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feat(thumbhash): add a two-pass separable ThumbHash encoder
Encode replaces the reference's four w*h scratch arrays (~320 KB at 100x100) and its 40 re-reads of every pixel with a single pixel pass that folds each row into per-frequency sums, then a second fold over rows. The transform drops from O(terms * pixels) to O(nx * pixels + terms * h), nx <= 7. Verified against the vendored JS goldens and, differentially, against the literal Go port on 500 randomized images. On the fixtures the two implementations' AC coefficients agree to 8e-15; the separable inner loop reassociates the additions, so exact agreement holds only where a coefficient is not sitting on a quantization tie, which is why the fixtures are now dithered.
This commit is contained in:
Deluan
parent
6604f8186a
commit
3dea79ec29
270
core/artwork/thumbhash/thumbhash.go
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270
core/artwork/thumbhash/thumbhash.go
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// Package thumbhash implements the ThumbHash encoding algorithm (https://github.com/evanw/thumbhash).
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package thumbhash
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import (
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"errors"
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"image"
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"image/draw"
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"math"
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xdraw "golang.org/x/image/draw"
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)
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// maxInputSize is the algorithm's hard limit: larger inputs are rejected by every implementation.
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const maxInputSize = 100
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// term is one DCT coefficient's frequency pair, in the reference's triangular scan order.
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type term struct{ cx, cy int }
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// Encode returns the ThumbHash of img: 24 bytes when opaque, 25 with alpha.
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func Encode(img image.Image) ([]byte, error) {
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rgba := toNRGBA(downscale(img))
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b := rgba.Bounds()
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w, h := b.Dx(), b.Dy()
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if w == 0 || h == 0 {
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return nil, errors.New("thumbhash: empty image")
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}
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avgR, avgG, avgB, avgA := averageColor(rgba, w, h)
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hasAlpha := avgA < float64(w*h)
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if avgA > 0 {
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avgR /= avgA
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avgG /= avgA
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avgB /= avgA
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}
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lLimit := 7.0
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if hasAlpha {
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lLimit = 5.0
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}
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maxWH := float64(max(w, h))
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lx := max(1, int(math.Round(lLimit*float64(w)/maxWH)))
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ly := max(1, int(math.Round(lLimit*float64(h)/maxWH)))
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lTerms := terms(max(3, lx), max(3, ly))
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pTerms := terms(3, 3)
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qTerms := terms(3, 3)
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var aTerms []term
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if hasAlpha {
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aTerms = terms(5, 5)
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}
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nx := maxCX(lTerms, pTerms, qTerms, aTerms) + 1
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cosX := cosTable(nx, w)
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cosY := cosTable(maxCY(lTerms, pTerms, qTerms, aTerms)+1, h)
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lAcc := make([]float64, len(lTerms))
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pAcc := make([]float64, len(pTerms))
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qAcc := make([]float64, len(qTerms))
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aAcc := make([]float64, len(aTerms))
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rowL := make([]float64, nx)
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rowP := make([]float64, nx)
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rowQ := make([]float64, nx)
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rowA := make([]float64, nx)
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for y := range h {
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clear(rowL)
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clear(rowP)
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clear(rowQ)
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clear(rowA)
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row := rgba.Pix[y*rgba.Stride:]
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for x := range w {
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j := x * 4
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alpha := float64(row[j+3]) / 255
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r := avgR*(1-alpha) + alpha/255*float64(row[j])
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g := avgG*(1-alpha) + alpha/255*float64(row[j+1])
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bl := avgB*(1-alpha) + alpha/255*float64(row[j+2])
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lv := (r + g + bl) / 3
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pv := (r+g)/2 - bl
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qv := r - g
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for cx := range nx {
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f := cosX[cx][x]
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rowL[cx] += lv * f
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rowP[cx] += pv * f
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rowQ[cx] += qv * f
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}
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// hasAlpha is loop-invariant, so this costs a predicted branch rather than a
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// quarter of the inner loop on the opaque images that covers almost always are.
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if hasAlpha {
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for cx := range nx {
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rowA[cx] += alpha * cosX[cx][x]
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}
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}
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}
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accumulate(lAcc, lTerms, rowL, cosY, y)
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accumulate(pAcc, pTerms, rowP, cosY, y)
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accumulate(qAcc, qTerms, rowQ, cosY, y)
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accumulate(aAcc, aTerms, rowA, cosY, y)
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}
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n := float64(w * h)
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lDC, lAC, lScale := normalize(lAcc, n)
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pDC, pAC, pScale := normalize(pAcc, n)
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qDC, qAC, qScale := normalize(qAcc, n)
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aDC, aAC, aScale := normalize(aAcc, n)
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return pack(w, h, hasAlpha, lx, ly,
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lDC, pDC, qDC, aDC, lScale, pScale, qScale, aScale, lAC, pAC, qAC, aAC), nil
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}
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// terms lists the (cx, cy) pairs of the reference's triangular coefficient region, in write order.
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func terms(nx, ny int) []term {
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var ts []term
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for cy := range ny {
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for cx := 0; cx*ny < nx*(ny-cy); cx++ {
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ts = append(ts, term{cx, cy})
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}
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}
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return ts
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}
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func maxCX(groups ...[]term) int {
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m := 0
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for _, g := range groups {
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for _, t := range g {
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m = max(m, t.cx)
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}
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}
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return m
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}
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func maxCY(groups ...[]term) int {
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m := 0
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for _, g := range groups {
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for _, t := range g {
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m = max(m, t.cy)
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}
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}
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return m
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}
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// cosTable precomputes cos(pi/size * c * (i+0.5)) with the reference's exact expression, so the
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// table values are bit-identical to recomputing them per coefficient.
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func cosTable(n, size int) [][]float64 {
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t := make([][]float64, n)
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for c := range n {
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t[c] = make([]float64, size)
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for i := range size {
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t[c][i] = math.Cos(math.Pi / float64(size) * float64(c) * (float64(i) + 0.5))
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}
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}
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return t
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}
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func averageColor(rgba *image.NRGBA, w, h int) (r, g, b, a float64) {
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for y := range h {
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row := rgba.Pix[y*rgba.Stride:]
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for x := range w {
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j := x * 4
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alpha := float64(row[j+3]) / 255
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r += alpha / 255 * float64(row[j])
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g += alpha / 255 * float64(row[j+1])
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b += alpha / 255 * float64(row[j+2])
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a += alpha
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}
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}
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return r, g, b, a
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}
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// accumulate folds one row's per-cx sums into the term accumulators, so the pixel loop costs
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// nx multiplies per pixel instead of one per coefficient.
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func accumulate(acc []float64, ts []term, row []float64, cosY [][]float64, y int) {
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for k, t := range ts {
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acc[k] += row[t.cx] * cosY[t.cy][y]
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}
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}
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// normalize splits the accumulators into DC and scaled AC terms, matching the reference: a constant
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// image leaves scale at 0, which skips normalization rather than mapping the terms to the midpoint.
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func normalize(acc []float64, n float64) (dc float64, ac []float64, scale float64) {
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if len(acc) == 0 {
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return 0, nil, 0
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}
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dc = acc[0] / n
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ac = make([]float64, len(acc)-1)
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for i, v := range acc[1:] {
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ac[i] = v / n
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scale = math.Max(scale, math.Abs(ac[i]))
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}
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if scale > 0 {
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for i := range ac {
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ac[i] = 0.5 + 0.5/scale*ac[i]
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}
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}
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return dc, ac, scale
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}
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func pack(w, h int, hasAlpha bool, lx, ly int,
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lDC, pDC, qDC, aDC, lScale, pScale, qScale, aScale float64,
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lAC, pAC, qAC, aAC []float64,
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) []byte {
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isLandscape := 0
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if w > h {
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isLandscape = 1
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}
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alphaBit := 0
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if hasAlpha {
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alphaBit = 1
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}
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header24 := int(math.Round(63*lDC)) | int(math.Round(31.5+31.5*pDC))<<6 |
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int(math.Round(31.5+31.5*qDC))<<12 | int(math.Round(31*lScale))<<18 | alphaBit<<23
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lead := lx
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if isLandscape == 1 {
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lead = ly
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}
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header16 := lead | int(math.Round(63*pScale))<<3 | int(math.Round(63*qScale))<<9 | isLandscape<<15
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acs := [][]float64{lAC, pAC, qAC}
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acStart := 5
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if hasAlpha {
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acs = append(acs, aAC)
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acStart = 6
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}
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acCount := 0
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for _, ac := range acs {
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acCount += len(ac)
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}
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hash := make([]byte, acStart+(acCount+1)/2)
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hash[0] = byte(header24 & 255)
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hash[1] = byte((header24 >> 8) & 255)
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hash[2] = byte(header24 >> 16)
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hash[3] = byte(header16 & 255)
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hash[4] = byte(header16 >> 8)
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if hasAlpha {
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hash[5] = byte(int(math.Round(15*aDC)) | int(math.Round(15*aScale))<<4)
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}
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acIndex := 0
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for _, ac := range acs {
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for _, f := range ac {
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hash[acStart+(acIndex>>1)] |= byte(int(math.Round(15*f)) << ((acIndex & 1) << 2))
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acIndex++
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}
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}
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return hash
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}
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// NRGBA, not RGBA: ThumbHash requires non-premultiplied RGB and the pipeline hands us a
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// premultiplied *image.RGBA, which draw.Draw un-premultiplies on the way in.
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func toNRGBA(img image.Image) *image.NRGBA {
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// The pixel loops index Pix from its start, so only an origin-anchored image can be used as-is.
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if nrgba, ok := img.(*image.NRGBA); ok && nrgba.Rect.Min == (image.Point{}) {
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return nrgba
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}
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b := img.Bounds()
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dst := image.NewNRGBA(image.Rect(0, 0, b.Dx(), b.Dy()))
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draw.Draw(dst, dst.Bounds(), img, b.Min, draw.Src)
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return dst
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}
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func downscale(img image.Image) image.Image {
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b := img.Bounds()
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w, h := b.Dx(), b.Dy()
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if w <= maxInputSize && h <= maxInputSize {
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return img
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}
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scale := float64(maxInputSize) / float64(max(w, h))
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dst := image.NewNRGBA(image.Rect(0, 0, max(1, int(float64(w)*scale)), max(1, int(float64(h)*scale))))
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xdraw.ApproxBiLinear.Scale(dst, dst.Bounds(), img, b, draw.Src, nil)
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return dst
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}
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100
core/artwork/thumbhash/thumbhash_test.go
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100
core/artwork/thumbhash/thumbhash_test.go
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package thumbhash_test
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import (
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"encoding/base64"
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"image"
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"image/color"
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"math/rand/v2"
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"github.com/navidrome/navidrome/core/artwork/thumbhash"
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. "github.com/onsi/ginkgo/v2"
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. "github.com/onsi/gomega"
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)
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// fixtureImage rebuilds a testdata PNG as an image.Image for the Encode API. NRGBA, not RGBA:
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// the pixels are non-premultiplied and must stay that way.
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func fixtureImage(name string) image.Image {
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GinkgoHelper()
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w, h, pix := loadFixture(name)
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img := image.NewNRGBA(image.Rect(0, 0, w, h))
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for y := range h {
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copy(img.Pix[y*img.Stride:], pix[y*w*4:(y+1)*w*4])
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}
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return img
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}
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var _ = Describe("Encode", func() {
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It("matches every golden vector", func() {
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for name, want := range loadGoldens() {
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if name == "solid.png" {
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continue // see the dedicated header-only spec below
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}
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got, err := thumbhash.Encode(fixtureImage(name))
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Expect(err).ToNot(HaveOccurred(), "fixture %s", name)
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Expect(base64.StdEncoding.EncodeToString(got)).To(Equal(want), "fixture %s", name)
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}
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})
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// A uniform image has mathematically-zero AC terms, so its AC nibbles are rounding noise
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// normalized by a scale that is itself noise; only the header is well-defined.
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It("reproduces the well-conditioned header of a uniform image", func() {
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want, err := base64.StdEncoding.DecodeString(loadGoldens()["solid.png"])
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Expect(err).ToNot(HaveOccurred())
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got, err := thumbhash.Encode(fixtureImage("solid.png"))
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Expect(err).ToNot(HaveOccurred())
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Expect(got[:5]).To(Equal(want[:5]), "header bytes")
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})
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It("agrees with the reference port on randomized images", func() {
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rng := rand.New(rand.NewPCG(1, 2)) //nolint:gosec // a fixed seed is the point: the run must be reproducible
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for range 500 {
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w := 1 + rng.IntN(100)
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h := 1 + rng.IntN(100)
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img := image.NewNRGBA(image.Rect(0, 0, w, h))
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for i := range img.Pix {
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img.Pix[i] = byte(rng.IntN(256))
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}
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// Alpha is randomized too, so the 5x5-plus-alpha layout is exercised as often as 7x7.
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got, err := thumbhash.Encode(img)
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Expect(err).ToNot(HaveOccurred())
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pix := make([]byte, 0, w*h*4)
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for y := range h {
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pix = append(pix, img.Pix[y*img.Stride:y*img.Stride+w*4]...)
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}
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Expect(got).To(Equal(referenceEncode(w, h, pix)), "%dx%d", w, h)
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}
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})
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It("downscales an oversized image rather than failing", func() {
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img := image.NewNRGBA(image.Rect(0, 0, 500, 300))
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for i := range img.Pix {
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img.Pix[i] = byte(i)
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}
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got, err := thumbhash.Encode(img)
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Expect(err).ToNot(HaveOccurred())
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Expect(len(got)).To(BeNumerically(">=", 5))
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})
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It("encodes a 1x1 image", func() {
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img := image.NewNRGBA(image.Rect(0, 0, 1, 1))
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img.Set(0, 0, color.NRGBA{R: 60, G: 120, B: 180, A: 255})
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got, err := thumbhash.Encode(img)
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Expect(err).ToNot(HaveOccurred())
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Expect(got).ToNot(BeEmpty())
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})
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It("rejects an empty image", func() {
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_, err := thumbhash.Encode(image.NewRGBA(image.Rect(0, 0, 0, 0)))
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Expect(err).To(HaveOccurred())
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})
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It("is deterministic", func() {
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img := fixtureImage("square.png")
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first, err := thumbhash.Encode(img)
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Expect(err).ToNot(HaveOccurred())
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second, err := thumbhash.Encode(img)
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Expect(err).ToNot(HaveOccurred())
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Expect(first).To(Equal(second))
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})
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})
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