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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.
// integralimg is a package for processing integral images, aka
// summed area tables. These are structures which precompute the
// sum of pixels to the left and above each pixel, which can make
// several common image processing operations much faster.
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 }
}
// GetHorizontalWindow gets the values of the corners of a horizontal
// slice of an Integral Image, starting at y
func (i I) GetHorizontalWindow(y, height int) Window {
maxy := y + height
maxx := len(i[0]) - 1
if maxy > len(i) - 1 {
maxy = len(i) - 1
}
return Window { i[y][0], i[y][maxx], i[maxy][0], i[maxy][maxx], maxx, height }
}
// 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)
}
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