module Ellipse open System open System.Collections.Generic open System.Drawing 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 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(r1) 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) -> 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 | _ -> () | _ -> () currentElements.Clear() ellipses