// Flip mirrors an image in x and y. func Flip(f *rimg64.Image) *rimg64.Image { g := rimg64.New(f.Width, f.Height) for i := 0; i < f.Width; i++ { for j := 0; j < f.Height; j++ { g.Set(f.Width-1-i, f.Height-1-j, f.At(i, j)) } } return g }
func square(f *rimg64.Image) *rimg64.Image { g := rimg64.New(f.Width, f.Height) for i := 0; i < f.Width; i++ { for j := 0; j < f.Height; j++ { g.Set(i, j, sqr(f.At(i, j))) } } return g }
// 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 }
// CorrBankStrideBLAS 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 CorrBankStrideBLAS(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)) // Size of filters. m, n := g.Width, g.Height // 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) { 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(stride*u+i, stride*v+j)) s++ } } r++ } } } x := blas.NewMat(m*n, h.Channels) { 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 }
// Decimate takes every r-th sample starting at (0, 0). func Decimate(f *rimg64.Image, r int) *rimg64.Image { out := ceilDivPt(f.Size(), r) g := rimg64.New(out.X, out.Y) for i := 0; i < g.Width; i++ { for j := 0; j < g.Height; j++ { g.Set(i, j, f.At(r*i, r*j)) } } return g }
func copyImageTo(x *fftw.Array2, f *rimg64.Image) { w, h := x.Dims() for u := 0; u < w; u++ { for v := 0; v < h; v++ { if u < f.Width && v < f.Height { x.Set(u, v, complex(f.At(u, v), 0)) } else { x.Set(u, v, 0) } } } }
// CorrStrideBLAS computes the strided correlation of an image with a filter. // h[u, v] = (f corr g)[stride*u, stride*v] func CorrStrideBLAS(f, g *rimg64.Image, stride int) (*rimg64.Image, error) { out := ValidSizeStride(f.Size(), g.Size(), stride) if out.X <= 0 || out.Y <= 0 { return nil, nil } h := rimg64.New(out.X, out.Y) // Size of filters. m, n := g.Width, g.Height // Express as dense matrix multiplication. // h[u, v] = (f corr g)[stride*u, stride*v] // y(h) = A(f) x(g) // where A is wh by mn // with w = ceil[(M-m+1)/stride], // h = ceil[(N-n+1)/stride]. a := blas.NewMat(h.Width*h.Height, 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(stride*u+i, stride*v+j)) s++ } } r++ } } } x := blas.NewMat(m*n, 1) { var r int for i := 0; i < g.Width; i++ { for j := 0; j < g.Height; j++ { x.Set(r, 0, g.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++ { h.Set(u, v, y.At(r, 0)) r++ } } } return h, nil }
func invNorm(f *rimg64.Image) float64 { var norm float64 for i := 0; i < f.Width; i++ { for j := 0; j < f.Height; j++ { norm += sqr(f.At(i, j)) } } norm = math.Sqrt(norm) // This will never be negative. if norm == 0 { return 0 } return 1 / norm }
func errIfNotEqImage(f, g *rimg64.Image, eps float64) error { if !f.Size().Eq(g.Size()) { return fmt.Errorf("different size: %v, %v", f.Size(), g.Size()) } for i := 0; i < f.Width; i++ { for j := 0; j < f.Height; j++ { a, b := f.At(i, j), g.At(i, j) if math.Abs(a-b) > eps*math.Max(math.Abs(a), math.Abs(b)) { return fmt.Errorf("different at x %d, y %d: %g, %g", i, j, a, b) } } } return nil }
// dst[i, j] = src[i*stride + offset.X, j*stride + offset.Y], // or zero if this is outside the boundary. func copyStrideTo(dst *fftw.Array2, src *rimg64.Image, stride int, offset image.Point) { m, n := dst.Dims() bnds := image.Rect(0, 0, src.Width, src.Height) for i := 0; i < m; i++ { for j := 0; j < n; j++ { p := image.Pt(i, j).Mul(stride).Add(offset) var val complex128 if p.In(bnds) { val = complex(src.At(p.X, p.Y), 0) } dst.Set(i, j, val) } } }
// Tests whether (u, v) is a local maximum. // Pixels at the edge can be maxima. func notLocalMax(r *rimg64.Image, u, v int) bool { uv := r.At(u, v) if u > 0 && r.At(u-1, v) > uv { return true } if u < r.Width-1 && r.At(u+1, v) > uv { return true } if v > 0 && r.At(u, v-1) > uv { return true } if v < r.Height-1 && r.At(u, v+1) > uv { return true } return false }
// CorrStrideNaive computes the strided correlation of an image with a filter. // h[u, v] = (f corr g)[stride*u, stride*v] func CorrStrideNaive(f, g *rimg64.Image, stride int) (*rimg64.Image, error) { out := ValidSizeStride(f.Size(), g.Size(), stride) h := rimg64.New(out.X, out.Y) for i := 0; i < h.Width; i++ { for j := 0; j < h.Height; j++ { var total float64 for u := 0; u < g.Width; u++ { for v := 0; v < g.Height; v++ { p := image.Pt(i, j).Mul(stride).Add(image.Pt(u, v)) total += f.At(p.X, p.Y) * g.At(u, v) } } h.Set(i, j, total) } } return h, nil }
// CorrNaive computes the correlation of an image with a filter. // h[u, v] = (f corr g)[u, v] func CorrNaive(f, g *rimg64.Image) (*rimg64.Image, error) { out := ValidSize(f.Size(), g.Size()) if out.X <= 0 || out.Y <= 0 { return nil, nil } h := rimg64.New(out.X, out.Y) for i := 0; i < out.X; i++ { for j := 0; j < out.Y; j++ { var total float64 for u := 0; u < g.Width; u++ { for v := 0; v < g.Height; v++ { total += f.At(i+u, j+v) * g.At(u, v) } } h.Set(i, j, total) } } 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 }
// 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 }
func adjSum(f *rimg64.Image, x1, y1, x2, y2 int) float64 { return f.At(x1, y1) + f.At(x1, y2) + f.At(x2, y1) + f.At(x2, y2) }
// Avoids f.Set(x, y, f.Get(x, y, ...)). func addTo(f *rimg64.Image, x, y int, v float64) { f.Set(x, y, f.At(x, y)+v) }