// 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
}
// CorrMultiBankFFT computes the correlation of
// a multi-channel image with a multi-channel filter.
// h[u, v] = sum_p (f_p corr g_p)[u, v]
func CorrMultiFFT(f, g *rimg64.Multi) (*rimg64.Image, error) {
if err := errIfChannelsNotEq(f, g); err != nil {
panic(err)
}
out := ValidSize(f.Size(), g.Size())
if out.Eq(image.ZP) {
return nil, nil
}
work, _ := FFT2Size(f.Size())
fhat := fftw.NewArray2(work.X, work.Y)
ghat := fftw.NewArray2(work.X, work.Y)
ffwd := fftw.NewPlan2(fhat, fhat, fftw.Forward, fftw.Estimate)
defer ffwd.Destroy()
gfwd := fftw.NewPlan2(ghat, ghat, fftw.Forward, fftw.Estimate)
defer gfwd.Destroy()
hhat := fftw.NewArray2(work.X, work.Y)
for p := 0; p < f.Channels; p++ {
// Take transform of each channel.
copyChannelTo(fhat, f, p)
ffwd.Execute()
copyChannelTo(ghat, g, p)
gfwd.Execute()
addMul(hhat, ghat, fhat)
}
n := float64(work.X * work.Y)
scale(complex(1/n, 0), hhat)
fftw.IFFT2To(hhat, hhat)
h := rimg64.New(out.X, out.Y)
copyRealTo(h, hhat)
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
}
// CorrMultiStrideFFT computes the correlation of
// a multi-channel image with a multi-channel filter.
// h[u, v] = sum_q (f_q corr g_q)[u, v]
func CorrMultiStrideFFT(f, g *rimg64.Multi, stride int) (*rimg64.Image, error) {
if err := errIfChannelsNotEq(f, g); err != nil {
panic(err)
}
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 each channel 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()
ghat := fftw.NewArray2(work.X, work.Y)
gfwd := fftw.NewPlan2(ghat, ghat, fftw.Forward, fftw.Estimate)
defer gfwd.Destroy()
// Normalization factor.
alpha := complex(1/float64(work.X*work.Y), 0)
// Add the convolutions over channels and strides.
hhat := fftw.NewArray2(work.X, work.Y)
for k := 0; k < f.Channels; k++ {
for i := 0; i < grid.X; i++ {
for j := 0; j < grid.Y; j++ {
// Copy each downsampled channel and take its transform.
copyChannelStrideTo(fhat, f, k, stride, image.Pt(i, j))
ffwd.Execute()
copyChannelStrideTo(ghat, g, k, stride, image.Pt(i, j))
gfwd.Execute()
addMul(hhat, ghat, fhat)
}
}
}
// Take the inverse transform.
h := rimg64.New(out.X, out.Y)
scale(alpha, hhat)
fftw.IFFT2To(hhat, hhat)
copyRealTo(h, hhat)
return h, 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
}
// CorrFFT computes the correlation of an image with a filter.
// h[u, v] = (f corr g)[u, v]
func CorrFFT(f, g *rimg64.Image) (*rimg64.Image, 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())
fhat := fftw.NewArray2(work.X, work.Y)
ghat := fftw.NewArray2(work.X, work.Y)
// Take forward transforms.
copyImageTo(fhat, f)
fftw.FFT2To(fhat, fhat)
copyImageTo(ghat, g)
fftw.FFT2To(ghat, ghat)
// Scale such that convolution theorem holds.
n := float64(work.X * work.Y)
scaleMul(fhat, complex(1/n, 0), ghat, fhat)
// Take inverse transform.
h := rimg64.New(out.X, out.Y)
fftw.IFFT2To(fhat, fhat)
copyRealTo(h, fhat)
return h, nil
}