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image/color: tweak the formula for converting to gray.

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This makes grayModel and gray16Model in color.go use the exact same
formula as RGBToYCbCr in ycbcr.go. They were the same formula in theory,
but in practice the color.go versions used a divide by 1000 and the
ycbcr.go versions used a (presumably faster) shift by 16.

This implies the nice property that converting an image.RGBA to an
image.YCbCr and then taking only the Y channel is equivalent to
converting an image.RGBA directly to an image.Gray.

The difference between the two formulae is non-zero, but small:
https://play.golang.org/p/qG7oe-eqHI

Updates #16251

Change-Id: I288ecb957fd6eceb9626410bd1a8084d2e4f8198
Reviewed-on: https://go-review.googlesource.com/31538
Reviewed-by: Rob Pike <r@golang.org>
This commit is contained in:
Nigel Tao 2016-10-20 16:57:55 +11:00
parent a190f3c8a3
commit 584e3ea258
2 changed files with 25 additions and 3 deletions
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23
src/image/color/color.go
View File

@ -246,8 +246,18 @@ func grayModel(c Color) Color {
return c return c
} }
r, g, b, _ := c.RGBA() r, g, b, _ := c.RGBA()
y := (299*r + 587*g + 114*b + 500) / 1000
return Gray{uint8(y >> 8)} // These coefficients (the fractions 0.299, 0.587 and 0.114) are the same
// as those given by the JFIF specification and used by func RGBToYCbCr in
// ycbcr.go.
//
// Note that 19595 + 38470 + 7471 equals 65536.
//
// The 24 is 16 + 8. The 16 is the same as used in RGBToYCbCr. The 8 is
// because the return value is 8 bit color, not 16 bit color.
y := (19595*r + 38470*g + 7471*b + 1<<15) >> 24
return Gray{uint8(y)}
} }
func gray16Model(c Color) Color { func gray16Model(c Color) Color {
@ -255,7 +265,14 @@ func gray16Model(c Color) Color {
return c return c
} }
r, g, b, _ := c.RGBA() r, g, b, _ := c.RGBA()
y := (299*r + 587*g + 114*b + 500) / 1000
// These coefficients (the fractions 0.299, 0.587 and 0.114) are the same
// as those given by the JFIF specification and used by func RGBToYCbCr in
// ycbcr.go.
//
// Note that 19595 + 38470 + 7471 equals 65536.
y := (19595*r + 38470*g + 7471*b + 1<<15) >> 16
return Gray16{uint16(y)} return Gray16{uint16(y)}
} }

5
src/image/color/ycbcr.go
View File

@ -17,6 +17,8 @@ func RGBToYCbCr(r, g, b uint8) (uint8, uint8, uint8) {
b1 := int32(b) b1 := int32(b)
// yy is in range [0,0xff]. // yy is in range [0,0xff].
//
// Note that 19595 + 38470 + 7471 equals 65536.
yy := (19595*r1 + 38470*g1 + 7471*b1 + 1<<15) >> 16 yy := (19595*r1 + 38470*g1 + 7471*b1 + 1<<15) >> 16
// The bit twiddling below is equivalent to // The bit twiddling below is equivalent to
@ -32,6 +34,8 @@ func RGBToYCbCr(r, g, b uint8) (uint8, uint8, uint8) {
// Note that the uint8 type conversion in the return // Note that the uint8 type conversion in the return
// statement will convert ^int32(0) to 0xff. // statement will convert ^int32(0) to 0xff.
// The code below to compute cr uses a similar pattern. // The code below to compute cr uses a similar pattern.
//
// Note that -11056 - 21712 + 32768 equals 0.
cb := -11056*r1 - 21712*g1 + 32768*b1 + 257<<15 cb := -11056*r1 - 21712*g1 + 32768*b1 + 257<<15
if uint32(cb)&0xff000000 == 0 { if uint32(cb)&0xff000000 == 0 {
cb >>= 16 cb >>= 16
@ -39,6 +43,7 @@ func RGBToYCbCr(r, g, b uint8) (uint8, uint8, uint8) {
cb = ^(cb >> 31) cb = ^(cb >> 31)
} }
// Note that 32768 - 27440 - 5328 equals 0.
cr := 32768*r1 - 27440*g1 - 5328*b1 + 257<<15 cr := 32768*r1 - 27440*g1 - 5328*b1 + 257<<15
if uint32(cr)&0xff000000 == 0 { if uint32(cr)&0xff000000 == 0 {
cr >>= 16 cr >>= 16