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# Source file src/image/color/ycbcr.go

## Documentation: image/color

```     1  // Copyright 2011 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
4
5  package color
6
7  // RGBToYCbCr converts an RGB triple to a Y'CbCr triple.
8  func RGBToYCbCr(r, g, b uint8) (uint8, uint8, uint8) {
9  	// The JFIF specification says:
10  	//	Y' =  0.2990*R + 0.5870*G + 0.1140*B
11  	//	Cb = -0.1687*R - 0.3313*G + 0.5000*B + 128
12  	//	Cr =  0.5000*R - 0.4187*G - 0.0813*B + 128
13  	// https://www.w3.org/Graphics/JPEG/jfif3.pdf says Y but means Y'.
14
15  	r1 := int32(r)
16  	g1 := int32(g)
17  	b1 := int32(b)
18
19  	// yy is in range [0,0xff].
20  	//
21  	// Note that 19595 + 38470 + 7471 equals 65536.
22  	yy := (19595*r1 + 38470*g1 + 7471*b1 + 1<<15) >> 16
23
24  	// The bit twiddling below is equivalent to
25  	//
26  	// cb := (-11056*r1 - 21712*g1 + 32768*b1 + 257<<15) >> 16
27  	// if cb < 0 {
28  	//     cb = 0
29  	// } else if cb > 0xff {
30  	//     cb = ^int32(0)
31  	// }
32  	//
33  	// but uses fewer branches and is faster.
34  	// Note that the uint8 type conversion in the return
35  	// statement will convert ^int32(0) to 0xff.
36  	// The code below to compute cr uses a similar pattern.
37  	//
38  	// Note that -11056 - 21712 + 32768 equals 0.
39  	cb := -11056*r1 - 21712*g1 + 32768*b1 + 257<<15
40  	if uint32(cb)&0xff000000 == 0 {
41  		cb >>= 16
42  	} else {
43  		cb = ^(cb >> 31)
44  	}
45
46  	// Note that 32768 - 27440 - 5328 equals 0.
47  	cr := 32768*r1 - 27440*g1 - 5328*b1 + 257<<15
48  	if uint32(cr)&0xff000000 == 0 {
49  		cr >>= 16
50  	} else {
51  		cr = ^(cr >> 31)
52  	}
53
54  	return uint8(yy), uint8(cb), uint8(cr)
55  }
56
57  // YCbCrToRGB converts a Y'CbCr triple to an RGB triple.
58  func YCbCrToRGB(y, cb, cr uint8) (uint8, uint8, uint8) {
59  	// The JFIF specification says:
60  	//	R = Y' + 1.40200*(Cr-128)
61  	//	G = Y' - 0.34414*(Cb-128) - 0.71414*(Cr-128)
62  	//	B = Y' + 1.77200*(Cb-128)
63  	// https://www.w3.org/Graphics/JPEG/jfif3.pdf says Y but means Y'.
64  	//
65  	// Those formulae use non-integer multiplication factors. When computing,
66  	// integer math is generally faster than floating point math. We multiply
67  	// all of those factors by 1<<16 and round to the nearest integer:
68  	//	 91881 = roundToNearestInteger(1.40200 * 65536).
69  	//	 22554 = roundToNearestInteger(0.34414 * 65536).
70  	//	 46802 = roundToNearestInteger(0.71414 * 65536).
71  	//	116130 = roundToNearestInteger(1.77200 * 65536).
72  	//
73  	// Adding a rounding adjustment in the range [0, 1<<16-1] and then shifting
74  	// right by 16 gives us an integer math version of the original formulae.
75  	//	R = (65536*Y' +  91881 *(Cr-128)                  + adjustment) >> 16
76  	//	G = (65536*Y' -  22554 *(Cb-128) - 46802*(Cr-128) + adjustment) >> 16
77  	//	B = (65536*Y' + 116130 *(Cb-128)                  + adjustment) >> 16
78  	// A constant rounding adjustment of 1<<15, one half of 1<<16, would mean
79  	// round-to-nearest when dividing by 65536 (shifting right by 16).
80  	// Similarly, a constant rounding adjustment of 0 would mean round-down.
81  	//
82  	// Defining YY1 = 65536*Y' + adjustment simplifies the formulae and
83  	// requires fewer CPU operations:
84  	//	R = (YY1 +  91881 *(Cr-128)                 ) >> 16
85  	//	G = (YY1 -  22554 *(Cb-128) - 46802*(Cr-128)) >> 16
86  	//	B = (YY1 + 116130 *(Cb-128)                 ) >> 16
87  	//
88  	// The inputs (y, cb, cr) are 8 bit color, ranging in [0x00, 0xff]. In this
89  	// function, the output is also 8 bit color, but in the related YCbCr.RGBA
90  	// method, below, the output is 16 bit color, ranging in [0x0000, 0xffff].
91  	// Outputting 16 bit color simply requires changing the 16 to 8 in the "R =
92  	// etc >> 16" equation, and likewise for G and B.
93  	//
94  	// As mentioned above, a constant rounding adjustment of 1<<15 is a natural
95  	// choice, but there is an additional constraint: if c0 := YCbCr{Y: y, Cb:
96  	// 0x80, Cr: 0x80} and c1 := Gray{Y: y} then c0.RGBA() should equal
97  	// c1.RGBA(). Specifically, if y == 0 then "R = etc >> 8" should yield
98  	// 0x0000 and if y == 0xff then "R = etc >> 8" should yield 0xffff. If we
99  	// used a constant rounding adjustment of 1<<15, then it would yield 0x0080
100  	// and 0xff80 respectively.
101  	//
102  	// Note that when cb == 0x80 and cr == 0x80 then the formulae collapse to:
103  	//	R = YY1 >> n
104  	//	G = YY1 >> n
105  	//	B = YY1 >> n
106  	// where n is 16 for this function (8 bit color output) and 8 for the
107  	// YCbCr.RGBA method (16 bit color output).
108  	//
109  	// The solution is to make the rounding adjustment non-constant, and equal
110  	// to 257*Y', which ranges over [0, 1<<16-1] as Y' ranges over [0, 255].
111  	// YY1 is then defined as:
112  	//	YY1 = 65536*Y' + 257*Y'
113  	// or equivalently:
114  	//	YY1 = Y' * 0x10101
115  	yy1 := int32(y) * 0x10101
116  	cb1 := int32(cb) - 128
117  	cr1 := int32(cr) - 128
118
119  	// The bit twiddling below is equivalent to
120  	//
121  	// r := (yy1 + 91881*cr1) >> 16
122  	// if r < 0 {
123  	//     r = 0
124  	// } else if r > 0xff {
125  	//     r = ^int32(0)
126  	// }
127  	//
128  	// but uses fewer branches and is faster.
129  	// Note that the uint8 type conversion in the return
130  	// statement will convert ^int32(0) to 0xff.
131  	// The code below to compute g and b uses a similar pattern.
132  	r := yy1 + 91881*cr1
133  	if uint32(r)&0xff000000 == 0 {
134  		r >>= 16
135  	} else {
136  		r = ^(r >> 31)
137  	}
138
139  	g := yy1 - 22554*cb1 - 46802*cr1
140  	if uint32(g)&0xff000000 == 0 {
141  		g >>= 16
142  	} else {
143  		g = ^(g >> 31)
144  	}
145
146  	b := yy1 + 116130*cb1
147  	if uint32(b)&0xff000000 == 0 {
148  		b >>= 16
149  	} else {
150  		b = ^(b >> 31)
151  	}
152
153  	return uint8(r), uint8(g), uint8(b)
154  }
155
156  // YCbCr represents a fully opaque 24-bit Y'CbCr color, having 8 bits each for
157  // one luma and two chroma components.
158  //
159  // JPEG, VP8, the MPEG family and other codecs use this color model. Such
160  // codecs often use the terms YUV and Y'CbCr interchangeably, but strictly
161  // speaking, the term YUV applies only to analog video signals, and Y' (luma)
162  // is Y (luminance) after applying gamma correction.
163  //
164  // Conversion between RGB and Y'CbCr is lossy and there are multiple, slightly
165  // different formulae for converting between the two. This package follows
166  // the JFIF specification at https://www.w3.org/Graphics/JPEG/jfif3.pdf.
167  type YCbCr struct {
168  	Y, Cb, Cr uint8
169  }
170
171  func (c YCbCr) RGBA() (uint32, uint32, uint32, uint32) {
172  	// This code is a copy of the YCbCrToRGB function above, except that it
173  	// returns values in the range [0, 0xffff] instead of [0, 0xff]. There is a
174  	// subtle difference between doing this and having YCbCr satisfy the Color
175  	// interface by first converting to an RGBA. The latter loses some
176  	// information by going to and from 8 bits per channel.
177  	//
178  	// For example, this code:
179  	//	const y, cb, cr = 0x7f, 0x7f, 0x7f
180  	//	r, g, b := color.YCbCrToRGB(y, cb, cr)
181  	//	r0, g0, b0, _ := color.YCbCr{y, cb, cr}.RGBA()
182  	//	r1, g1, b1, _ := color.RGBA{r, g, b, 0xff}.RGBA()
183  	//	fmt.Printf("0x%04x 0x%04x 0x%04x\n", r0, g0, b0)
184  	//	fmt.Printf("0x%04x 0x%04x 0x%04x\n", r1, g1, b1)
185  	// prints:
186  	//	0x7e18 0x808d 0x7db9
187  	//	0x7e7e 0x8080 0x7d7d
188
189  	yy1 := int32(c.Y) * 0x10101
190  	cb1 := int32(c.Cb) - 128
191  	cr1 := int32(c.Cr) - 128
192
193  	// The bit twiddling below is equivalent to
194  	//
195  	// r := (yy1 + 91881*cr1) >> 8
196  	// if r < 0 {
197  	//     r = 0
198  	// } else if r > 0xff {
199  	//     r = 0xffff
200  	// }
201  	//
202  	// but uses fewer branches and is faster.
203  	// The code below to compute g and b uses a similar pattern.
204  	r := yy1 + 91881*cr1
205  	if uint32(r)&0xff000000 == 0 {
206  		r >>= 8
207  	} else {
208  		r = ^(r >> 31) & 0xffff
209  	}
210
211  	g := yy1 - 22554*cb1 - 46802*cr1
212  	if uint32(g)&0xff000000 == 0 {
213  		g >>= 8
214  	} else {
215  		g = ^(g >> 31) & 0xffff
216  	}
217
218  	b := yy1 + 116130*cb1
219  	if uint32(b)&0xff000000 == 0 {
220  		b >>= 8
221  	} else {
222  		b = ^(b >> 31) & 0xffff
223  	}
224
225  	return uint32(r), uint32(g), uint32(b), 0xffff
226  }
227
228  // YCbCrModel is the Model for Y'CbCr colors.
229  var YCbCrModel Model = ModelFunc(yCbCrModel)
230
231  func yCbCrModel(c Color) Color {
232  	if _, ok := c.(YCbCr); ok {
233  		return c
234  	}
235  	r, g, b, _ := c.RGBA()
236  	y, u, v := RGBToYCbCr(uint8(r>>8), uint8(g>>8), uint8(b>>8))
237  	return YCbCr{y, u, v}
238  }
239
240  // NYCbCrA represents a non-alpha-premultiplied Y'CbCr-with-alpha color, having
241  // 8 bits each for one luma, two chroma and one alpha component.
242  type NYCbCrA struct {
243  	YCbCr
244  	A uint8
245  }
246
247  func (c NYCbCrA) RGBA() (uint32, uint32, uint32, uint32) {
248  	// The first part of this method is the same as YCbCr.RGBA.
249  	yy1 := int32(c.Y) * 0x10101
250  	cb1 := int32(c.Cb) - 128
251  	cr1 := int32(c.Cr) - 128
252
253  	// The bit twiddling below is equivalent to
254  	//
255  	// r := (yy1 + 91881*cr1) >> 8
256  	// if r < 0 {
257  	//     r = 0
258  	// } else if r > 0xff {
259  	//     r = 0xffff
260  	// }
261  	//
262  	// but uses fewer branches and is faster.
263  	// The code below to compute g and b uses a similar pattern.
264  	r := yy1 + 91881*cr1
265  	if uint32(r)&0xff000000 == 0 {
266  		r >>= 8
267  	} else {
268  		r = ^(r >> 31) & 0xffff
269  	}
270
271  	g := yy1 - 22554*cb1 - 46802*cr1
272  	if uint32(g)&0xff000000 == 0 {
273  		g >>= 8
274  	} else {
275  		g = ^(g >> 31) & 0xffff
276  	}
277
278  	b := yy1 + 116130*cb1
279  	if uint32(b)&0xff000000 == 0 {
280  		b >>= 8
281  	} else {
282  		b = ^(b >> 31) & 0xffff
283  	}
284
285  	// The second part of this method applies the alpha.
286  	a := uint32(c.A) * 0x101
287  	return uint32(r) * a / 0xffff, uint32(g) * a / 0xffff, uint32(b) * a / 0xffff, a
288  }
289
290  // NYCbCrAModel is the Model for non-alpha-premultiplied Y'CbCr-with-alpha
291  // colors.
292  var NYCbCrAModel Model = ModelFunc(nYCbCrAModel)
293
294  func nYCbCrAModel(c Color) Color {
295  	switch c := c.(type) {
296  	case NYCbCrA:
297  		return c
298  	case YCbCr:
299  		return NYCbCrA{c, 0xff}
300  	}
301  	r, g, b, a := c.RGBA()
302
303  	// Convert from alpha-premultiplied to non-alpha-premultiplied.
304  	if a != 0 {
305  		r = (r * 0xffff) / a
306  		g = (g * 0xffff) / a
307  		b = (b * 0xffff) / a
308  	}
309
310  	y, u, v := RGBToYCbCr(uint8(r>>8), uint8(g>>8), uint8(b>>8))
311  	return NYCbCrA{YCbCr{Y: y, Cb: u, Cr: v}, uint8(a >> 8)}
312  }
313
314  // RGBToCMYK converts an RGB triple to a CMYK quadruple.
315  func RGBToCMYK(r, g, b uint8) (uint8, uint8, uint8, uint8) {
316  	rr := uint32(r)
317  	gg := uint32(g)
318  	bb := uint32(b)
319  	w := rr
320  	if w < gg {
321  		w = gg
322  	}
323  	if w < bb {
324  		w = bb
325  	}
326  	if w == 0 {
327  		return 0, 0, 0, 0xff
328  	}
329  	c := (w - rr) * 0xff / w
330  	m := (w - gg) * 0xff / w
331  	y := (w - bb) * 0xff / w
332  	return uint8(c), uint8(m), uint8(y), uint8(0xff - w)
333  }
334
335  // CMYKToRGB converts a CMYK quadruple to an RGB triple.
336  func CMYKToRGB(c, m, y, k uint8) (uint8, uint8, uint8) {
337  	w := 0xffff - uint32(k)*0x101
338  	r := (0xffff - uint32(c)*0x101) * w / 0xffff
339  	g := (0xffff - uint32(m)*0x101) * w / 0xffff
340  	b := (0xffff - uint32(y)*0x101) * w / 0xffff
341  	return uint8(r >> 8), uint8(g >> 8), uint8(b >> 8)
342  }
343
344  // CMYK represents a fully opaque CMYK color, having 8 bits for each of cyan,
345  // magenta, yellow and black.
346  //
347  // It is not associated with any particular color profile.
348  type CMYK struct {
349  	C, M, Y, K uint8
350  }
351
352  func (c CMYK) RGBA() (uint32, uint32, uint32, uint32) {
353  	// This code is a copy of the CMYKToRGB function above, except that it
354  	// returns values in the range [0, 0xffff] instead of [0, 0xff].
355
356  	w := 0xffff - uint32(c.K)*0x101
357  	r := (0xffff - uint32(c.C)*0x101) * w / 0xffff
358  	g := (0xffff - uint32(c.M)*0x101) * w / 0xffff
359  	b := (0xffff - uint32(c.Y)*0x101) * w / 0xffff
360  	return r, g, b, 0xffff
361  }
362
363  // CMYKModel is the Model for CMYK colors.
364  var CMYKModel Model = ModelFunc(cmykModel)
365
366  func cmykModel(c Color) Color {
367  	if _, ok := c.(CMYK); ok {
368  		return c
369  	}
370  	r, g, b, _ := c.RGBA()
371  	cc, mm, yy, kk := RGBToCMYK(uint8(r>>8), uint8(g>>8), uint8(b>>8))
372  	return CMYK{cc, mm, yy, kk}
373  }
374
```

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