1 files changed, 173 insertions, 0 deletions
diff --git a/integralimg.go b/integralimg.go
new file mode 100644
index 0000000..5cfbaf3
--- /dev/null
+++ b/integralimg.go
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+// Copyright 2019 Nick White.
+// Use of this source code is governed by the GPLv3
+// license that can be found in the LICENSE file.
+
+package integralimg
+
+import (
+	"image"
+	"math"
+)
+
+// I is the Integral Image
+type I [][]uint64
+
+// Sq contains an Integral Image and its Square
+type WithSq struct {
+	Img I
+	Sq I
+}
+
+// Window is a part of an Integral Image
+type Window struct {
+	topleft uint64
+	topright uint64
+	bottomleft uint64
+	bottomright uint64
+	width int
+	height int
+}
+
+// ToIntegralImg creates an integral image
+func ToIntegralImg(img *image.Gray) I {
+	var integral I
+	var oldy, oldx, oldxy uint64
+	b := img.Bounds()
+	for y := b.Min.Y; y < b.Max.Y; y++ {
+		newrow := []uint64{}
+		for x := b.Min.X; x < b.Max.X; x++ {
+			oldx, oldy, oldxy = 0, 0, 0
+			if x > 0 {
+				oldx = newrow[x-1]
+			}
+			if y > 0 {
+				oldy = integral[y-1][x]
+			}
+			if x > 0 && y > 0 {
+				oldxy = integral[y-1][x-1]
+			}
+			pixel := uint64(img.GrayAt(x, y).Y)
+			i := pixel + oldx + oldy - oldxy
+			newrow = append(newrow, i)
+		}
+		integral = append(integral, newrow)
+	}
+	return integral
+}
+
+// ToSqIntegralImg creates an integral image of the square of all
+// pixel values
+func ToSqIntegralImg(img *image.Gray) I {
+	var integral I
+	var oldy, oldx, oldxy uint64
+	b := img.Bounds()
+	for y := b.Min.Y; y < b.Max.Y; y++ {
+		newrow := []uint64{}
+		for x := b.Min.X; x < b.Max.X; x++ {
+			oldx, oldy, oldxy = 0, 0, 0
+			if x > 0 {
+				oldx = newrow[x-1]
+			}
+			if y > 0 {
+				oldy = integral[y-1][x]
+			}
+			if x > 0 && y > 0 {
+				oldxy = integral[y-1][x-1]
+			}
+			pixel := uint64(img.GrayAt(x, y).Y)
+			i := pixel * pixel + oldx + oldy - oldxy
+			newrow = append(newrow, i)
+		}
+		integral = append(integral, newrow)
+	}
+	return integral
+}
+
+// ToAllIntegralImg creates a WithSq containing a regular and
+// squared Integral Image
+func ToAllIntegralImg(img *image.Gray) WithSq {
+	var s WithSq
+	s.Img = ToIntegralImg(img)
+	s.Sq = ToSqIntegralImg(img)
+	return s
+}
+
+
+// GetWindow gets the values of the corners of a square part of an
+// Integral Image, plus the dimensions of the part, which can
+// be used to quickly calculate the mean of the area
+func (i I) GetWindow(x, y, size int) Window {
+	step := size / 2
+
+	minx, miny := 0, 0
+	maxy := len(i)-1
+	maxx := len(i[0])-1
+
+	if y > (step+1) {
+		miny = y - step - 1
+	}
+	if x > (step+1) {
+		minx = x - step - 1
+	}
+
+	if maxy > (y + step) {
+		maxy = y + step
+	}
+	if maxx > (x + step) {
+		maxx = x + step
+	}
+
+	return Window { i[miny][minx], i[miny][maxx], i[maxy][minx], i[maxy][maxx], maxx-minx, maxy-miny}
+}
+
+// GetVerticalWindow gets the values of the corners of a vertical
+// slice of an Integral Image, starting at x
+func (i I) GetVerticalWindow(x, width int) Window {
+	maxy := len(i) - 1
+	maxx := x + width
+	if maxx > len(i[0])-1 {
+		maxx = len(i[0]) - 1
+	}
+
+	return Window { i[0][x], i[0][maxx], i[maxy][x], i[maxy][maxx], width, maxy }
+}
+
+// Sum returns the sum of all pixels in a Window
+func (w Window) Sum() uint64 {
+	return w.bottomright + w.topleft - w.topright - w.bottomleft
+}
+
+// Size returns the total size of a Window
+func (w Window) Size() int {
+	return w.width * w.height
+}
+
+// Mean returns the average value of pixels in a Window
+func (w Window) Mean() float64 {
+	return float64(w.Sum()) / float64(w.Size())
+}
+
+// Proportion returns the proportion of pixels which are on
+func (w Window) Proportion() float64 {
+	area := w.width * w.height
+	// divide by 255 as each on pixel has the value of 255
+	sum := float64(w.Sum()) / 255
+	return float64(area) / sum - 1
+}
+
+// MeanWindow calculates the mean value of a section of an Integral
+// Image
+func (i I) MeanWindow(x, y, size int) float64 {
+	return i.GetWindow(x, y, size).Mean()
+}
+
+// MeanStdDevWindow calculates the mean and standard deviation of
+// a section on an Integral Image
+func (i WithSq) MeanStdDevWindow(x, y, size int) (float64, float64) {
+	imean := i.Img.GetWindow(x, y, size).Mean()
+	smean := i.Sq.GetWindow(x, y, size).Mean()
+
+	variance := smean - (imean * imean)
+
+	return imean, math.Sqrt(variance)
+}