func (phi *AdjChanNorm) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
y := rimg64.NewMulti(x.Width, x.Height, x.Channels)
r := (phi.Num - 1) / 2
for i := 0; i < x.Width; i++ {
for j := 0; j < x.Height; j++ {
k := 0
// Range over which to compute sum.
a, b := k-r, k+r+1
// Take sum excluding leading element.
var t float64
for p := 0; p < min(b, x.Channels); p++ {
t += sqr(x.At(i, j, p))
}
for ; k < x.Channels; k++ {
a, b = k-r, k+r+1
// Set element.
norm := math.Pow(phi.K+phi.Alpha*t, phi.Beta)
y.Set(i, j, k, x.At(i, j, k)/norm)
// Subtract trailing element.
if a >= 0 {
t -= sqr(x.At(i, j, a))
}
// Add leading element.
if b < x.Channels {
t += sqr(x.At(i, j, b))
}
}
}
}
return y, nil
}
func (phi SumPool) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
if phi.Field.X <= 0 || phi.Field.Y <= 0 {
err := fmt.Errorf("invalid field size: %v", phi.Field)
return nil, err
}
if phi.Stride <= 0 {
err := fmt.Errorf("invalid stride: %d", phi.Stride)
return nil, err
}
size := image.Pt(
ceilDiv(x.Width-phi.Field.X+1, phi.Stride),
ceilDiv(x.Height-phi.Field.Y+1, phi.Stride),
)
y := rimg64.NewMulti(size.X, size.Y, x.Channels)
for i := 0; i < y.Width; i++ {
for j := 0; j < y.Height; j++ {
for k := 0; k < x.Channels; k++ {
// Position in original image.
p := image.Pt(i, j).Mul(phi.Stride)
var t float64
for u := p.X; u < p.X+phi.Field.X; u++ {
for v := p.Y; v < p.Y+phi.Field.Y; v++ {
t += x.At(u, v, k)
}
}
y.Set(i, j, k, t)
}
}
}
return y, nil
}
// CorrBankFFT computes the correlation of an image with a bank of filters.
// h_p[u, v] = (f corr g_p)[u, v]
func CorrBankFFT(f *rimg64.Image, g *Bank) (*rimg64.Multi, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
// Determine optimal size for FFT.
work, _ := FFT2Size(f.Size())
// Re-use FFT of image.
fhat := fftw.NewArray2(work.X, work.Y)
copyImageTo(fhat, f)
fftw.FFT2To(fhat, fhat)
// Transform of each filter.
curr := fftw.NewArray2(work.X, work.Y)
fwd := fftw.NewPlan2(curr, curr, fftw.Forward, fftw.Estimate)
defer fwd.Destroy()
bwd := fftw.NewPlan2(curr, curr, fftw.Backward, fftw.Estimate)
defer bwd.Destroy()
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
alpha := complex(1/float64(work.X*work.Y), 0)
// For each output channel.
for p, gp := range g.Filters {
// Take FFT.
copyImageTo(curr, gp)
fwd.Execute()
// h_p[x] = (G_p corr F)[x]
// H_p[x] = conj(G_p[x]) F[x]
scaleMul(curr, alpha, curr, fhat)
bwd.Execute()
copyRealToChannel(h, p, curr)
}
return h, nil
}
// EvalFunc evaluates a function on every window in an image.
// If the input image is M x N and the window size is m x n,
// then the output is (M-m+1) x (N-n+1).
// If the window size is larger than the image size in either dimension,
// a nil image is returned with no error.
func EvalFunc(im *rimg64.Multi, size image.Point, f ScoreFunc) (*rimg64.Image, error) {
if im.Width < size.X || im.Height < size.Y {
return nil, nil
}
r := rimg64.New(im.Width-size.X+1, im.Height-size.Y+1)
x := rimg64.NewMulti(size.X, size.Y, im.Channels)
for i := 0; i < r.Width; i++ {
for j := 0; j < r.Height; j++ {
// Copy window into x.
for u := 0; u < size.X; u++ {
for v := 0; v < size.Y; v++ {
for p := 0; p < im.Channels; p++ {
x.Set(u, v, p, im.At(i+u, j+v, p))
}
}
}
y, err := f(x)
if err != nil {
return nil, err
}
r.Set(i, j, y)
}
}
return r, nil
}
// CorrMultiBankStrideBLAS computes the strided correlation of
// a multi-channel image with a bank of multi-channel filters.
// h_p[u, v] = sum_q (f_q corr g_pq)[stride*u, stride*v]
func CorrMultiBankStrideBLAS(f *rimg64.Multi, g *MultiBank, stride int) (*rimg64.Multi, error) {
out := ValidSizeStride(f.Size(), g.Size(), stride)
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
// Size of filters.
m, n, k := g.Width, g.Height, g.Channels
// Express as dense matrix multiplication.
// h_p[u, v] = sum_q (f_q corr g_pq)[u, v]
// h = A(f) X(g)
// where A is whk by mnk
// with w = ceil[(M-m+1)/stride],
// h = ceil[(N-n+1)/stride].
a := blas.NewMat(h.Width*h.Height, m*n*k)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
var s int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
a.Set(r, s, f.At(stride*u+i, stride*v+j, q))
s++
}
}
}
r++
}
}
}
x := blas.NewMat(m*n*k, h.Channels)
{
var r int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
for p := 0; p < h.Channels; p++ {
x.Set(r, p, g.Filters[p].At(i, j, q))
}
r++
}
}
}
}
y := blas.MatMul(1, a, x)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
for p := 0; p < h.Channels; p++ {
h.Set(u, v, p, y.At(r, p))
}
r++
}
}
}
return h, nil
}
// CorrBankStrideFFT computes the strided correlation of
// an image with a bank of filters.
// h_p[u, v] = (f corr g_p)[stride*u, stride*v]
func CorrBankStrideFFT(f *rimg64.Image, g *Bank, stride int) (*rimg64.Multi, error) {
out := ValidSizeStride(f.Size(), g.Size(), stride)
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
// Compute strided convolution as the sum over
// a stride x stride grid of small convolutions.
grid := image.Pt(stride, stride)
// But do not divide into a larger grid than the size of the filter.
// If the filter is smaller than the stride,
// then some pixels in the image will not affect the output.
grid.X = min(grid.X, g.Width)
grid.Y = min(grid.Y, g.Height)
// Determine the size of the sub-sampled filter.
gsub := image.Pt(ceilDiv(g.Width, grid.X), ceilDiv(g.Height, grid.Y))
// The sub-sampled size of the image should be such that
// the output size is attained.
fsub := image.Pt(out.X+gsub.X-1, out.Y+gsub.Y-1)
// Determine optimal size for FFT.
work, _ := FFT2Size(fsub)
// Cache FFT of image for convolving with multiple filters.
// Re-use plan for multiple convolutions too.
fhat := fftw.NewArray2(work.X, work.Y)
ffwd := fftw.NewPlan2(fhat, fhat, fftw.Forward, fftw.Estimate)
defer ffwd.Destroy()
// FFT for current filter.
ghat := fftw.NewArray2(work.X, work.Y)
gfwd := fftw.NewPlan2(ghat, ghat, fftw.Forward, fftw.Estimate)
defer gfwd.Destroy()
// Allocate one array per output channel.
hhat := make([]*fftw.Array2, len(g.Filters))
for k := range hhat {
hhat[k] = fftw.NewArray2(work.X, work.Y)
}
// Normalization factor.
alpha := complex(1/float64(work.X*work.Y), 0)
// Add the convolutions over channels and strides.
for i := 0; i < grid.X; i++ {
for j := 0; j < grid.Y; j++ {
// Take transform of downsampled image given offset (i, j).
copyStrideTo(fhat, f, stride, image.Pt(i, j))
ffwd.Execute()
// Take transform of each downsampled channel given offset (i, j).
for q := range hhat {
copyStrideTo(ghat, g.Filters[q], stride, image.Pt(i, j))
gfwd.Execute()
addMul(hhat[q], ghat, fhat)
}
}
}
// Take the inverse transform of each channel.
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
for q := range hhat {
scale(alpha, hhat[q])
fftw.IFFT2To(hhat[q], hhat[q])
copyRealToChannel(h, q, hhat[q])
}
return h, nil
}
func (phi *MaxPool) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
if phi.Field.X <= 0 || phi.Field.Y <= 0 {
err := fmt.Errorf("invalid field size: %v", phi.Field)
return nil, err
}
if phi.Stride <= 0 {
err := fmt.Errorf("invalid stride: %d", phi.Stride)
return nil, err
}
size := image.Pt(
ceilDiv(x.Width-phi.Field.X+1, phi.Stride),
ceilDiv(x.Height-phi.Field.Y+1, phi.Stride),
)
y := rimg64.NewMulti(size.X, size.Y, x.Channels)
for i := 0; i < y.Width; i++ {
for j := 0; j < y.Height; j++ {
for k := 0; k < x.Channels; k++ {
// Position in original image.
p := image.Pt(i, j).Mul(phi.Stride)
max := math.Inf(-1)
for u := 0; u < phi.Field.X; u++ {
for v := 0; v < phi.Field.Y; v++ {
q := p.Add(image.Pt(u, v))
max = math.Max(max, x.At(q.X, q.Y, k))
}
}
y.Set(i, j, k, max)
}
}
}
return y, nil
}
// CorrBankBLAS computes the correlation of an image with a bank of filters.
// h_p[u, v] = (f corr g_p)[u, v]
func CorrBankBLAS(f *rimg64.Image, g *Bank) (*rimg64.Multi, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
// Express as dense matrix multiplication.
// h_p[u, v] = (f corr g_q)[u, v]
// Y(h) = A(f) X(g)
// If the number of output channels is k, then
// A is (M-m+1)(N-n+1) x mn and
// X is mn x k, so that
// Y is (M-m+1)(N-n+1) x k.
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
m, n, k := g.Width, g.Height, len(g.Filters)
a := blas.NewMat(out.X*out.Y, m*n)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
var s int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
a.Set(r, s, f.At(i+u, j+v))
s++
}
}
r++
}
}
}
x := blas.NewMat(m*n, k)
{
var r int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for p := 0; p < h.Channels; p++ {
x.Set(r, p, g.Filters[p].At(i, j))
}
r++
}
}
}
y := blas.MatMul(1, a, x)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
for p := 0; p < h.Channels; p++ {
h.Set(u, v, p, y.At(r, p))
}
r++
}
}
}
return h, nil
}
func (phi *PosPart) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
y := rimg64.NewMulti(x.Width, x.Height, x.Channels)
for i := 0; i < x.Width; i++ {
for j := 0; j < x.Height; j++ {
for k := 0; k < x.Channels; k++ {
y.Set(i, j, k, math.Max(0, x.At(i, j, k)))
}
}
}
return y, nil
}
// FlipMulti mirrors a multi-channel image in x and y.
func FlipMulti(f *rimg64.Multi) *rimg64.Multi {
g := rimg64.NewMulti(f.Width, f.Height, f.Channels)
for i := 0; i < f.Width; i++ {
for j := 0; j < f.Height; j++ {
for k := 0; k < f.Channels; k++ {
g.Set(f.Width-1-i, f.Height-1-j, k, f.At(i, j, k))
}
}
}
return g
}
func randMulti(width, height, channels int) *rimg64.Multi {
f := rimg64.NewMulti(width, height, channels)
for i := 0; i < width; i++ {
for j := 0; j < height; j++ {
for k := 0; k < channels; k++ {
f.Set(i, j, k, rand.NormFloat64())
}
}
}
return f
}
func (phi *ChannelInterval) Apply(f *rimg64.Multi) (*rimg64.Multi, error) {
g := rimg64.NewMulti(f.Width, f.Height, phi.B-phi.A)
for u := 0; u < f.Width; u++ {
for v := 0; v < f.Height; v++ {
for p := phi.A; p < phi.B; p++ {
g.Set(u, v, p-phi.A, f.At(u, v, p))
}
}
}
return g, nil
}
func (phi *SelectChannels) Apply(f *rimg64.Multi) (*rimg64.Multi, error) {
g := rimg64.NewMulti(f.Width, f.Height, len(phi.Set))
for u := 0; u < f.Width; u++ {
for v := 0; v < f.Height; v++ {
for i, p := range phi.Set {
g.Set(u, v, i, f.At(u, v, p))
}
}
}
return g, nil
}
func (phi *Scale) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
y := rimg64.NewMulti(x.Width, x.Height, x.Channels)
for u := 0; u < x.Width; u++ {
for v := 0; v < x.Height; v++ {
for p := 0; p < x.Channels; p++ {
y.Set(u, v, p, float64(*phi)*x.At(u, v, p))
}
}
}
return y, nil
}
// DecimateMulti takes every r-th sample starting at (0, 0).
func DecimateMulti(f *rimg64.Multi, r int) *rimg64.Multi {
out := ceilDivPt(f.Size(), r)
g := rimg64.NewMulti(out.X, out.Y, f.Channels)
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for k := 0; k < g.Channels; k++ {
g.Set(i, j, k, f.At(r*i, r*j, k))
}
}
}
return g
}
func (phi *IsPos) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
y := rimg64.NewMulti(x.Width, x.Height, x.Channels)
for i := 0; i < x.Width; i++ {
for j := 0; j < x.Height; j++ {
for k := 0; k < x.Channels; k++ {
if x.At(i, j, k) > 0 {
y.Set(i, j, k, 1)
}
}
}
}
return y, nil
}
func (phi *PosNegPart) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
channels := x.Channels * 2
y := rimg64.NewMulti(x.Width, x.Height, channels)
for i := 0; i < x.Width; i++ {
for j := 0; j < x.Height; j++ {
for k := 0; k < x.Channels; k++ {
pos, neg := posNegPart(x.At(i, j, k))
y.Set(i, j, 2*k, pos)
y.Set(i, j, 2*k+1, neg)
}
}
}
return y, nil
}
func parseImageCSV(rows [][]string) (*rimg64.Multi, error) {
// Convert to numbers.
var (
u, v, w []int
f []float64
)
for _, r := range rows {
if len(r) == 0 {
continue
}
if len(r) != 4 {
panic("wrong number of elements in row")
}
ui, err := strconv.ParseInt(r[0], 10, 32)
if err != nil {
return nil, err
}
vi, err := strconv.ParseInt(r[1], 10, 32)
if err != nil {
return nil, err
}
wi, err := strconv.ParseInt(r[2], 10, 32)
if err != nil {
return nil, err
}
fi, err := strconv.ParseFloat(r[3], 64)
if err != nil {
return nil, err
}
u = append(u, int(ui))
v = append(v, int(vi))
w = append(w, int(wi))
f = append(f, fi)
}
// Take max over u, v, w.
var width, height, channels int
for i := range u {
width = max(u[i]+1, width)
height = max(v[i]+1, height)
channels = max(w[i]+1, channels)
}
// Set pixels in image.
im := rimg64.NewMulti(width, height, channels)
for i := range u {
im.Set(u[i], v[i], w[i], f[i])
}
return im, nil
}
func (phi *AddConst) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
if x.Channels != len(*phi) {
err := fmt.Errorf("channels: image has %d, filter bank has %d", x.Channels, len(*phi))
return nil, err
}
y := rimg64.NewMulti(x.Width, x.Height, x.Channels)
for u := 0; u < x.Width; u++ {
for v := 0; v < x.Height; v++ {
for p := 0; p < x.Channels; p++ {
y.Set(u, v, p, x.At(u, v, p)+(*phi)[p])
}
}
}
return y, nil
}
func (phi *ConvEach) Apply(x *rimg64.Multi) (*rimg64.Multi, error) {
channels := x.Channels * len(phi.Filters.Filters)
field := image.Pt(phi.Filters.Width, phi.Filters.Height)
size := slide.ValidSize(x.Size(), field)
y := rimg64.NewMulti(size.X, size.Y, channels)
var n int
for i := 0; i < x.Channels; i++ {
// Convolve each channel of the input with the bank.
yi, err := slide.CorrBankBLAS(x.Channel(i), phi.Filters)
if err != nil {
return nil, err
}
for j := 0; j < yi.Channels; j++ {
// Copy the channels into the output.
y.SetChannel(n, yi.Channel(j))
n++
}
}
return y, nil
}
// CorrMultiBankFFT computes the correlation of
// a multi-channel image with a bank of multi-channel filters.
// h_p[u, v] = sum_q (f_q corr g_pq)[u, v]
func CorrMultiBankFFT(f *rimg64.Multi, g *MultiBank) (*rimg64.Multi, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
// Determine optimal size for FFT.
work, _ := FFT2Size(f.Size())
// Cache FFT of each channel of image.
fhat := make([]*fftw.Array2, f.Channels)
for i := range fhat {
fhat[i] = fftw.NewArray2(work.X, work.Y)
copyChannelTo(fhat[i], f, i)
fftw.FFT2To(fhat[i], fhat[i])
}
curr := fftw.NewArray2(work.X, work.Y)
fwd := fftw.NewPlan2(curr, curr, fftw.Forward, fftw.Estimate)
defer fwd.Destroy()
sum := fftw.NewArray2(work.X, work.Y)
bwd := fftw.NewPlan2(sum, sum, fftw.Backward, fftw.Estimate)
defer bwd.Destroy()
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
alpha := complex(1/float64(work.X*work.Y), 0)
// For each output channel.
for p, gp := range g.Filters {
zero(sum)
// For each input channel.
for q := 0; q < f.Channels; q++ {
// Take FFT of this input channel.
copyChannelTo(curr, gp, q)
fwd.Execute()
// h_p[x] = (G_qp corr F_p)[x]
// H_p[x] = conj(G_qp[x]) F_p[x]
addScaleMul(sum, alpha, curr, fhat[q])
}
bwd.Execute()
copyRealToChannel(h, p, sum)
}
return h, nil
}
// CorrBankStrideNaive computes the strided correlation of
// an image with a bank of filters.
// h_p[u, v] = (f corr g_p)[stride*u, stride*v]
func CorrBankStrideNaive(f *rimg64.Image, g *Bank, stride int) (*rimg64.Multi, error) {
out := ValidSizeStride(f.Size(), g.Size(), stride)
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
for p := 0; p < h.Channels; p++ {
var sum float64
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
sum += f.At(stride*u+i, stride*v+j) * g.Filters[p].At(i, j)
}
}
h.Set(u, v, p, sum)
}
}
}
return h, nil
}
// CorrBankNaive computes the correlation of an image with a bank of filters.
// h_p[u, v] = (f corr g_p)[u, v]
func CorrBankNaive(f *rimg64.Image, g *Bank) (*rimg64.Multi, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
for p := 0; p < h.Channels; p++ {
var total float64
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
total += f.At(i+u, j+v) * g.Filters[p].At(i, j)
}
}
h.Set(u, v, p, total)
}
}
}
return h, nil
}
// Flattens 31 (or 27) channels down to 9 for visualization.
func compress(src *rimg64.Multi, weights WeightSet) *rimg64.Multi {
dst := rimg64.NewMulti(src.Width, src.Height, 9)
for i := 0; i < 27; i++ {
for x := 0; x < src.Width; x++ {
for y := 0; y < src.Height; y++ {
v := src.At(x, y, i)
switch weights {
default:
case Pos:
v = math.Max(0, v)
case Neg:
v = math.Min(0, v)
case Abs:
v = math.Abs(v)
}
dst.Set(x, y, i%9, dst.At(x, y, i%9)+v)
}
}
}
return dst
}
// CorrMultiBankStrideNaive computes the strided correlation of
// a multi-channel image with a bank of multi-channel filters.
// h_p[u, v] = sum_q (f_q corr g_pq)[stride*u, stride*v]
func CorrMultiBankStrideNaive(f *rimg64.Multi, g *MultiBank, stride int) (*rimg64.Multi, error) {
out := ValidSizeStride(f.Size(), g.Size(), stride)
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
for p := 0; p < h.Channels; p++ {
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
val := f.At(stride*u+i, stride*v+j, q) * g.Filters[p].At(i, j, q)
h.Set(u, v, p, h.At(u, v, p)+val)
}
}
}
}
}
}
return h, nil
}
func fgmr(im *rimg64.Multi, sbin int) *rimg64.Multi {
if im.Channels != 3 {
panic("Input image must have three channels")
}
if sbin < 1 {
panic("Bin size must be positive")
}
// Query size of workspace and output.
var (
dims = [3]C.int{C.int(im.Height), C.int(im.Width), 3}
cells [2]C.int
out [3]C.int
)
C.size(&dims[0], C.int(sbin), &cells[0], &out[0])
var (
// Allocate output.
hog = rimg64.NewMulti(int(out[1]), int(out[0]), int(out[2]))
// Allocate workspace.
numCells = cells[0] * cells[1]
hist = make([]C.double, 18*numCells)
norm = make([]C.double, numCells)
)
// Compute HOG features.
C.compute(
&dims[0],
(*C.double)(unsafe.Pointer(&im.Elems[0])),
(*C.double)(unsafe.Pointer(&hist[0])),
(*C.double)(unsafe.Pointer(&norm[0])),
C.int(sbin),
&cells[0],
&out[0],
(*C.double)(unsafe.Pointer(&hog.Elems[0])))
return hog
}
// CorrMultiBankNaive computes the correlation of
// a multi-channel image with a bank of multi-channel filters.
// h_p[u, v] = sum_q (f_q corr g_pq)[u, v]
func CorrMultiBankNaive(f *rimg64.Multi, g *MultiBank) (*rimg64.Multi, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
for p := 0; p < h.Channels; p++ {
var sum float64
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
sum += f.At(i+u, j+v, q) * g.Filters[p].At(i, j, q)
}
}
}
h.Set(u, v, p, sum)
}
}
}
return h, nil
}
func TestAdjChanNorm_Apply(t *testing.T) {
const eps = 1e-9
const (
k = 2
n = 5
a = 1e-4
b = 0.75
)
phi := &convfeat.AdjChanNorm{K: k, Num: n, Alpha: a, Beta: b}
elems := []float64{-1, 2, 3, 2, 1, -1, -3}
cases := []struct {
In, Out []float64
}{{
In: elems,
Out: []float64{
elems[0] / math.Pow(k+a*sumsqr(elems[:3]), b),
elems[1] / math.Pow(k+a*sumsqr(elems[:4]), b),
elems[2] / math.Pow(k+a*sumsqr(elems[:5]), b),
elems[3] / math.Pow(k+a*sumsqr(elems[1:6]), b),
elems[4] / math.Pow(k+a*sumsqr(elems[2:]), b),
elems[5] / math.Pow(k+a*sumsqr(elems[3:]), b),
elems[6] / math.Pow(k+a*sumsqr(elems[4:]), b),
},
}, {
In: elems[:6],
Out: []float64{
elems[0] / math.Pow(k+a*sumsqr(elems[:6][:3]), b),
elems[1] / math.Pow(k+a*sumsqr(elems[:6][:4]), b),
elems[2] / math.Pow(k+a*sumsqr(elems[:6][:5]), b),
elems[3] / math.Pow(k+a*sumsqr(elems[:6][1:]), b),
elems[4] / math.Pow(k+a*sumsqr(elems[:6][2:]), b),
elems[5] / math.Pow(k+a*sumsqr(elems[:6][3:]), b),
},
}, {
In: elems[:5],
Out: []float64{
elems[0] / math.Pow(k+a*sumsqr(elems[:5][:3]), b),
elems[1] / math.Pow(k+a*sumsqr(elems[:5][:4]), b),
elems[2] / math.Pow(k+a*sumsqr(elems[:5]), b),
elems[3] / math.Pow(k+a*sumsqr(elems[:5][1:]), b),
elems[4] / math.Pow(k+a*sumsqr(elems[:5][2:]), b),
},
}, {
In: elems[:3],
Out: []float64{
elems[0] / math.Pow(k+a*sumsqr(elems[:3]), b),
elems[1] / math.Pow(k+a*sumsqr(elems[:3]), b),
elems[2] / math.Pow(k+a*sumsqr(elems[:3]), b),
},
}, {
In: elems[:2],
Out: []float64{
elems[0] / math.Pow(k+a*sumsqr(elems[:2]), b),
elems[1] / math.Pow(k+a*sumsqr(elems[:2]), b),
},
}, {
In: elems[:1],
Out: []float64{
elems[0] / math.Pow(k+a*sumsqr(elems[:1]), b),
},
}}
for _, test := range cases {
f := rimg64.NewMulti(1, 1, len(test.In))
f.SetPixel(0, 0, test.In)
y, err := phi.Apply(f)
if err != nil {
t.Fatal(err)
}
for i := range test.Out {
want, got := test.Out[i], y.At(0, 0, i)
if math.Abs(want-got) > eps {
t.Errorf("with %d channels: different at %d: want %g, got %g", len(test.In), i, want, got)
}
}
}
}
// CorrMultiBankBLAS computes the correlation of
// a multi-channel image with a bank of multi-channel filters.
// h_p[u, v] = sum_q (f_q corr g_pq)[u, v]
func CorrMultiBankBLAS(f *rimg64.Multi, g *MultiBank) (*rimg64.Multi, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
// Express as dense matrix multiplication.
// h_p[u, v] = sum_q (f_q corr g_pq)[u, v]
// Y(h) = A(f) X(g)
// If the number of input and output channels are Q and P, then
// A is (M-m+1)(N-n+1) x mnQ and
// X is mnQ x P, so that
// Y is (M-m+1)(N-n+1) x P.
// Note that the time to build the system is therefore
// affected more by the number of input channels Q than outputs P.
h := rimg64.NewMulti(out.X, out.Y, len(g.Filters))
M, N, K := h.Width, h.Height, h.Channels
m, n, k := g.Width, g.Height, g.Channels
a := blas.NewMat(M*N, m*n*k)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
var s int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
a.Set(r, s, f.At(i+u, j+v, q))
s++
}
}
}
r++
}
}
}
x := blas.NewMat(m*n*k, K)
{
var r int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
for p := 0; p < h.Channels; p++ {
x.Set(r, p, g.Filters[p].At(i, j, q))
}
r++
}
}
}
}
y := blas.MatMul(1, a, x)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
for p := 0; p < h.Channels; p++ {
h.Set(u, v, p, y.At(r, p))
}
r++
}
}
}
return h, nil
}
func HOG(f *rimg64.Multi, conf Config) *rimg64.Multi {
const eps = 0.0001
// Leave a one-pixel border to compute derivatives.
inside := image.Rectangle{image.ZP, f.Size()}.Inset(1)
// Leave a half-cell border.
half := conf.CellSize / 2
valid := inside.Inset(half)
// Number of whole cells inside valid region.
cells := valid.Size().Div(conf.CellSize)
if cells.X <= 0 || cells.Y <= 0 {
return nil
}
// Remove one cell on all sides for output.
out := cells.Sub(image.Pt(2, 2))
// Region to iterate over.
size := cells.Mul(conf.CellSize).Add(image.Pt(2*half, 2*half))
vis := image.Rectangle{inside.Min, inside.Min.Add(size)}
// Accumulate edges into cell histograms.
hist := rimg64.NewMulti(cells.X, cells.Y, 2*conf.Angles)
quantizer := makeQuantizer(conf.Angles)
for a := vis.Min.X; a < vis.Max.X; a++ {
for b := vis.Min.Y; b < vis.Max.Y; b++ {
x, y := a-half-vis.Min.X, b-half-vis.Min.Y
// Pick channel with strongest gradient.
grad, v := maxGrad(f, a, b)
v = math.Sqrt(v)
// Snap to orientation.
q := quantizer.quantize(grad)
// Add to 4 histograms around pixel using bilinear interpolation.
xp := (float64(x)+0.5)/float64(conf.CellSize) - 0.5
yp := (float64(y)+0.5)/float64(conf.CellSize) - 0.5
// Extract integer and fractional part.
ixp, vx0 := modf(xp)
iyp, vy0 := modf(yp)
// Complement of fraction part.
vx1 := 1 - vx0
vy1 := 1 - vy0
if ixp >= 0 && iyp >= 0 {
addToMulti(hist, ixp, iyp, q, vx1*vy1*v)
}
if ixp+1 < cells.X && iyp >= 0 {
addToMulti(hist, ixp+1, iyp, q, vx0*vy1*v)
}
if ixp >= 0 && iyp+1 < cells.Y {
addToMulti(hist, ixp, iyp+1, q, vx1*vy0*v)
}
if ixp+1 < cells.X && iyp+1 < cells.Y {
addToMulti(hist, ixp+1, iyp+1, q, vx0*vy0*v)
}
}
}
// compute energy in each block by summing over orientations
norm := rimg64.New(cells.X, cells.Y)
for x := 0; x < cells.X; x++ {
for y := 0; y < cells.Y; y++ {
for d := 0; d < conf.Angles; d++ {
s := hist.At(x, y, d) + hist.At(x, y, d+conf.Angles)
addTo(norm, x, y, s*s)
}
}
}
feat := rimg64.NewMulti(out.X, out.Y, conf.Channels())
for x := 0; x < out.X; x++ {
for y := 0; y < out.Y; y++ {
a, b := x+1, y+1
// Normalization factors.
var n [4]float64
n[0] = 1 / math.Sqrt(adjSum(norm, a, b, a+1, b+1)+eps)
n[1] = 1 / math.Sqrt(adjSum(norm, a, b, a+1, b-1)+eps)
n[2] = 1 / math.Sqrt(adjSum(norm, a, b, a-1, b+1)+eps)
n[3] = 1 / math.Sqrt(adjSum(norm, a, b, a-1, b-1)+eps)
var off int
// Contrast-sensitive features.
if !conf.NoContrastVar {
for d := 0; d < 2*conf.Angles; d++ {
h := hist.At(a, b, d)
var sum float64
for _, ni := range n {
val := h * ni
if !conf.NoClip {
val = math.Min(val, 0.2)
}
sum += val
}
feat.Set(x, y, off+d, sum/2)
}
off += 2 * conf.Angles
}
// Contrast-insensitive features.
if !conf.NoContrastInvar {
for d := 0; d < conf.Angles; d++ {
h := hist.At(a, b, d) + hist.At(a, b, conf.Angles+d)
var sum float64
for _, ni := range n {
val := h * ni
if !conf.NoClip {
val = math.Min(val, 0.2)
}
sum += val
}
feat.Set(x, y, off+d, sum/2)
}
off += conf.Angles
}
// Texture features.
if !conf.NoTexture {
for i, ni := range n {
var sum float64
for d := 0; d < 2*conf.Angles; d++ {
h := hist.At(a, b, d)
val := h * ni
if !conf.NoClip {
val = math.Min(val, 0.2)
}
sum += val
}
feat.Set(x, y, off+i, sum/math.Sqrt(float64(2*conf.Angles)))
}
off += 4
}
}
}
return feat
}