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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"
"image/color"
"math"
)
// Image is an integral Image
type Image [][]uint64
// SqImage is a Square integral Image.
// A squared integral image is an integral image for which the square of
// each pixel is saved; this is useful for efficiently calculating
// Standard Deviation.
type SqImage [][]uint64
func (i Image) ColorModel() color.Model { return color.Gray16Model }
func (i Image) Bounds() image.Rectangle {
return image.Rectangle {image.Point{0, 0}, image.Point{len(i[0]), len(i)}}
}
// at64 is used to return the raw uint64 for a given pixel. Accessing
// this separately to a (potentially lossy) conversion to a Gray16 is
// necessary for SqImage to function accurately.
func (i Image) at64(x, y int) uint64 {
if !(image.Point{x, y}.In(i.Bounds())) {
return 0
}
var prevx, prevy, prevxy uint64
prevx, prevy, prevxy = 0, 0, 0
if x > 0 {
prevx = i[y][x-1]
}
if y > 0 {
prevy = i[y-1][x]
}
if x > 0 && y > 0 {
prevxy = i[y-1][x-1]
}
orig := i[y][x] + prevxy - prevx - prevy
return orig
}
func (i Image) At(x, y int) color.Color {
c := i.at64(x, y)
return color.Gray16{uint16(c)}
}
func (i Image) set64(x, y int, c uint64) {
var prevx, prevy, prevxy uint64
prevx, prevy, prevxy = 0, 0, 0
if x > 0 {
prevx = i[y][x-1]
}
if y > 0 {
prevy = i[y-1][x]
}
if x > 0 && y > 0 {
prevxy = i[y-1][x-1]
}
final := c + prevx + prevy - prevxy
i[y][x] = final
}
func (i Image) Set(x, y int, c color.Color) {
gray := color.Gray16Model.Convert(c).(color.Gray16).Y
i.set64(x, y, uint64(gray))
}
// NewImage returns a new integral Image with the given bounds.
func NewImage(r image.Rectangle) *Image {
w, h := r.Dx(), r.Dy()
var rows Image
for i := 0; i < h; i++ {
col := make([]uint64, w)
rows = append(rows, col)
}
return &rows
}
func (i SqImage) ColorModel() color.Model { return Image(i).ColorModel() }
func (i SqImage) Bounds() image.Rectangle {
return Image(i).Bounds()
}
func (i SqImage) At(x, y int) color.Color {
c := Image(i).at64(x, y)
rt := math.Sqrt(float64(c))
return color.Gray16{uint16(rt)}
}
func (i SqImage) Set(x, y int, c color.Color) {
gray := uint64(color.Gray16Model.Convert(c).(color.Gray16).Y)
Image(i).set64(x, y, gray * gray)
}
// NewSqImage returns a new squared integral Image with the given bounds.
func NewSqImage(r image.Rectangle) *SqImage {
i := NewImage(r)
s := SqImage(*i)
return &s
}
// Window is a section of an Integral Image
type Window struct {
topleft uint64
topright uint64
bottomleft uint64
bottomright uint64
width int
height int
}
// 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 Image) 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}
}
func (i SqImage) GetWindow(x, y, size int) Window {
return Image(i).GetWindow(x, y, size)
}
// GetVerticalWindow gets the values of the corners of a vertical
// slice of an Integral Image, starting at x
func (i Image) 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 }
}
func (i SqImage) GetVerticalWindow(x, width int) Window {
return Image(i).GetVerticalWindow(x, width)
}
// 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
}
// MeanStdDevWindow calculates the mean and standard deviation of
// a section on an Integral Image, using the corresponding Square
// Integral Image.
func MeanStdDevWindow(i Image, sq SqImage, x, y, size int) (float64, float64) {
imean := i.GetWindow(x, y, size).Mean()
smean := sq.GetWindow(x, y, size).Mean()
variance := smean - (imean * imean)
return imean, math.Sqrt(variance)
}
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