Optimize data-locality for a huge increase in processing speed.
This is a complete rewrite! The tight scaling loop needs data locality for optimal performance. The old version used lots of pointer redirections to access image data which was bad for data locality. By providing the complete loop for each image type, this problem is solved. Unfortunately this increases code duplication but the result should be worth it: I could measure a ~6x speed-up for certain test cases!
This commit is contained in:
jst
parent
bdfbbead13
commit
016a61cd31
278
converter.go
278
converter.go
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@ -21,110 +21,236 @@ import (
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"image/color"
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"image/color"
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)
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)
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type colorArray [4]float32
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// Keep value in [0,255] range.
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func clampUint8(in int32) uint8 {
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func replicateBorder1d(x, min, max int) int {
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if in < 0 {
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if x < min {
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return 0
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x = min
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}
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} else if x >= max {
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if in > 255 {
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x = max - 1
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return 255
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}
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return uint8(in)
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}
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}
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return x
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// Keep value in [0,65535] range.
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func clampUint16(in int64) uint16 {
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if in < 0 {
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return 0
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}
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if in > 65535 {
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return 65535
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}
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return uint16(in)
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}
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}
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func replicateBorder(x, y int, rect image.Rectangle) (xx, yy int) {
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func resizeGeneric(in image.Image, out *image.RGBA64, scale float64, coeffs []int32, filterLength int) {
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xx = replicateBorder1d(x, rect.Min.X, rect.Max.X)
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oldBounds := in.Bounds()
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yy = replicateBorder1d(y, rect.Min.Y, rect.Max.Y)
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newBounds := out.Bounds()
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return
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for x := newBounds.Min.X; x < newBounds.Max.X; x++ {
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for y := newBounds.Min.Y; y < newBounds.Max.Y; y++ {
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interpX := scale*(float64(y)+0.5) + float64(oldBounds.Min.X)
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start := int(interpX) - filterLength/2 + 1
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var rgba [4]int64
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var sum int64
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for i := 0; i < filterLength; i++ {
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xx := start + i
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if xx < oldBounds.Min.X {
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xx = oldBounds.Min.X
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} else if xx >= oldBounds.Max.X {
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xx = oldBounds.Max.X - 1
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}
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}
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// converter allows to retrieve a colorArray for points of an image.
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coeff := coeffs[(y-newBounds.Min.Y)*filterLength+i]
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// the idea is to speed up computation by providing optimized implementations
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r, g, b, a := in.At(xx, x).RGBA()
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// for different image types instead of relying on image.Image.At().
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rgba[0] += int64(coeff) * int64(r)
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type converter interface {
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rgba[1] += int64(coeff) * int64(g)
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at(x, y int, color *colorArray)
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rgba[2] += int64(coeff) * int64(b)
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rgba[3] += int64(coeff) * int64(a)
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sum += int64(coeff)
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}
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}
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type genericConverter struct {
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offset := (y-newBounds.Min.Y)*out.Stride + (x-newBounds.Min.X)*8
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src image.Image
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value := clampUint16(rgba[0] / sum)
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out.Pix[offset+0] = uint8(value >> 8)
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out.Pix[offset+1] = uint8(value)
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value = clampUint16(rgba[1] / sum)
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out.Pix[offset+2] = uint8(value >> 8)
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out.Pix[offset+3] = uint8(value)
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value = clampUint16(rgba[2] / sum)
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out.Pix[offset+4] = uint8(value >> 8)
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out.Pix[offset+5] = uint8(value)
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value = clampUint16(rgba[3] / sum)
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out.Pix[offset+6] = uint8(value >> 8)
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out.Pix[offset+7] = uint8(value)
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}
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}
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}
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}
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func (c *genericConverter) at(x, y int, result *colorArray) {
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func resizeRGBA(in *image.RGBA, out *image.RGBA, scale float64, coeffs []int16, filterLength int) {
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r, g, b, a := c.src.At(replicateBorder(x, y, c.src.Bounds())).RGBA()
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oldBounds := in.Bounds()
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result[0] = float32(r)
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newBounds := out.Bounds()
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result[1] = float32(g)
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result[2] = float32(b)
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for x := newBounds.Min.X; x < newBounds.Max.X; x++ {
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result[3] = float32(a)
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row := in.Pix[(x-oldBounds.Min.Y)*in.Stride:]
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return
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for y := newBounds.Min.Y; y < newBounds.Max.Y; y++ {
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interpX := scale*(float64(y)+0.5) + float64(oldBounds.Min.X)
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start := int(interpX) - filterLength/2 + 1
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var rgba [4]int32
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var sum int32
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for i := 0; i < filterLength; i++ {
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xx := start + i
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if xx < oldBounds.Min.X {
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xx = oldBounds.Min.X
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} else if xx >= oldBounds.Max.X {
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xx = oldBounds.Max.X - 1
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}
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}
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type rgbaConverter struct {
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coeff := coeffs[(y-newBounds.Min.Y)*filterLength+i]
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src *image.RGBA
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offset := (xx - oldBounds.Min.X) * 4
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rgba[0] += int32(coeff) * int32(row[offset+0])
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rgba[1] += int32(coeff) * int32(row[offset+1])
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rgba[2] += int32(coeff) * int32(row[offset+2])
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rgba[3] += int32(coeff) * int32(row[offset+3])
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sum += int32(coeff)
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}
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}
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func (c *rgbaConverter) at(x, y int, result *colorArray) {
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offset := (y-newBounds.Min.Y)*out.Stride + (x-newBounds.Min.X)*4
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i := c.src.PixOffset(replicateBorder(x, y, c.src.Rect))
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out.Pix[offset+0] = clampUint8(rgba[0] / sum)
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result[0] = float32(uint16(c.src.Pix[i+0])<<8 | uint16(c.src.Pix[i+0]))
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out.Pix[offset+1] = clampUint8(rgba[1] / sum)
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result[1] = float32(uint16(c.src.Pix[i+1])<<8 | uint16(c.src.Pix[i+1]))
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out.Pix[offset+2] = clampUint8(rgba[2] / sum)
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result[2] = float32(uint16(c.src.Pix[i+2])<<8 | uint16(c.src.Pix[i+2]))
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out.Pix[offset+3] = clampUint8(rgba[3] / sum)
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result[3] = float32(uint16(c.src.Pix[i+3])<<8 | uint16(c.src.Pix[i+3]))
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}
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return
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}
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}
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}
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type rgba64Converter struct {
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func resizeRGBA64(in *image.RGBA64, out *image.RGBA64, scale float64, coeffs []int32, filterLength int) {
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src *image.RGBA64
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oldBounds := in.Bounds()
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newBounds := out.Bounds()
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for x := newBounds.Min.X; x < newBounds.Max.X; x++ {
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row := in.Pix[(x-oldBounds.Min.Y)*in.Stride:]
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for y := newBounds.Min.Y; y < newBounds.Max.Y; y++ {
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interpX := scale*(float64(y)+0.5) + float64(oldBounds.Min.X)
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start := int(interpX) - filterLength/2 + 1
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var rgba [4]int64
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var sum int64
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for i := 0; i < filterLength; i++ {
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xx := start + i
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if xx < oldBounds.Min.X {
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xx = oldBounds.Min.X
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} else if xx >= oldBounds.Max.X {
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xx = oldBounds.Max.X - 1
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}
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}
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func (c *rgba64Converter) at(x, y int, result *colorArray) {
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coeff := coeffs[(y-newBounds.Min.Y)*filterLength+i]
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i := c.src.PixOffset(replicateBorder(x, y, c.src.Rect))
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offset := (xx - oldBounds.Min.X) * 8
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result[0] = float32(uint16(c.src.Pix[i+0])<<8 | uint16(c.src.Pix[i+1]))
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rgba[0] += int64(coeff) * int64(uint16(row[offset+0])<<8|uint16(row[offset+1]))
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result[1] = float32(uint16(c.src.Pix[i+2])<<8 | uint16(c.src.Pix[i+3]))
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rgba[1] += int64(coeff) * int64(uint16(row[offset+2])<<8|uint16(row[offset+3]))
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result[2] = float32(uint16(c.src.Pix[i+4])<<8 | uint16(c.src.Pix[i+5]))
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rgba[2] += int64(coeff) * int64(uint16(row[offset+4])<<8|uint16(row[offset+5]))
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result[3] = float32(uint16(c.src.Pix[i+6])<<8 | uint16(c.src.Pix[i+7]))
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rgba[3] += int64(coeff) * int64(uint16(row[offset+6])<<8|uint16(row[offset+7]))
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return
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sum += int64(coeff)
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}
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}
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type grayConverter struct {
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offset := (y-newBounds.Min.Y)*out.Stride + (x-newBounds.Min.X)*8
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src *image.Gray
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value := clampUint16(rgba[0] / sum)
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out.Pix[offset+0] = uint8(value >> 8)
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out.Pix[offset+1] = uint8(value)
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value = clampUint16(rgba[1] / sum)
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out.Pix[offset+2] = uint8(value >> 8)
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out.Pix[offset+3] = uint8(value)
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value = clampUint16(rgba[2] / sum)
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out.Pix[offset+4] = uint8(value >> 8)
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out.Pix[offset+5] = uint8(value)
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value = clampUint16(rgba[3] / sum)
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out.Pix[offset+6] = uint8(value >> 8)
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out.Pix[offset+7] = uint8(value)
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}
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}
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}
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}
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func (c *grayConverter) at(x, y int, result *colorArray) {
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func resizeGray(in *image.Gray, out *image.Gray, scale float64, coeffs []int16, filterLength int) {
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i := c.src.PixOffset(replicateBorder(x, y, c.src.Rect))
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oldBounds := in.Bounds()
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g := float32(uint16(c.src.Pix[i])<<8 | uint16(c.src.Pix[i]))
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newBounds := out.Bounds()
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result[0] = g
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result[1] = g
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for x := newBounds.Min.X; x < newBounds.Max.X; x++ {
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result[2] = g
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row := in.Pix[(x-oldBounds.Min.Y)*in.Stride:]
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result[3] = float32(0xffff)
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for y := newBounds.Min.Y; y < newBounds.Max.Y; y++ {
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return
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interpX := scale*(float64(y)+0.5) + float64(oldBounds.Min.X)
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start := int(interpX) - filterLength/2 + 1
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var gray int32
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var sum int32
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for i := 0; i < filterLength; i++ {
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xx := start + i
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if xx < oldBounds.Min.X {
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xx = oldBounds.Min.X
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} else if xx >= oldBounds.Max.X {
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xx = oldBounds.Max.X - 1
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}
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}
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type gray16Converter struct {
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coeff := coeffs[(y-newBounds.Min.Y)*filterLength+i]
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src *image.Gray16
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offset := (xx - oldBounds.Min.X)
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gray += int32(coeff) * int32(row[offset])
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sum += int32(coeff)
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}
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}
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func (c *gray16Converter) at(x, y int, result *colorArray) {
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offset := (y-newBounds.Min.Y)*out.Stride + (x - newBounds.Min.X)
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i := c.src.PixOffset(replicateBorder(x, y, c.src.Rect))
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out.Pix[offset] = clampUint8(gray / sum)
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g := float32(uint16(c.src.Pix[i+0])<<8 | uint16(c.src.Pix[i+1]))
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}
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result[0] = g
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}
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result[1] = g
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result[2] = g
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result[3] = float32(0xffff)
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return
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}
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}
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type ycbcrConverter struct {
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func resizeGray16(in *image.Gray16, out *image.Gray16, scale float64, coeffs []int32, filterLength int) {
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src *image.YCbCr
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oldBounds := in.Bounds()
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newBounds := out.Bounds()
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for x := newBounds.Min.X; x < newBounds.Max.X; x++ {
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row := in.Pix[(x-oldBounds.Min.Y)*in.Stride:]
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for y := newBounds.Min.Y; y < newBounds.Max.Y; y++ {
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interpX := scale*(float64(y)+0.5) + float64(oldBounds.Min.X)
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start := int(interpX) - filterLength/2 + 1
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var gray int64
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var sum int64
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for i := 0; i < filterLength; i++ {
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xx := start + i
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if xx < oldBounds.Min.X {
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xx = oldBounds.Min.X
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} else if xx >= oldBounds.Max.X {
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xx = oldBounds.Max.X - 1
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}
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}
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func (c *ycbcrConverter) at(x, y int, result *colorArray) {
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coeff := coeffs[(y-newBounds.Min.Y)*filterLength+i]
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xx, yy := replicateBorder(x, y, c.src.Rect)
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offset := (xx - oldBounds.Min.X) * 2
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yi := c.src.YOffset(xx, yy)
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gray += int64(coeff) * int64(uint16(row[offset+0])<<8|uint16(row[offset+1]))
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ci := c.src.COffset(xx, yy)
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sum += int64(coeff)
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r, g, b := color.YCbCrToRGB(c.src.Y[yi], c.src.Cb[ci], c.src.Cr[ci])
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}
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result[0] = float32(uint16(r) * 0x101)
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result[1] = float32(uint16(g) * 0x101)
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offset := (y-newBounds.Min.Y)*out.Stride + (x-newBounds.Min.X)*2
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result[2] = float32(uint16(b) * 0x101)
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value := clampUint16(gray / sum)
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result[3] = float32(0xffff)
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out.Pix[offset+0] = uint8(value >> 8)
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return
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out.Pix[offset+1] = uint8(value)
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}
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}
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}
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func convertYCbCrToRGBA(in *image.YCbCr) *image.RGBA {
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out := image.NewRGBA(in.Bounds())
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for y := 0; y < out.Bounds().Dy(); y++ {
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for x := 0; x < out.Bounds().Dx(); x++ {
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p := out.Pix[y*out.Stride+4*x:]
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yi := in.YOffset(x, y)
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ci := in.COffset(x, y)
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r, g, b := color.YCbCrToRGB(in.Y[yi], in.Cb[ci], in.Cr[ci])
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p[0] = r
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p[1] = g
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p[2] = b
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p[3] = 0xff
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}
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}
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return out
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}
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}
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282
filters.go
282
filters.go
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@ -17,222 +17,100 @@ THIS SOFTWARE.
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package resize
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package resize
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import (
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import (
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"image"
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"image/color"
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"math"
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"math"
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)
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)
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// restrict an input float32 to the range of uint16 values
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func nearest(in float64) float64 {
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func clampToUint16(x float32) (y uint16) {
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if in >= -0.5 && in < 0.5 {
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y = uint16(x)
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return 1
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if x < 0 {
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}
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y = 0
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return 0
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} else if x > float32(0xfffe) {
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// "else if x > float32(0xffff)" will cause overflows!
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y = 0xffff
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}
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}
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return
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func linear(in float64) float64 {
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in = math.Abs(in)
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if in <= 1 {
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return 1 - in
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}
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return 0
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}
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}
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// describe a resampling filter
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func cubic(in float64) float64 {
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type filterModel struct {
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in = math.Abs(in)
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// resampling is done by convolution with a (scaled) kernel
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if in <= 1 {
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kernel func(float32) float32
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return in*in*(1.5*in-2.5) + 1.0
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}
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// instead of blurring an image before downscaling to avoid aliasing,
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if in <= 2 {
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// the filter is scaled by a factor which leads to a similar effect
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return in*(in*(2.5-0.5*in)-4.0) + 2.0
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factorInv float32
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}
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return 0
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// for optimized access to image points
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converter
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// temporary used by Interpolate
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tempRow []colorArray
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kernelWeight []float32
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weightSum float32
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}
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}
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func (f *filterModel) SetKernelWeights(u float32) {
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func mitchellnetravali(in float64) float64 {
|
||||||
uf := int(u) - len(f.tempRow)/2 + 1
|
in = math.Abs(in)
|
||||||
u -= float32(uf)
|
if in <= 1 {
|
||||||
f.weightSum = 0
|
return (7.0*in*in*in - 12.0*in*in + 5.33333333333) * 0.16666666666
|
||||||
|
}
|
||||||
|
if in <= 2 {
|
||||||
|
return (-2.33333333333*in*in*in + 12.0*in*in - 20.0*in + 10.6666666667) * 0.16666666666
|
||||||
|
}
|
||||||
|
return 0
|
||||||
|
}
|
||||||
|
|
||||||
for j := range f.tempRow {
|
func sinc(x float64) float64 {
|
||||||
f.kernelWeight[j] = f.kernel((u - float32(j)) * f.factorInv)
|
x = math.Abs(x) * math.Pi
|
||||||
f.weightSum += f.kernelWeight[j]
|
if x >= 1.220703e-4 {
|
||||||
|
return math.Sin(x) / x
|
||||||
|
}
|
||||||
|
return 1
|
||||||
|
}
|
||||||
|
|
||||||
|
func lanczos2(in float64) float64 {
|
||||||
|
if in > -2 && in < 2 {
|
||||||
|
return sinc(in) * sinc(in*0.5)
|
||||||
|
}
|
||||||
|
return 0
|
||||||
|
}
|
||||||
|
|
||||||
|
func lanczos3(in float64) float64 {
|
||||||
|
if in > -3 && in < 3 {
|
||||||
|
return sinc(in) * sinc(in*0.3333333333333333)
|
||||||
|
}
|
||||||
|
return 0
|
||||||
|
}
|
||||||
|
|
||||||
|
// range [-256,256]
|
||||||
|
func createWeights8(dy, minx, filterLength int, blur, scale float64, kernel func(float64) float64) ([]int16, int) {
|
||||||
|
filterLength = filterLength * int(math.Max(math.Ceil(blur*scale), 1))
|
||||||
|
filterFactor := math.Min(1./(blur*scale), 1)
|
||||||
|
|
||||||
|
coeffs := make([]int16, dy*filterLength)
|
||||||
|
for y := 0; y < dy; y++ {
|
||||||
|
interpX := scale*(float64(y)+0.5) + float64(minx)
|
||||||
|
start := int(interpX) - filterLength/2 + 1
|
||||||
|
for i := 0; i < filterLength; i++ {
|
||||||
|
in := (interpX - float64(start) - float64(i)) * filterFactor
|
||||||
|
coeffs[y*filterLength+i] = int16(kernel(in) * 256)
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
func (f *filterModel) convolution1d() (c colorArray) {
|
return coeffs, filterLength
|
||||||
for j := range f.tempRow {
|
}
|
||||||
for i := range c {
|
|
||||||
c[i] += f.tempRow[j][i] * f.kernelWeight[j]
|
// range [-65536,65536]
|
||||||
|
func createWeights16(dy, minx, filterLength int, blur, scale float64, kernel func(float64) float64) ([]int32, int) {
|
||||||
|
filterLength = filterLength * int(math.Max(math.Ceil(blur*scale), 1))
|
||||||
|
filterFactor := math.Min(1./(blur*scale), 1)
|
||||||
|
|
||||||
|
coeffs := make([]int32, dy*filterLength)
|
||||||
|
for y := 0; y < dy; y++ {
|
||||||
|
interpX := scale*(float64(y)+0.5) + float64(minx)
|
||||||
|
start := int(interpX) - filterLength/2 + 1
|
||||||
|
for i := 0; i < filterLength; i++ {
|
||||||
|
in := (interpX - float64(start) - float64(i)) * filterFactor
|
||||||
|
coeffs[y*filterLength+i] = int32(kernel(in) * 65536)
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
// normalize values
|
return coeffs, filterLength
|
||||||
for i := range c {
|
|
||||||
c[i] = c[i] / f.weightSum
|
|
||||||
}
|
|
||||||
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
func (f *filterModel) Interpolate(u float32, y int) color.RGBA64 {
|
|
||||||
uf := int(u) - len(f.tempRow)/2 + 1
|
|
||||||
u -= float32(uf)
|
|
||||||
|
|
||||||
for i := range f.tempRow {
|
|
||||||
f.at(uf+i, y, &f.tempRow[i])
|
|
||||||
}
|
|
||||||
|
|
||||||
c := f.convolution1d()
|
|
||||||
return color.RGBA64{
|
|
||||||
clampToUint16(c[0]),
|
|
||||||
clampToUint16(c[1]),
|
|
||||||
clampToUint16(c[2]),
|
|
||||||
clampToUint16(c[3]),
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// createFilter tries to find an optimized converter for the given input image
|
|
||||||
// and initializes all filterModel members to their defaults
|
|
||||||
func createFilter(img image.Image, factor float32, size int, kernel func(float32) float32) (f Filter) {
|
|
||||||
sizeX := size * (int(math.Ceil(float64(factor))))
|
|
||||||
|
|
||||||
switch img.(type) {
|
|
||||||
default:
|
|
||||||
f = &filterModel{
|
|
||||||
kernel, 1. / factor,
|
|
||||||
&genericConverter{img},
|
|
||||||
make([]colorArray, sizeX),
|
|
||||||
make([]float32, sizeX),
|
|
||||||
0,
|
|
||||||
}
|
|
||||||
case *image.RGBA:
|
|
||||||
f = &filterModel{
|
|
||||||
kernel, 1. / factor,
|
|
||||||
&rgbaConverter{img.(*image.RGBA)},
|
|
||||||
make([]colorArray, sizeX),
|
|
||||||
make([]float32, sizeX),
|
|
||||||
0,
|
|
||||||
}
|
|
||||||
case *image.RGBA64:
|
|
||||||
f = &filterModel{
|
|
||||||
kernel, 1. / factor,
|
|
||||||
&rgba64Converter{img.(*image.RGBA64)},
|
|
||||||
make([]colorArray, sizeX),
|
|
||||||
make([]float32, sizeX),
|
|
||||||
0,
|
|
||||||
}
|
|
||||||
case *image.Gray:
|
|
||||||
f = &filterModel{
|
|
||||||
kernel, 1. / factor,
|
|
||||||
&grayConverter{img.(*image.Gray)},
|
|
||||||
make([]colorArray, sizeX),
|
|
||||||
make([]float32, sizeX),
|
|
||||||
0,
|
|
||||||
}
|
|
||||||
case *image.Gray16:
|
|
||||||
f = &filterModel{
|
|
||||||
kernel, 1. / factor,
|
|
||||||
&gray16Converter{img.(*image.Gray16)},
|
|
||||||
make([]colorArray, sizeX),
|
|
||||||
make([]float32, sizeX),
|
|
||||||
0,
|
|
||||||
}
|
|
||||||
case *image.YCbCr:
|
|
||||||
f = &filterModel{
|
|
||||||
kernel, 1. / factor,
|
|
||||||
&ycbcrConverter{img.(*image.YCbCr)},
|
|
||||||
make([]colorArray, sizeX),
|
|
||||||
make([]float32, sizeX),
|
|
||||||
0,
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
// Nearest-neighbor interpolation
|
|
||||||
func NearestNeighbor(img image.Image, factor float32) Filter {
|
|
||||||
return createFilter(img, factor, 2, func(x float32) (y float32) {
|
|
||||||
if x >= -0.5 && x < 0.5 {
|
|
||||||
y = 1
|
|
||||||
} else {
|
|
||||||
y = 0
|
|
||||||
}
|
|
||||||
|
|
||||||
return
|
|
||||||
})
|
|
||||||
}
|
|
||||||
|
|
||||||
// Bilinear interpolation
|
|
||||||
func Bilinear(img image.Image, factor float32) Filter {
|
|
||||||
return createFilter(img, factor, 2, func(x float32) (y float32) {
|
|
||||||
absX := float32(math.Abs(float64(x)))
|
|
||||||
if absX <= 1 {
|
|
||||||
y = 1 - absX
|
|
||||||
} else {
|
|
||||||
y = 0
|
|
||||||
}
|
|
||||||
|
|
||||||
return
|
|
||||||
})
|
|
||||||
}
|
|
||||||
|
|
||||||
// Bicubic interpolation (with cubic hermite spline)
|
|
||||||
func Bicubic(img image.Image, factor float32) Filter {
|
|
||||||
return createFilter(img, factor, 4, splineKernel(0, 0.5))
|
|
||||||
}
|
|
||||||
|
|
||||||
// Mitchell-Netravali interpolation
|
|
||||||
func MitchellNetravali(img image.Image, factor float32) Filter {
|
|
||||||
return createFilter(img, factor, 4, splineKernel(1.0/3.0, 1.0/3.0))
|
|
||||||
}
|
|
||||||
|
|
||||||
func splineKernel(B, C float32) func(float32) float32 {
|
|
||||||
factorA := 2.0 - 1.5*B - C
|
|
||||||
factorB := -3.0 + 2.0*B + C
|
|
||||||
factorC := 1.0 - 1.0/3.0*B
|
|
||||||
factorD := -B/6.0 - C
|
|
||||||
factorE := B + 5.0*C
|
|
||||||
factorF := -2.0*B - 8.0*C
|
|
||||||
factorG := 4.0/3.0*B + 4.0*C
|
|
||||||
return func(x float32) (y float32) {
|
|
||||||
absX := float32(math.Abs(float64(x)))
|
|
||||||
if absX <= 1 {
|
|
||||||
y = absX*absX*(factorA*absX+factorB) + factorC
|
|
||||||
} else if absX <= 2 {
|
|
||||||
y = absX*(absX*(absX*factorD+factorE)+factorF) + factorG
|
|
||||||
} else {
|
|
||||||
y = 0
|
|
||||||
}
|
|
||||||
|
|
||||||
return
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func lanczosKernel(a uint) func(float32) float32 {
|
|
||||||
return func(x float32) (y float32) {
|
|
||||||
if x > -float32(a) && x < float32(a) {
|
|
||||||
y = float32(Sinc(float64(x))) * float32(Sinc(float64(x/float32(a))))
|
|
||||||
} else {
|
|
||||||
y = 0
|
|
||||||
}
|
|
||||||
|
|
||||||
return
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
// Lanczos interpolation (a=2)
|
|
||||||
func Lanczos2(img image.Image, factor float32) Filter {
|
|
||||||
return createFilter(img, factor, 4, lanczosKernel(2))
|
|
||||||
}
|
|
||||||
|
|
||||||
// Lanczos interpolation (a=3)
|
|
||||||
func Lanczos3(img image.Image, factor float32) Filter {
|
|
||||||
return createFilter(img, factor, 6, lanczosKernel(3))
|
|
||||||
}
|
}
|
||||||
|
|
|
||||||
313
resize.go
313
resize.go
|
|
@ -26,124 +26,275 @@ package resize
|
||||||
|
|
||||||
import (
|
import (
|
||||||
"image"
|
"image"
|
||||||
"image/color"
|
|
||||||
"runtime"
|
"runtime"
|
||||||
|
"sync"
|
||||||
)
|
)
|
||||||
|
|
||||||
// Filter can interpolate at points (x,y)
|
// An InterpolationFunction provides the parameters that describe an
|
||||||
type Filter interface {
|
// interpolation kernel. It returns the number of samples to take
|
||||||
SetKernelWeights(u float32)
|
// and the kernel function to use for sampling.
|
||||||
Interpolate(u float32, y int) color.RGBA64
|
type InterpolationFunction func() (int, func(float64) float64)
|
||||||
|
|
||||||
|
// Nearest-neighbor interpolation
|
||||||
|
func NearestNeighbor() (int, func(float64) float64) {
|
||||||
|
return 2, nearest
|
||||||
}
|
}
|
||||||
|
|
||||||
// InterpolationFunction return a Filter implementation
|
// Bilinear interpolation
|
||||||
// that operates on an image. Two factors
|
func Bilinear() (int, func(float64) float64) {
|
||||||
// allow to scale the filter kernels in x- and y-direction
|
return 2, linear
|
||||||
// to prevent moire patterns.
|
}
|
||||||
type InterpolationFunction func(image.Image, float32) Filter
|
|
||||||
|
|
||||||
// Resize an image to new width and height using the interpolation function interp.
|
// Bicubic interpolation (with cubic hermite spline)
|
||||||
|
func Bicubic() (int, func(float64) float64) {
|
||||||
|
return 4, cubic
|
||||||
|
}
|
||||||
|
|
||||||
|
// Mitchell-Netravali interpolation
|
||||||
|
func MitchellNetravali() (int, func(float64) float64) {
|
||||||
|
return 4, mitchellnetravali
|
||||||
|
}
|
||||||
|
|
||||||
|
// Lanczos interpolation (a=2)
|
||||||
|
func Lanczos2() (int, func(float64) float64) {
|
||||||
|
return 4, lanczos2
|
||||||
|
}
|
||||||
|
|
||||||
|
// Lanczos interpolation (a=3)
|
||||||
|
func Lanczos3() (int, func(float64) float64) {
|
||||||
|
return 6, lanczos3
|
||||||
|
}
|
||||||
|
|
||||||
|
// values <1 will sharpen the image
|
||||||
|
var blur = 1.0
|
||||||
|
|
||||||
|
// Resize scales an image to new width and height using the interpolation function interp.
|
||||||
// A new image with the given dimensions will be returned.
|
// A new image with the given dimensions will be returned.
|
||||||
// If one of the parameters width or height is set to 0, its size will be calculated so that
|
// If one of the parameters width or height is set to 0, its size will be calculated so that
|
||||||
// the aspect ratio is that of the originating image.
|
// the aspect ratio is that of the originating image.
|
||||||
// The resizing algorithm uses channels for parallel computation.
|
// The resizing algorithm uses channels for parallel computation.
|
||||||
func Resize(width, height uint, img image.Image, interp InterpolationFunction) image.Image {
|
func Resize(width, height uint, img image.Image, interp InterpolationFunction) image.Image {
|
||||||
oldBounds := img.Bounds()
|
scaleX, scaleY := calcFactors(width, height, float64(img.Bounds().Dx()), float64(img.Bounds().Dy()))
|
||||||
oldWidth := float32(oldBounds.Dx())
|
if width == 0 {
|
||||||
oldHeight := float32(oldBounds.Dy())
|
width = uint(0.7 + float64(img.Bounds().Dx())/scaleX)
|
||||||
scaleX, scaleY := calcFactors(width, height, oldWidth, oldHeight)
|
|
||||||
|
|
||||||
tempImg := image.NewRGBA64(image.Rect(0, 0, oldBounds.Dy(), int(0.7+oldWidth/scaleX)))
|
|
||||||
b := tempImg.Bounds()
|
|
||||||
adjust := 0.5 * ((oldWidth-1.0)/scaleX - float32(b.Dy()-1))
|
|
||||||
|
|
||||||
n := numJobs(b.Dy())
|
|
||||||
c := make(chan int, n)
|
|
||||||
for i := 0; i < n; i++ {
|
|
||||||
slice := image.Rect(b.Min.X, b.Min.Y+i*(b.Dy())/n, b.Max.X, b.Min.Y+(i+1)*(b.Dy())/n)
|
|
||||||
go resizeSlice(img, tempImg, interp, scaleX, adjust, float32(oldBounds.Min.X), oldBounds.Min.Y, slice, c)
|
|
||||||
}
|
}
|
||||||
for i := 0; i < n; i++ {
|
if height == 0 {
|
||||||
<-c
|
height = uint(0.7 + float64(img.Bounds().Dy())/scaleY)
|
||||||
}
|
}
|
||||||
|
|
||||||
resultImg := image.NewRGBA64(image.Rect(0, 0, int(0.7+oldWidth/scaleX), int(0.7+oldHeight/scaleY)))
|
taps, kernel := interp()
|
||||||
b = resultImg.Bounds()
|
cpus := runtime.NumCPU()
|
||||||
adjust = 0.5 * ((oldHeight-1.0)/scaleY - float32(b.Dy()-1))
|
wg := sync.WaitGroup{}
|
||||||
|
|
||||||
for i := 0; i < n; i++ {
|
// Generic access to image.Image is slow in tight loops.
|
||||||
slice := image.Rect(b.Min.X, b.Min.Y+i*(b.Dy())/n, b.Max.X, b.Min.Y+(i+1)*(b.Dy())/n)
|
// The optimal access has to be determined from the concrete image type.
|
||||||
go resizeSlice(tempImg, resultImg, interp, scaleY, adjust, 0, 0, slice, c)
|
switch input := img.(type) {
|
||||||
}
|
case *image.RGBA:
|
||||||
for i := 0; i < n; i++ {
|
// 8-bit precision
|
||||||
<-c
|
temp := image.NewRGBA(image.Rect(0, 0, input.Bounds().Dy(), int(width)))
|
||||||
}
|
result := image.NewRGBA(image.Rect(0, 0, int(width), int(height)))
|
||||||
|
|
||||||
return resultImg
|
// horizontal filter, results in transposed temporary image
|
||||||
|
coeffs, filterLength := createWeights8(temp.Bounds().Dy(), input.Bounds().Min.X, taps, blur, scaleX, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(temp, i, cpus).(*image.RGBA)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeRGBA(input, slice, scaleX, coeffs, filterLength)
|
||||||
|
}()
|
||||||
}
|
}
|
||||||
|
wg.Wait()
|
||||||
|
|
||||||
// Resize a rectangle image slice
|
// horizontal filter on transposed image, result is not transposed
|
||||||
func resizeSlice(input image.Image, output *image.RGBA64, interp InterpolationFunction, scale, adjust, xoffset float32, yoffset int, slice image.Rectangle, c chan int) {
|
coeffs, filterLength = createWeights8(result.Bounds().Dy(), temp.Bounds().Min.X, taps, blur, scaleY, kernel)
|
||||||
filter := interp(input, float32(clampFactor(scale)))
|
wg.Add(cpus)
|
||||||
var u float32
|
for i := 0; i < cpus; i++ {
|
||||||
var color color.RGBA64
|
slice := makeSlice(result, i, cpus).(*image.RGBA)
|
||||||
for y := slice.Min.Y; y < slice.Max.Y; y++ {
|
go func() {
|
||||||
u = scale*(float32(y)+adjust) + xoffset
|
defer wg.Done()
|
||||||
filter.SetKernelWeights(u)
|
resizeRGBA(temp, slice, scaleY, coeffs, filterLength)
|
||||||
for x := slice.Min.X; x < slice.Max.X; x++ {
|
}()
|
||||||
color = filter.Interpolate(u, x+yoffset)
|
}
|
||||||
i := output.PixOffset(x, y)
|
wg.Wait()
|
||||||
output.Pix[i+0] = uint8(color.R >> 8)
|
return result
|
||||||
output.Pix[i+1] = uint8(color.R)
|
case *image.YCbCr:
|
||||||
output.Pix[i+2] = uint8(color.G >> 8)
|
// 8-bit precision
|
||||||
output.Pix[i+3] = uint8(color.G)
|
// accessing the YCbCr arrays in a tight loop is slow.
|
||||||
output.Pix[i+4] = uint8(color.B >> 8)
|
// converting the image before filtering will improve performance.
|
||||||
output.Pix[i+5] = uint8(color.B)
|
inputAsRGBA := convertYCbCrToRGBA(input)
|
||||||
output.Pix[i+6] = uint8(color.A >> 8)
|
temp := image.NewRGBA(image.Rect(0, 0, input.Bounds().Dy(), int(width)))
|
||||||
output.Pix[i+7] = uint8(color.A)
|
result := image.NewRGBA(image.Rect(0, 0, int(width), int(height)))
|
||||||
|
|
||||||
|
// horizontal filter, results in transposed temporary image
|
||||||
|
coeffs, filterLength := createWeights8(temp.Bounds().Dy(), input.Bounds().Min.X, taps, blur, scaleX, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(temp, i, cpus).(*image.RGBA)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeRGBA(inputAsRGBA, slice, scaleX, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
|
||||||
|
// horizontal filter on transposed image, result is not transposed
|
||||||
|
coeffs, filterLength = createWeights8(result.Bounds().Dy(), temp.Bounds().Min.X, taps, blur, scaleY, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(result, i, cpus).(*image.RGBA)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeRGBA(temp, slice, scaleY, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
return result
|
||||||
|
case *image.RGBA64:
|
||||||
|
// 16-bit precision
|
||||||
|
temp := image.NewRGBA64(image.Rect(0, 0, input.Bounds().Dy(), int(width)))
|
||||||
|
result := image.NewRGBA64(image.Rect(0, 0, int(width), int(height)))
|
||||||
|
|
||||||
|
// horizontal filter, results in transposed temporary image
|
||||||
|
coeffs, filterLength := createWeights16(temp.Bounds().Dy(), input.Bounds().Min.X, taps, blur, scaleX, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(temp, i, cpus).(*image.RGBA64)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeRGBA64(input, slice, scaleX, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
|
||||||
|
// horizontal filter on transposed image, result is not transposed
|
||||||
|
coeffs, filterLength = createWeights16(result.Bounds().Dy(), temp.Bounds().Min.X, taps, blur, scaleY, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(result, i, cpus).(*image.RGBA64)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeGeneric(temp, slice, scaleY, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
return result
|
||||||
|
case *image.Gray:
|
||||||
|
// 8-bit precision
|
||||||
|
temp := image.NewGray(image.Rect(0, 0, input.Bounds().Dy(), int(width)))
|
||||||
|
result := image.NewGray(image.Rect(0, 0, int(width), int(height)))
|
||||||
|
|
||||||
|
// horizontal filter, results in transposed temporary image
|
||||||
|
coeffs, filterLength := createWeights8(temp.Bounds().Dy(), input.Bounds().Min.X, taps, blur, scaleX, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(temp, i, cpus).(*image.Gray)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeGray(input, slice, scaleX, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
|
||||||
|
// horizontal filter on transposed image, result is not transposed
|
||||||
|
coeffs, filterLength = createWeights8(result.Bounds().Dy(), temp.Bounds().Min.X, taps, blur, scaleY, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(result, i, cpus).(*image.Gray)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeGray(temp, slice, scaleY, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
return result
|
||||||
|
case *image.Gray16:
|
||||||
|
// 16-bit precision
|
||||||
|
temp := image.NewGray16(image.Rect(0, 0, input.Bounds().Dy(), int(width)))
|
||||||
|
result := image.NewGray16(image.Rect(0, 0, int(width), int(height)))
|
||||||
|
|
||||||
|
// horizontal filter, results in transposed temporary image
|
||||||
|
coeffs, filterLength := createWeights16(temp.Bounds().Dy(), input.Bounds().Min.X, taps, blur, scaleX, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(temp, i, cpus).(*image.Gray16)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeGray16(input, slice, scaleX, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
|
||||||
|
// horizontal filter on transposed image, result is not transposed
|
||||||
|
coeffs, filterLength = createWeights16(result.Bounds().Dy(), temp.Bounds().Min.X, taps, blur, scaleY, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(result, i, cpus).(*image.Gray16)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeGray16(temp, slice, scaleY, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
return result
|
||||||
|
default:
|
||||||
|
// 16-bit precision
|
||||||
|
temp := image.NewRGBA64(image.Rect(0, 0, img.Bounds().Dy(), int(width)))
|
||||||
|
result := image.NewRGBA64(image.Rect(0, 0, int(width), int(height)))
|
||||||
|
|
||||||
|
// horizontal filter, results in transposed temporary image
|
||||||
|
coeffs, filterLength := createWeights16(temp.Bounds().Dy(), img.Bounds().Min.X, taps, blur, scaleX, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(temp, i, cpus).(*image.RGBA64)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeGeneric(img, slice, scaleX, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
|
||||||
|
// horizontal filter on transposed image, result is not transposed
|
||||||
|
coeffs, filterLength = createWeights16(result.Bounds().Dy(), temp.Bounds().Min.X, taps, blur, scaleY, kernel)
|
||||||
|
wg.Add(cpus)
|
||||||
|
for i := 0; i < cpus; i++ {
|
||||||
|
slice := makeSlice(result, i, cpus).(*image.RGBA64)
|
||||||
|
go func() {
|
||||||
|
defer wg.Done()
|
||||||
|
resizeRGBA64(temp, slice, scaleY, coeffs, filterLength)
|
||||||
|
}()
|
||||||
|
}
|
||||||
|
wg.Wait()
|
||||||
|
return result
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
c <- 1
|
// Calculates scaling factors using old and new image dimensions.
|
||||||
}
|
func calcFactors(width, height uint, oldWidth, oldHeight float64) (scaleX, scaleY float64) {
|
||||||
|
|
||||||
// Calculate scaling factors using old and new image dimensions.
|
|
||||||
func calcFactors(width, height uint, oldWidth, oldHeight float32) (scaleX, scaleY float32) {
|
|
||||||
if width == 0 {
|
if width == 0 {
|
||||||
if height == 0 {
|
if height == 0 {
|
||||||
scaleX = 1.0
|
scaleX = 1.0
|
||||||
scaleY = 1.0
|
scaleY = 1.0
|
||||||
} else {
|
} else {
|
||||||
scaleY = oldHeight / float32(height)
|
scaleY = oldHeight / float64(height)
|
||||||
scaleX = scaleY
|
scaleX = scaleY
|
||||||
}
|
}
|
||||||
} else {
|
} else {
|
||||||
scaleX = oldWidth / float32(width)
|
scaleX = oldWidth / float64(width)
|
||||||
if height == 0 {
|
if height == 0 {
|
||||||
scaleY = scaleX
|
scaleY = scaleX
|
||||||
} else {
|
} else {
|
||||||
scaleY = oldHeight / float32(height)
|
scaleY = oldHeight / float64(height)
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
return
|
return
|
||||||
}
|
}
|
||||||
|
|
||||||
// Set filter scaling factor to avoid moire patterns.
|
type imageWithSubImage interface {
|
||||||
// This is only useful in case of downscaling (factor>1).
|
image.Image
|
||||||
func clampFactor(factor float32) float32 {
|
SubImage(image.Rectangle) image.Image
|
||||||
if factor < 1 {
|
|
||||||
factor = 1
|
|
||||||
}
|
|
||||||
return factor
|
|
||||||
}
|
}
|
||||||
|
|
||||||
// Set number of parallel jobs
|
func makeSlice(img imageWithSubImage, i, n int) image.Image {
|
||||||
// but prevent resize from doing too much work
|
return img.SubImage(image.Rect(img.Bounds().Min.X, img.Bounds().Min.Y+i*img.Bounds().Dy()/n, img.Bounds().Max.X, img.Bounds().Min.Y+(i+1)*img.Bounds().Dy()/n))
|
||||||
// if #CPUs > width
|
|
||||||
func numJobs(d int) (n int) {
|
|
||||||
n = runtime.NumCPU()
|
|
||||||
if n > d {
|
|
||||||
n = d
|
|
||||||
}
|
|
||||||
return
|
|
||||||
}
|
}
|
||||||
|
|
|
||||||
|
|
@ -14,13 +14,6 @@ func init() {
|
||||||
img.Set(1, 1, color.White)
|
img.Set(1, 1, color.White)
|
||||||
}
|
}
|
||||||
|
|
||||||
func Test_Nearest(t *testing.T) {
|
|
||||||
m := Resize(6, 0, img, NearestNeighbor)
|
|
||||||
if m.At(1, 1) == m.At(2, 2) {
|
|
||||||
t.Fail()
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func Test_Param1(t *testing.T) {
|
func Test_Param1(t *testing.T) {
|
||||||
m := Resize(0, 0, img, NearestNeighbor)
|
m := Resize(0, 0, img, NearestNeighbor)
|
||||||
if m.Bounds() != img.Bounds() {
|
if m.Bounds() != img.Bounds() {
|
||||||
|
|
@ -53,6 +46,24 @@ func Test_CorrectResize(t *testing.T) {
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
func Test_SameColor(t *testing.T) {
|
||||||
|
img := image.NewRGBA(image.Rect(0, 0, 20, 20))
|
||||||
|
for y := img.Bounds().Min.Y; y < img.Bounds().Max.Y; y++ {
|
||||||
|
for x := img.Bounds().Min.X; x < img.Bounds().Max.X; x++ {
|
||||||
|
img.SetRGBA(x, y, color.RGBA{0x80, 0x80, 0x80, 0xFF})
|
||||||
|
}
|
||||||
|
}
|
||||||
|
out := Resize(10, 10, img, Lanczos3)
|
||||||
|
for y := out.Bounds().Min.Y; y < out.Bounds().Max.Y; y++ {
|
||||||
|
for x := out.Bounds().Min.X; x < out.Bounds().Max.X; x++ {
|
||||||
|
color := img.At(x, y).(color.RGBA)
|
||||||
|
if color.R != 0x80 || color.G != 0x80 || color.B != 0x80 || color.A != 0xFF {
|
||||||
|
t.Fail()
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
func Benchmark_BigResizeLanczos3(b *testing.B) {
|
func Benchmark_BigResizeLanczos3(b *testing.B) {
|
||||||
var m image.Image
|
var m image.Image
|
||||||
for i := 0; i < b.N; i++ {
|
for i := 0; i < b.N; i++ {
|
||||||
|
|
|
||||||
49
sinc.go
49
sinc.go
|
|
@ -1,49 +0,0 @@
|
||||||
/*
|
|
||||||
Copyright (c) 2012, Jan Schlicht <jan.schlicht@gmail.com>
|
|
||||||
|
|
||||||
Permission to use, copy, modify, and/or distribute this software for any purpose
|
|
||||||
with or without fee is hereby granted, provided that the above copyright notice
|
|
||||||
and this permission notice appear in all copies.
|
|
||||||
|
|
||||||
THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
|
|
||||||
REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
|
|
||||||
FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
|
|
||||||
INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
|
|
||||||
OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
|
|
||||||
TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
|
|
||||||
THIS SOFTWARE.
|
|
||||||
*/
|
|
||||||
|
|
||||||
package resize
|
|
||||||
|
|
||||||
import (
|
|
||||||
"math"
|
|
||||||
)
|
|
||||||
|
|
||||||
var (
|
|
||||||
epsilon = math.Nextafter(1.0, 2.0) - 1.0 // machine epsilon
|
|
||||||
taylor2bound = math.Sqrt(epsilon)
|
|
||||||
taylorNbound = math.Sqrt(taylor2bound)
|
|
||||||
)
|
|
||||||
|
|
||||||
// unnormalized sinc function
|
|
||||||
func Sinc1(x float64) (y float64) {
|
|
||||||
if math.Abs(x) >= taylorNbound {
|
|
||||||
y = math.Sin(x) / x
|
|
||||||
} else {
|
|
||||||
y = 1.0
|
|
||||||
if math.Abs(x) >= epsilon {
|
|
||||||
x2 := x * x
|
|
||||||
y -= x2 / 6.0
|
|
||||||
if math.Abs(x) >= taylor2bound {
|
|
||||||
y += (x2 * x2) / 120.0
|
|
||||||
}
|
|
||||||
}
|
|
||||||
}
|
|
||||||
return
|
|
||||||
}
|
|
||||||
|
|
||||||
// normalized sinc function
|
|
||||||
func Sinc(x float64) float64 {
|
|
||||||
return Sinc1(x * math.Pi)
|
|
||||||
}
|
|
||||||
38
sinc_test.go
38
sinc_test.go
|
|
@ -1,38 +0,0 @@
|
||||||
package resize
|
|
||||||
|
|
||||||
import (
|
|
||||||
"fmt"
|
|
||||||
"math"
|
|
||||||
"testing"
|
|
||||||
)
|
|
||||||
|
|
||||||
const limit = 1e-12
|
|
||||||
|
|
||||||
func Test_SincOne(t *testing.T) {
|
|
||||||
zero := Sinc(1)
|
|
||||||
if zero >= limit {
|
|
||||||
t.Error("Sinc(1) != 0")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func Test_SincZero(t *testing.T) {
|
|
||||||
one := Sinc(0)
|
|
||||||
if math.Abs(one-1) >= limit {
|
|
||||||
t.Error("Sinc(0) != 1")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func Test_SincDotOne(t *testing.T) {
|
|
||||||
res := Sinc(0.1)
|
|
||||||
if math.Abs(res-0.983631643083466) >= limit {
|
|
||||||
t.Error("Sinc(0.1) wrong")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
|
|
||||||
func Test_SincNearZero(t *testing.T) {
|
|
||||||
res := Sinc(0.000001)
|
|
||||||
if math.Abs(res-0.9999999999983551) >= limit {
|
|
||||||
fmt.Println(res)
|
|
||||||
t.Error("Sinc near zero not stable")
|
|
||||||
}
|
|
||||||
}
|
|
||||||
Loading…
Reference in New Issue
Block a user