Beispiel #1
0
// 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
}
Beispiel #2
0
// 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
}
Beispiel #3
0
// 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
}
Beispiel #4
0
// 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
}