if fc < fd
then
- b <- d;
- d <- c;
- c <- b - gr * (b - a);
+ b <- d
+ d <- c
+ c <- b - gr * (b - a)
else
- a <- c;
- c <- d;
- d <- a + gr * (b - a);
+ a <- c
+ c <- d
+ d <- a + gr * (b - a)
let x = (b + a) / 2.0
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 = 4;
- let accuracy_extremum_search_2 = 3;
+ let accuracy_extremum_search_1 = 4
+ let accuracy_extremum_search_2 = 3
// p3 as the referencial.
let p1x = p1x - p3x
let alpha1 = atan m1
let alpha2 = atan m2
- let r1 = sqrt (p1x**2.0 + p1y**2.0)
+ let r1 = sqrt (p1x ** 2.0 + p1y ** 2.0)
let theta1 = atan2 p1y p1x
let r2 = sqrt (p2x**2.0 + p2y**2.0)
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
+ 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)
+ (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
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 -
+ 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))
+ (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 cx = cx + p3x
let cy = cy + p3y
- Some { cx = cx; cy = cy; a = r1e; b = r2e; alpha = alpha }
+ Some (Types.Ellipse(cx, cy, r1e, r2e, alpha))
else
None
else
Some (m1, m2)
-
let find (edges: Matrix<byte>)
(xDir: Image<Gray, float>)
(yDir: Image<Gray, float>)
(windowSize: int)
(factorNbPick: float) : Types.Ellipse list =
- let increment = windowSize / 4;
+ 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 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 xDirData = xDir.Data
let yDirData = yDir.Data
- let rng = Random()
+ let rng = Random(42)
- let ellipses = MatchingEllipses ()
+ let ellipses = MatchingEllipses(r1)
for window_i in -windowSize + increment .. increment .. h - increment do
for window_j in -windowSize + increment .. increment .. w - increment do
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 ->
+ | 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
| _ -> ()
| _ -> ()