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// Copyright 2020 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.
//
// A lot of image processing operations rely on many calculations
// of the sum or mean of a set of pixels. As these have been
// precalculated for an integral Image, these calculations are
// much faster. Image.Sum() and Image.Mean() functions are provided
// by this package to take advantage of this.
//
// Another common requirement is standard deviation over an area
// of an image. This can be calculated by creating an integral
// Image and squared integral Image (SqImage) for a base image, and
// passing them to the MeanStdDev() function provided.
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.Rect(0, 0, 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
}
func lowest(a, b int) int {
if a < b {
return a
}
return b
}
func highest(a, b int) int {
if a > b {
return a
}
return b
}
func (i Image) topLeft(r image.Rectangle) uint64 {
b := i.Bounds()
x := r.Min.X - 1
y := r.Min.Y - 1
x = lowest(x, b.Max.X-1)
y = lowest(y, b.Max.Y-1)
if x < 0 || y < 0 {
return 0
}
return i[y][x]
}
func (i Image) topRight(r image.Rectangle) uint64 {
b := i.Bounds()
x := lowest(r.Max.X-1, b.Max.X-1)
y := r.Min.Y - 1
y = lowest(y, b.Max.Y-1)
if x < 0 || y < 0 {
return 0
}
return i[y][x]
}
func (i Image) bottomLeft(r image.Rectangle) uint64 {
b := i.Bounds()
x := r.Min.X - 1
x = lowest(x, b.Max.X-1)
y := lowest(r.Max.Y-1, b.Max.Y-1)
if x < 0 || y < 0 {
return 0
}
return i[y][x]
}
func (i Image) bottomRight(r image.Rectangle) uint64 {
b := i.Bounds()
x := lowest(r.Max.X-1, b.Max.X-1)
y := lowest(r.Max.Y-1, b.Max.Y-1)
return i[y][x]
}
// Sum returns the sum of all pixels in a section of an image
func (i Image) Sum(r image.Rectangle) uint64 {
return i.bottomRight(r) + i.topLeft(r) - i.topRight(r) - i.bottomLeft(r)
}
// Mean returns the average value of pixels in a section of an image
func (i Image) Mean(r image.Rectangle) float64 {
in := r.Intersect(i.Bounds())
return float64(i.Sum(r)) / float64(in.Dx()*in.Dy())
}
// Sum returns the sum of all pixels in a section of an image
func (i SqImage) Sum(r image.Rectangle) uint64 {
return Image(i).Sum(r)
}
// Mean returns the average value of pixels in a section of an image
func (i SqImage) Mean(r image.Rectangle) float64 {
return Image(i).Mean(r)
}
// MeanStdDev calculates the mean and standard deviation of a
// section of an image, using the corresponding regular and square
// integral images.
func MeanStdDev(i Image, sq SqImage, r image.Rectangle) (float64, float64) {
imean := i.Mean(r)
smean := sq.Mean(r)
variance := smean - (imean * imean)
return imean, math.Sqrt(variance)
}
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