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dithering.rkt
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dithering.rkt
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#lang racket
(require racket/draw)
(provide bitmap->burkes)
(provide bitmap->floyd-steinberg)
; Fred Martin, [email protected]
; Nov 18 2017
; exported functions are:
; bitmap->floyd-steinberg
; bitmap->burkes
;
; each accepts an alpha-red-green-blue "argb" bitmap
; and returns a dithered bitmap also in argb format,
; but with each pixel either pure white or pure black.
; these exprs are demo/test code (e.g. type them into REPL):
;
; (require net/url)
; (define flowers
; (read-bitmap
; (get-pure-port
; (string->url "https://www.almanac.com/sites/default/files/birth_month_flowers-primary-1920x1280px_pixabay.jpg"))
; #:backing-scale 3.))
; flowers
; (bitmap->floyd-steinberg flowers)
; (bitmap->burkes flowers)
; accepts a bitmap, outputs vector of grayscale values in range 0. to 1.
; adds an extra row + 1 so the floyd-steinberg can complete.
; adds another one for burkes
(define (bitmap->grayscale-vector bm)
(define (gray pixels pos)
(/ (+ (* 0.2126 (bytes-ref pixels (+ pos 1)))
(* 0.7152 (bytes-ref pixels (+ pos 2)))
(* 0.0722 (bytes-ref pixels (+ pos 3))))
255.))
(let* ((width (send bm get-width))
(height (send bm get-height))
(pixels (make-bytes (* 4 width height)))
(grays (make-vector (+ (* width (add1 height)) 2) 0.)))
(begin
(send bm get-argb-pixels 0 0 (sub1 width) (sub1 height) pixels)
(for ((y (in-range 0 height)))
(for ((x (in-range 0 width)))
(vector-set! grays (+ x (* y width))
(gray pixels (+ (* x 4) (* y width 4))))))
grays)))
; this version outputs nums from 0 to 255 instead of floats.
(define (bitmap->grayscale-vector-int bm)
(define (gray pixels pos)
(inexact->exact
(round (+ (* 0.2126 (bytes-ref pixels (+ pos 1)))
(* 0.7152 (bytes-ref pixels (+ pos 2)))
(* 0.0722 (bytes-ref pixels (+ pos 3)))))))
(let* ((width (send bm get-width))
(height (send bm get-height))
(pixels (make-bytes (* 4 width height)))
(grays (make-vector (+ (* width (add1 height)) 2) 0)))
(begin
(send bm get-argb-pixels 0 0 (sub1 width) (sub1 height) pixels)
(for ((y (in-range 0 height)))
(for ((x (in-range 0 width)))
(vector-set! grays (+ x (* y width))
(gray pixels (+ (* x 4) (* y width 4))))))
grays)))
; Floyd-Steinberg pseudocode from Wikipedia
; https://en.wikipedia.org/wiki/Floyd%E2%80%93Steinberg_dithering
;
; for each y from top to bottom
; for each x from left to right
; oldpixel := pixel[x][y]
; newpixel := find_closest_palette_color(oldpixel)
; pixel[x][y] := newpixel
; quant_error := oldpixel - newpixel
; pixel[x + 1][y ] := pixel[x + 1][y ] + quant_error * 7 / 16
; pixel[x - 1][y + 1] := pixel[x - 1][y + 1] + quant_error * 3 / 16
; pixel[x ][y + 1] := pixel[x ][y + 1] + quant_error * 5 / 16
; pixel[x + 1][y + 1] := pixel[x + 1][y + 1] + quant_error * 1 / 16
; mutates vector v based on floyd-steinberg algorithm
; assumes v has values from 0. to 1.
(define (floyd-steinberg v width height)
(for ((y (in-range 0 height)))
(for ((x (in-range 0 width)))
(let* ((oldpx (vector-ref v (+ (* y width) x)))
(newpx (if (> oldpx 0.5) 1. 0.))
(error (- oldpx newpx)))
(begin
(vector-set! v (+ (* y width) x) newpx)
(vector-set! v (+ (add1 x) (* y width))
(+ (/ (* 7 error) 16) (vector-ref v (+ (add1 x) (* y width)))))
(vector-set! v (+ (sub1 x) (* (add1 y) width))
(+ (/ (* 3 error) 16) (vector-ref v (+ (sub1 x) (* (add1 y) width)))))
(vector-set! v (+ x (* (add1 y) width))
(+ (/ (* 5 error) 16) (vector-ref v (+ x (* (add1 y) width)))))
(vector-set! v (+ (add1 x) (* (add1 y) width))
(+ (/ error 16) (vector-ref v (+ (add1 x) (* (add1 y) width))))))))))
; Burkes dithering, as described at
; http://www.tannerhelland.com/4660/dithering-eleven-algorithms-source-code/
;
; X 8 4
; 2 4 8 4 2
;
; (1/32)
; this version operates on the floating point [0., 1.] grayscale vector
(define (burkes v width height)
(for ((y (in-range 0 height)))
(for ((x (in-range 0 width)))
(let* ((oldpx (vector-ref v (+ (* y width) x)))
(newpx (if (> oldpx 0.5) 1. 0.))
(error (- oldpx newpx)))
(begin
(vector-set! v (+ (* y width) x) newpx)
(vector-set! v (+ (+ x 1) (* y width))
(+ (/ (* 8 error) 32) (vector-ref v (+ (+ x 1) (* y width)))))
(vector-set! v (+ (+ x 2) (* y width))
(+ (/ (* 4 error) 32) (vector-ref v (+ (+ x 2) (* y width)))))
(vector-set! v (+ (- x 2) (* (add1 y) width))
(+ (/ (* 2 error) 32) (vector-ref v (+ (- x 2) (* (add1 y) width)))))
(vector-set! v (+ (- x 1) (* (add1 y) width))
(+ (/ (* 4 error) 32) (vector-ref v (+ (- x 1) (* (add1 y) width)))))
(vector-set! v (+ x (* (add1 y) width))
(+ (/ (* 8 error) 32) (vector-ref v (+ x (* (add1 y) width)))))
(vector-set! v (+ (+ x 1) (* (add1 y) width))
(+ (/ (* 4 error) 32) (vector-ref v (+ (+ x 1) (* (add1 y) width)))))
(vector-set! v (+ (+ x 2) (* (add1 y) width))
(+ (/ (* 2 error) 32) (vector-ref v (+ (+ x 2) (* (add1 y) width))))))))))
; this version operates on the integer bitmap vector [0, 255]
(define (burkes-int v width height)
(for ((y (in-range 0 height)))
(for ((x (in-range 0 width)))
(let* ((oldpx (vector-ref v (+ (* y width) x)))
(newpx (if (> oldpx 127) 255 0))
(error (- oldpx newpx)))
(begin
(vector-set! v (+ (* y width) x) newpx)
(vector-set! v (+ (+ x 1) (* y width))
(+ (arithmetic-shift (arithmetic-shift error 3) -5)
(vector-ref v (+ (+ x 1) (* y width)))))
(vector-set! v (+ (+ x 2) (* y width))
(+ (arithmetic-shift (arithmetic-shift error 2) -5)
(vector-ref v (+ (+ x 2) (* y width)))))
(vector-set! v (+ (- x 2) (* (add1 y) width))
(+ (arithmetic-shift (arithmetic-shift error 1) -5)
(vector-ref v (+ (- x 2) (* (add1 y) width)))))
(vector-set! v (+ (- x 1) (* (add1 y) width))
(+ (arithmetic-shift (arithmetic-shift error 2) -5)
(vector-ref v (+ (- x 1) (* (add1 y) width)))))
(vector-set! v (+ x (* (add1 y) width))
(+ (arithmetic-shift (arithmetic-shift error 3) -5)
(vector-ref v (+ x (* (add1 y) width)))))
(vector-set! v (+ (+ x 1) (* (add1 y) width))
(+ (arithmetic-shift (arithmetic-shift error 2) -5)
(vector-ref v (+ (+ x 1) (* (add1 y) width)))))
(vector-set! v (+ (+ x 2) (* (add1 y) width))
(+ (arithmetic-shift (arithmetic-shift error 1) -5)
(vector-ref v (+ (+ x 2) (* (add1 y) width))))))))))
; convert the grayscale vector back to a bitmap
; works for either float or integer representation of vector
; because floating point zero = integer zero:
; (rgb (if (= 0 (vector-ref v vix)) 0 255))
(define (grayscale-vector->bitmap v width height)
(let ((pixels (make-bytes (* 4 width height)))
(bm (make-bitmap width height)))
(begin
(for ((y (in-range 0 height)))
(for ((x (in-range 0 width)))
(let* ((vix (+ (* y width) x))
(rgb (if (= 0 (vector-ref v vix)) 0 255))
(pix (* 4 vix)))
(begin
(bytes-set! pixels pix 255) ; alpha
(bytes-set! pixels (add1 pix) rgb) ; r
(bytes-set! pixels (+ 2 pix) rgb) ; g
(bytes-set! pixels (+ 3 pix) rgb))))) ;b
(send bm set-argb-pixels 0 0 (sub1 width) (sub1 height) pixels)
bm)))
; use this function
(define (bitmap->floyd-steinberg bm)
(let ((width (send bm get-width))
(height (send bm get-height))
(v (bitmap->grayscale-vector bm)))
(begin
(floyd-steinberg v width height)
(grayscale-vector->bitmap v width height))))
; use this function
(define (bitmap->burkes bm)
(let ((width (send bm get-width))
(height (send bm get-height))
(v (bitmap->grayscale-vector-int bm)))
(begin
(burkes-int v width height)
(grayscale-vector->bitmap v width height))))