] + let d = conicMat.[0, 2] + let e = conicMat.[1, 2] + let f = conicMat.[2, 2] + + // Center. + let cx = b / a + let cy = d / a + + let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy + 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 eigenValues = eigen.EigenValues + let lambda = eigenValues.[1].Real + let mu = eigenValues.[0].Real + + if lambda <= 0. || mu <= 0. + then + None + else + let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu) + + let eigenVectors = eigen.EigenVectors + let v_a = eigenVectors.[0, 0] + let v_b = eigenVectors.[1, 0] // [0, 1] + + // Angle against the longest axis. + let phi = (if r2 > r1 then atan (v_b / v_a) else atan (v_a / v_b)) + + 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 = + 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 rot1 = vectorRotation p1x p1y v1x v1y px py + let rot2 = vectorRotation p2x p2y v2x v2y px py + + if rot1 = rot2 + then + None + else + let alpha1 = atan2 (p1y - py) (p1x - px) + let alpha2 = atan2 (p2y - py) (p2x - px) + + 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 diff = rot1 * alpha1' + rot2 * alpha2' + + if diff > PI || (diff < 0.f && diff > -PI) + then + None + else + Some (m1, m2) + + +let find (edges: Matrix) + (xGradient: Image) + (yGradient: Image) + (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 increment = windowSize / (int incrementWindowDivisor) + + let radiusTolerance = (r2 - r1) * 0.2f + + let squaredMinimumDistance = (float r2 / 1.5) ** 2. + let inline squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2. + (y1 - y2) ** 2. + + let h = edges.Height + let w = edges.Width + let h_f = float32 h + let w_f = float32 w + + let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue + + let currentElements = List() + + let edgesData = edges.Data + let xDirData = xGradient.Data + let yDirData = yGradient.Data + + let rng = Random(42) + + 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_i_begin = if window_i < 0 then 0 else window_i + let window_i_end = if window_i + windowSize - 1 >= h then h - 1 else window_i + windowSize - 1 + let window_j_begin = if window_j < 0 then 0 else window_j + 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) + + // 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 + nbOfPicks <- nbOfPicks - 1 + let p1yf, p1xf = float p1.Y, float p1.X + let p2yf, p2xf = float p2.Y, float p2.X + let p3yf, p3xf = float p3.Y, float p3.X + if squaredDistance p1xf p1yf p2xf p2yf >= squaredMinimumDistance && + 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 + | 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 && + e.A >= r1 - radiusTolerance && e.A <= r2 + radiusTolerance && e.B >= r1 - radiusTolerance && e.B <= r2 + radiusTolerance -> + ellipses.Add e + | _ -> () + | _ -> () + + currentElements.Clear() + + ellipses +