+ ((img.Convert<Gray, float32>() - (!min).[0]) / ((!max).[0] - (!min).[0]) * 255.0).Convert<Gray, byte>()
+
+
+let saveImg (img: Image<'TColor, 'TDepth>) (filepath: string) =
+ img.Save(filepath)
+
+
+let saveMat (mat: Matrix<'TDepth>) (filepath: string) =
+ use img = new Image<Gray, 'TDeph>(mat.Size)
+ mat.CopyTo(img)
+ saveImg img filepath
+
+
+type Histogram = { data: int[]; total: int; sum: int; min: float32; max: float32 }
+
+let histogramImg (img: Image<Gray, float32>) (nbSamples: int) : Histogram =
+ let imgData = img.Data
+
+ let min, max =
+ let min = ref [| 0.0 |]
+ let minLocation = ref <| [| Point() |]
+ let max = ref [| 0.0 |]
+ let maxLocation = ref <| [| Point() |]
+ img.MinMax(min, max, minLocation, maxLocation)
+ float32 (!min).[0], float32 (!max).[0]
+
+ let bin (x: float32) : int =
+ let p = int ((x - min) / (max - min) * float32 nbSamples)
+ if p >= nbSamples then nbSamples - 1 else p
+
+ let data = Array.zeroCreate nbSamples
+
+ for i in 0 .. img.Height - 1 do
+ for j in 0 .. img.Width - 1 do
+ let p = bin imgData.[i, j, 0]
+ data.[p] <- data.[p] + 1
+
+ { data = data; total = img.Height * img.Width; sum = Array.sum data; min = min; max = max }
+
+let histogramMat (mat: Matrix<float32>) (nbSamples: int) : Histogram =
+ let matData = mat.Data
+
+ let min, max =
+ let min = ref 0.0
+ let minLocation = ref <| Point()
+ let max = ref 0.0
+ let maxLocation = ref <| Point()
+ mat.MinMax(min, max, minLocation, maxLocation)
+ float32 !min, float32 !max
+
+ let bin (x: float32) : int =
+ let p = int ((x - min) / (max - min) * float32 nbSamples)
+ if p >= nbSamples then nbSamples - 1 else p
+
+ let data = Array.zeroCreate nbSamples
+
+ for i in 0 .. mat.Height - 1 do
+ for j in 0 .. mat.Width - 1 do
+ let p = bin matData.[i, j]
+ data.[p] <- data.[p] + 1
+
+ { data = data; total = mat.Height * mat.Width; sum = Array.sum data; min = min; max = max }
+
+let histogram (values: float32 seq) (nbSamples: int) : Histogram =
+ let mutable min = Single.MaxValue
+ let mutable max = Single.MinValue
+ let mutable n = 0
+
+ for v in values do
+ n <- n + 1
+ if v < min then min <- v
+ if v > max then max <- v
+
+ let bin (x: float32) : int =
+ let p = int ((x - min) / (max - min) * float32 nbSamples)
+ if p >= nbSamples then nbSamples - 1 else p
+
+ let data = Array.zeroCreate nbSamples
+
+ for v in values do
+ let p = bin v
+ data.[p] <- data.[p] + 1
+
+ { data = data; total = n; sum = Array.sum data; min = min; max = max }
+
+let otsu (hist: Histogram) : float32 * float32 * float32 =
+ let mutable sumB = 0
+ let mutable wB = 0
+ let mutable maximum = 0.0
+ let mutable level = 0
+ let sum = hist.data |> Array.mapi (fun i v -> i * v) |> Array.sum |> float
+
+ for i in 0 .. hist.data.Length - 1 do
+ wB <- wB + hist.data.[i]
+ if wB <> 0
+ then
+ let wF = hist.total - wB
+ if wF <> 0
+ then
+ sumB <- sumB + i * hist.data.[i]
+ let mB = (float sumB) / (float wB)
+ let mF = (sum - float sumB) / (float wF)
+ let between = (float wB) * (float wF) * (mB - mF) ** 2.;
+ if between >= maximum
+ then
+ level <- i
+ maximum <- between
+
+ let mean1 =
+ let mutable sum = 0
+ let mutable nb = 0
+ for i in 0 .. level - 1 do
+ sum <- sum + i * hist.data.[i]
+ nb <- nb + hist.data.[i]
+ (sum + level * hist.data.[level] / 2) / (nb + hist.data.[level] / 2)
+
+ let mean2 =
+ let mutable sum = 0
+ let mutable nb = 0
+ for i in level + 1 .. hist.data.Length - 1 do
+ sum <- sum + i * hist.data.[i]
+ nb <- nb + hist.data.[i]
+ (sum + level * hist.data.[level] / 2) / (nb + hist.data.[level] / 2)
+
+ let toFloat l =
+ float32 l / float32 hist.data.Length * (hist.max - hist.min) + hist.min
+
+ toFloat level, toFloat mean1, toFloat mean2
+
+
+let suppressMConnections (img: Matrix<byte>) =
+ let w = img.Width
+ let h = img.Height
+ for i in 1 .. h - 2 do
+ for j in 1 .. w - 2 do
+ if img.[i, j] > 0uy && img.Data.[i + 1, j] > 0uy && (img.Data.[i, j - 1] > 0uy && img.Data.[i - 1, j + 1] = 0uy || img.Data.[i, j + 1] > 0uy && img.Data.[i - 1, j - 1] = 0uy)
+ then
+ img.[i, j] <- 0uy
+ for i in 1 .. h - 2 do
+ for j in 1 .. w - 2 do
+ if img.[i, j] > 0uy && img.Data.[i - 1, j] > 0uy && (img.Data.[i, j - 1] > 0uy && img.Data.[i + 1, j + 1] = 0uy || img.Data.[i, j + 1] > 0uy && img.Data.[i + 1, j - 1] = 0uy)
+ then
+ img.[i, j] <- 0uy
+
+
+let findEdges (img: Image<Gray, float32>) : Matrix<byte> * Image<Gray, float32> * Image<Gray, float32> =
+ let w = img.Width
+ let h = img.Height
+
+ use sobelKernel =
+ new ConvolutionKernelF(array2D [[ 1.0f; 0.0f; -1.0f ]
+ [ 2.0f; 0.0f; -2.0f ]
+ [ 1.0f; 0.0f; -1.0f ]], Point(1, 1))
+
+ let xGradient = img.Convolution(sobelKernel)
+ let yGradient = img.Convolution(sobelKernel.Transpose())
+
+ let xGradientData = xGradient.Data
+ let yGradientData = yGradient.Data
+ for r in 0 .. h - 1 do
+ xGradientData.[r, 0, 0] <- 0.f
+ xGradientData.[r, w - 1, 0] <- 0.f
+ yGradientData.[r, 0, 0] <- 0.f
+ yGradientData.[r, w - 1, 0] <- 0.f
+
+ for c in 0 .. w - 1 do
+ xGradientData.[0, c, 0] <- 0.f
+ xGradientData.[h - 1, c, 0] <- 0.f
+ yGradientData.[0, c, 0] <- 0.f
+ yGradientData.[h - 1, c, 0] <- 0.f
+
+ use magnitudes = new Matrix<float32>(xGradient.Size)
+ use angles = new Matrix<float32>(xGradient.Size)
+ CvInvoke.CartToPolar(xGradient, yGradient, magnitudes, angles) // Compute the magnitudes (without angles).
+
+ let thresholdHigh, thresholdLow =
+ let sensibilityHigh = 0.1f
+ let sensibilityLow = 0.0f
+ use magnitudesByte = magnitudes.Convert<byte>()
+ let threshold, _, _ = otsu (histogramMat magnitudes 300)
+ threshold + (sensibilityHigh * threshold), threshold - (sensibilityLow * threshold)
+
+ // Non-maximum suppression.
+ use nms = new Matrix<byte>(xGradient.Size)
+
+ let nmsData = nms.Data
+ let anglesData = angles.Data
+ let magnitudesData = magnitudes.Data
+ let xGradientData = xGradient.Data
+ let yGradientData = yGradient.Data
+
+ let PI = float32 Math.PI
+
+ for i in 0 .. h - 1 do
+ nmsData.[i, 0] <- 0uy
+ nmsData.[i, w - 1] <- 0uy
+
+ for j in 0 .. w - 1 do
+ nmsData.[0, j] <- 0uy
+ nmsData.[h - 1, j] <- 0uy
+
+ for i in 1 .. h - 2 do
+ for j in 1 .. w - 2 do
+ let vx = xGradientData.[i, j, 0]
+ let vy = yGradientData.[i, j, 0]
+ if vx <> 0.f || vy <> 0.f
+ then
+ let angle = anglesData.[i, j]
+
+ let vx', vy' = abs vx, abs vy
+ let ratio2 = if vx' > vy' then vy' / vx' else vx' / vy'
+ let ratio1 = 1.f - ratio2
+
+ let mNeigbors (sign: int) : float32 =
+ if angle < PI / 4.f
+ then ratio1 * magnitudesData.[i, j + sign] + ratio2 * magnitudesData.[i + sign, j + sign]
+ elif angle < PI / 2.f
+ then ratio2 * magnitudesData.[i + sign, j + sign] + ratio1 * magnitudesData.[i + sign, j]
+ elif angle < 3.f * PI / 4.f
+ then ratio1 * magnitudesData.[i + sign, j] + ratio2 * magnitudesData.[i + sign, j - sign]
+ elif angle < PI
+ then ratio2 * magnitudesData.[i + sign, j - sign] + ratio1 * magnitudesData.[i, j - sign]
+ elif angle < 5.f * PI / 4.f
+ then ratio1 * magnitudesData.[i, j - sign] + ratio2 * magnitudesData.[i - sign, j - sign]
+ elif angle < 3.f * PI / 2.f
+ then ratio2 * magnitudesData.[i - sign, j - sign] + ratio1 * magnitudesData.[i - sign, j]
+ elif angle < 7.f * PI / 4.f
+ then ratio1 * magnitudesData.[i - sign, j] + ratio2 * magnitudesData.[i - sign, j + sign]
+ else ratio2 * magnitudesData.[i - sign, j + sign] + ratio1 * magnitudesData.[i, j + sign]
+
+ let m = magnitudesData.[i, j]
+ if m >= thresholdLow && m > mNeigbors 1 && m > mNeigbors -1
+ then
+ nmsData.[i, j] <- 1uy
+
+ // suppressMConnections nms // It's not helpful for the rest of the process (ellipse detection).
+
+ let edges = new Matrix<byte>(xGradient.Size)
+ let edgesData = edges.Data
+
+ // Hysteresis thresholding.
+ let toVisit = Stack<Point>()
+ for i in 0 .. h - 1 do
+ for j in 0 .. w - 1 do
+ if nmsData.[i, j] = 1uy && magnitudesData.[i, j] >= thresholdHigh
+ then
+ nmsData.[i, j] <- 0uy
+ toVisit.Push(Point(j, i))
+ while toVisit.Count > 0 do
+ let p = toVisit.Pop()
+ edgesData.[p.Y, p.X] <- 1uy
+ for i' in -1 .. 1 do
+ for j' in -1 .. 1 do
+ if i' <> 0 || j' <> 0
+ then
+ let ni = p.Y + i'
+ let nj = p.X + j'
+ if ni >= 0 && ni < h && nj >= 0 && nj < w && nmsData.[ni, nj] = 1uy
+ then
+ nmsData.[ni, nj] <- 0uy
+ toVisit.Push(Point(nj, ni))
+
+ edges, xGradient, yGradient