--- /dev/null
+module Ellipse
+
+open System
+open System.Collections.Generic
+
+open Emgu.CV
+open Emgu.CV.Structure
+
+open Utils
+open MatchingEllipses
+
+
+type private SearchExtremum = Minimum | Maximum
+
+let private goldenSectionSearch (f: float -> float) (nbIter: int) (xmin: float) (xmax: float) (searchExtremum: SearchExtremum) : (float * float) =
+ let gr = 1.0 / 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) / 2.0
+ x, f x
+
+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 = 4;
+ let accuracy_extremum_search_2 = 3;
+
+ // 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**2.0 + p1y**2.0)
+ let theta1 = atan2 p1y p1x
+
+ let r2 = sqrt (p2x**2.0 + p2y**2.0)
+ let theta2 = atan2 p2y p2x
+
+ let valid =
+ 4.0 * 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) **2.0 * sin (theta1 - theta2) **2.0 < 0.0
+
+ 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))**2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2)**2.0)
+
+ 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 0.0 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 = -1.0 / 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) / 2.0
+ let Wy = p1y + (p2y - p1y) / 2.0
+
+ let Zx = p1x + (PTanx - p1x) / 2.0
+ let Zy = p1y + (PTany - p1y) / 2.0
+
+ 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**2.0 + cy**2.0)
+ let psi = atan2 cy cx
+
+ let rellipse theta =
+ sqrt (
+ rc**2.0 + (r1**2.0 * r2**2.0 * (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))**2.0 * sin (theta1 - theta2)**2.0) /
+ (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2))**2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2)**2.0)**2.0 -
+ (2.0 * 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))**2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2)**2.0))
+
+ // 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 0.0 (Math.PI / 2.0) Maximum // Pi/2 and not pi because the period is Pi.
+ let r2eTheta, r2e = goldenSectionSearch rellipse accuracy_extremum_search_2 0.0 (Math.PI / 2.0) 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 < 0.0
+ then
+ alpha <- alpha + Math.PI
+
+ // Ride off the p3 referential.
+ let cx = cx + p3x
+ let cy = cy + p3y
+
+ Some { cx = cx; cy = cy; a = r1e; b = r2e; alpha = alpha }
+ else
+ None
+
+
+let private vectorRotation (p1x: float) (p1y: float) (v1x: float) (v1y: float) (px: float) (py: float) : float =
+ let mutable rotation = 1.0
+ if p1y > py
+ then
+ if v1x > 0.0
+ then
+ rotation <- -1.0
+ elif p1y < py
+ then
+ if v1x < 0.0
+ then
+ rotation <- -1.0
+ elif p1x > px
+ then
+ if v1y < 0.0
+ then
+ rotation <- -1.0
+ elif p1x < px
+ then
+ if v1y > 0.0
+ then
+ rotation <- -1.0
+ rotation
+
+
+let private areVectorsValid (p1x: float) (p1y: float) (p2x: float) (p2y: float) (v1x: float) (v1y: float) (v2x: float) (v2y: float) : (float * float) 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 || rot1 * atan2 (p1y - py) (p1x - px) + rot2 * atan2 (p2y - py) (p2x - px) <= 0.0
+ then
+ None
+ else
+ Some (m1, m2)
+
+
+let find (edges: Matrix<byte>)
+ (xDir: Image<Gray, float>)
+ (yDir: Image<Gray, float>)
+ (radiusRange: float * float)
+ (windowSize: int)
+ (factorNbPick: float) : Types.Ellipse list =
+
+ let increment = windowSize / 4;
+
+ let r1, r2 = radiusRange
+ let radiusTolerance = (r2 - r1) * 0.2
+
+ let minimumDistance = (r2 / 1.5) ** 2.0;
+ let squaredDistance x1 y1 x2 y2 = (x1 - x2) ** 2.0 + (y1 - y2) ** 2.0;
+
+ let h = edges.Height
+ let w = edges.Width
+
+ let mutable last_i, last_j = Int32.MaxValue, Int32.MaxValue
+
+ let currentElements = List<(int * int)>()
+
+ let edgesData = edges.Data
+ let xDirData = xDir.Data
+ let yDirData = yDir.Data
+
+ let rng = Random()
+
+ let ellipses = MatchingEllipses ()
+
+ 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 (_, pj) -> pj >= window_j)
+ if indexFirstElement > 0
+ then currentElements.RemoveRange(0, indexFirstElement)
+
+ // Add the new elements.
+ for j in window_j + windowSize - increment .. window_j + windowSize - 1 do
+ for i in window_i_begin .. window_i_end do
+ if j >= 0 && j < w && edgesData.[i, j] = 1uy
+ then currentElements.Add((i, j))
+
+ if currentElements.Count >= 10
+ then
+ let mutable nbOfPicks = (float currentElements.Count) * factorNbPick |> int
+ while nbOfPicks > 0 do
+ let (p1y, p1x) as p1 = currentElements.[rng.Next(currentElements.Count)]
+ let (p2y, p2x) as p2 = currentElements.[rng.Next(currentElements.Count)]
+ let (p3y, p3x) as p3 = currentElements.[rng.Next(currentElements.Count)]
+ if p1 <> p2 && p1 <> p3 && p2 <> p3
+ then
+ nbOfPicks <- nbOfPicks - 1
+ let p1yf, p1xf = float p1y, float p1x
+ let p2yf, p2xf = float p2y, float p2x
+ let p3yf, p3xf = float p3y, float p3x
+ if squaredDistance p1xf p1yf p2xf p2yf >= minimumDistance &&
+ squaredDistance p1xf p1yf p3xf p3yf >= minimumDistance &&
+ squaredDistance p2xf p2yf p3xf p3yf >= minimumDistance
+ then
+ match areVectorsValid p1xf p1yf p2xf p2yf -xDirData.[p1y, p1x, 0] -yDirData.[p1y, p1x, 0] -xDirData.[p2y, p2x, 0] -yDirData.[p2y, p2x, 0] with
+ | Some (m1, m2) ->
+ match ellipse p1xf p1yf m1 p2xf p2yf m2 p3xf p3yf with
+ | Some e when e.cx > 0.0 && e.cx < (float w) - 1.0 && e.cy > 0.0 && e.cy < (float h) - 1.0 &&
+ e.a >= r1 - radiusTolerance && e.a <= r2 + radiusTolerance && e.b >= r1 - radiusTolerance && e.b <= r2 + radiusTolerance ->
+ ellipses.Add e
+ | _ -> ()
+ | _ -> ()
+
+ currentElements.Clear()
+
+ ellipses.Ellipses
+
projects / master-thesis.git / blobdiff