Merge pull request #266 from maxfreu/master

improve bilinear upsampling

Author: CarloLucibello

src/upsample.jl

@@ -64,235 +64,166 @@ function ChainRulesCore.rrule(::typeof(upsample_nearest), x::AbstractArray, s::T
     return Ω, upsample_nearest_pullback
 end
 
-"""
-    upsample_bilinear(x::AbstractArray{<:Number,4}, k::NTuple{2,Int})
-
-Upsamples the first 2 dimensions of the array `x` by the upsample factors stored in `k`,
-using bilinear interpolation. 
-
-The size of the output is equal to 
-`(k[1]*S1, k[2]*S2, S3, S4)`, where `S1, S2, S3, S4 = size(x)`.
-
-The interpolation grid is identical to the one used by `imresize` from `Images.jl`.
-
-Currently only 2d upsampling is supported.
-"""
-function upsample_bilinear(x::AbstractArray{T,4}, k::NTuple{2,Int}) where T
-    # This function is gpu friendly
-    
-    imgsize = size(x)
-    newsize = get_newsize(imgsize, k)
-
-    # Get linear interpolation lower- and upper index, and weights
-    ilow1, ihigh1, wdiff1 = get_inds_and_ws(x, imgsize[1], newsize[1], 1)
-    ilow2, ihigh2, wdiff2 = get_inds_and_ws(x, imgsize[2], newsize[2], 2)
-
-    # Adjust the upper interpolation indices of the second dimension
-    ihigh2_r = adjoint_of_idx(ilow2)[ihigh2]
-
-    @inbounds y = @view(x[ilow1,ilow2,:,:]) .* (1 .- wdiff1) .+ @view(x[ihigh1,ilow2,:,:]) .* wdiff1
-    @inbounds y .= y .* (1 .- wdiff2) .+ y[:,ihigh2_r,:,:] .* wdiff2
-    # @inbounds y = y .* (1 .- wdiff2) .+ @view(y[:,ihigh2_r,:,:]) .* wdiff2 # equivalent to line above
-    return y
-end
-
-function get_inds_and_ws(x::T, n::Int, m::Int, dim::Int) where T <: AbstractArray
-    # Creates interpolation grid for resampling. 
-    # Creates the same grid as used in Image.jl `imresize`.
-    step = n // m
-    offset = (n + 1)//2 - step//2 - step * (m//2 - 1)
-    xq = clamp.(range(offset, step=step, length=m), 1, n)
-
-    # Creates interpolation lower and upper indices, and broadcastable weights
-    ilow = floor.(Int, xq)
-    ihigh = ceil.(Int, xq)
-    sizew = ntuple(i-> i == dim ? length(xq) : 1, ndims(x))
-    wdiff = convert(T, reshape(xq .- ilow, sizew)) # wdiff possibly lives on gpu
-    return ilow, ihigh, wdiff
+# utility function
+@inline function compute_source_index_and_lambda(
+    ratio, # 0 < ratio < 1
+    output_index,
+    input_size,
+    output_size
+)
+    real_input_index = ratio*output_index
+    input_index0 = floor(Int, real_input_index) # typecast to int was here in C++
+    offset = (input_index0 < input_size - 1) ? 1 : 0
+    input_index1 = input_index0 + offset
+    lambda1 = real_input_index - input_index0
+    lambda0 = 1 - lambda1
+    return input_index0, input_index1, lambda0, lambda1
 end
 
 """
-    adjoint_of_idx(idx::Vector{<:Integer})
-
-# Arguments
-- `idx`: a vector of indices from which you want the adjoint.
+    upsample_bilinear(x::AbstractArray{T,4}, scale::NTuple{2,Real})
+    upsample_bilinear(x::AbstractArray{T,4}; size::NTuple{2,Integer})
 
-# Outputs
--`idx_adjoint`: index that inverses the operation `x[idx]`.
+Upsamples the first 2 dimensions of the array `x` by the upsample factors stored in `scale`,
+using bilinear interpolation. As an alternative to using `scale`, the resulting image `size`
+can be directly specified with a keyword argument.
 
-# Explanation
-Determines the adjoint of the vector of indices `idx`, based on the following assumptions:
-* `idx[1] == 1`
-* `all(d in [0,1] for d in diff(idx))`
-The adjoint of `idx` can be seen as an inverse operation such that:
+The size of the output is equal to
+`(scale[1]*S1, scale[2]*S2, S3, S4)`, where `S1, S2, S3, S4 = size(x)`.
 
+Examples:
 ```julia
-x = [1, 2, 3, 4, 5]
-idx = [1, 2, 2, 3, 4, 4, 5]
-idx_adjoint = adjoint_of_idx(idx)
-@assert x[idx][idx_adjoint] == x
+upsample_bilinear(x, (2, pi)) # real scaling factors are allowed
+upsample_bilinear(x; size=(64,64)) # specify ouput size
 ```
-The above holds as long as `idx` contains every index in `x`.
 """
-function adjoint_of_idx(idx::Vector{Int})
-    d = trues(length(idx))
-    d[2:end] .= diff(idx)
-    idx_adjoint = findall(d)
-    return idx_adjoint
-end
-
-function get_newsize(sz, k)
-    return ntuple(i -> i <= length(k) ? sz[i]*k[i] : sz[i], length(sz))
+function upsample_bilinear(x::AbstractArray{<:Any,4}, scale::NTuple{2,Real})
+    outsize = ntuple(i -> floor(Int, scale[i] * Base.size(x, i)), 2)
+    return upsample_bilinear(x; size=outsize)
 end
 
+upsample_bilinear(x, scale::Real) = upsample_bilinear(x, (scale,scale))
 
-"""
-    ∇upsample_bilinear(Δ::AbstractArray{<:Number,4}, k::NTuple{2,Int})
-    
-# Arguments
-- `Δ`: array that has been upsampled using the upsample factors in `k`
-
-# Outputs
-- `dx`: downsampled version of `Δ`
-
-# Explanation
-
-Custom adjoint for [`upsample_bilinear`](@ref). 
-The adjoint of upsampling is a downsampling operation, which
-in this implementation is performed using `NNlib.conv` in combination with a downsampling kernel based on the
-upsampling factors. Because of the zero-padding during convolution, the values at the boundary are polluted by edge-effects,
-which have been corrected for manually.
-"""
-function ∇upsample_bilinear(Δ::AbstractArray{<:Number, 4}, k::NTuple{2,Int})
-    # This function is gpu friendly
-    
-    # Be more efficient on some corner cases
-    if size(Δ, 1) == k[1]
-        Δ = sum(Δ, dims=1)
-        k = (1, k[2])
-    end
-    if size(Δ, 2) == k[2]
-        Δ = sum(Δ, dims=2)
-        k = (k[1], 1)
+function upsample_bilinear(x::AbstractArray{T,4}; size::NTuple{2,Integer}) where T
+    w,h,c,n = Base.size(x)
+    if (w,h) == size
+        return x
     end
-    if (size(Δ, 1) == 1) && (size(Δ, 2) == 1)
-        dx = Δ
-        return dx
-    end
-
-    n_chan, n_batch = size(Δ, 3), size(Δ, 4)
-
-    kern1 = get_downsamplekernel(Δ, k[1])
-    kern2 = get_downsamplekernel(Δ, k[2])
-    kern = kern1 * kern2'
-    
-    pad = (floor(Int, k[1]//2), floor(Int, k[2]//2))
-    stride = k
-    
-    weight = similar(Δ, eltype(Δ), (size(kern)..., n_chan, n_chan))
-    weight .= 0
-    for i in 1:n_chan
-        weight[:,:,i,i] .= kern
-    end
-    # weight = cat(fill(kern, n_chan)..., dims=(3,4)) # slow
-    dx = conv(Δ, weight, pad=pad, stride=stride)
+    y = similar(x, T, size..., c, n)
+    return upsample_bilinear_whcn!(y, x)
+end
 
-    # Still have to fix edge effects due to zero-padding of convolution,
-    # TODO: Could be circumvented by having padding that just extrapolates the value at the first/last index
-    # nextras = tuple((Int.(floor(factor//2)) for factor in k)...)
-    nextras = (floor(Int, k[1]//2), floor(Int, k[2]//2))
+function upsample_bilinear(x::AbstractArray{T,4}; size::NTuple{2,Integer}) where T<:Integer
+    y = float.(x)
+    res = upsample_bilinear(y; size=size)
+    return round.(T, res)
+end
 
-    # First dimension edge-effect correction
-    if nextras[1] > 0
-        kern1 = kern[1:nextras[1],:]
-        pad1 = (0, pad[2])
-        stride1 = (1, stride[2])
-        weight1 = similar(Δ, eltype(Δ), (size(kern1)..., n_chan, n_chan))
-        weight1 .= 0
-        for i in 1:n_chan
-            weight1[:,:,i,i] .= kern1
+# this is the core function which works on arrays of arbitrary size
+# the implementation is a translation of https://github.com/pytorch/pytorch/blob/master/aten/src/ATen/native/cpu/UpSampleMoreKernel.cpp
+# which implements open-cv style linear interpolation / upsampling
+# for simplicity, corners are aligned and all logic for other behaviour has been stripped
+# - whcn because there is also a cwhn implementation
+# - the function is parallelized using @threads
+# - RGB types could be supported via reinterpreting
+# - integer types need to be converted to Float and back
+# - rationals work, but are slow
+function upsample_bilinear_whcn!(output::AbstractArray{T,4}, input::AbstractArray{T,4}) where T
+    size(input)[3:4] == size(output)[3:4] || error("Number of input and output channels and batches must match. Got input $(size(input)) and output $(size(output))")
+    in_w, in_h, channels, batches = size(input)
+    # treat batch and channel dimension as one for better parallelization granularity
+    channels *= batches
+    out_w, out_h, _, _ = size(output)
+    output_slice_size = out_h * out_w
+
+    # T() and // so that we can handle rationals (super slow)
+    width_scale  = T((in_w - 1) // (out_w - 1))
+    height_scale = T((in_h - 1) // (out_h - 1))
+
+    @inline idx(c, h, w) = c * in_h * in_w + h * in_w + w + 1
+
+    @inbounds Threads.@threads for c in 0:channels-1
+        for oh in 0:out_h-1
+            ih0, ih1, h0lambda, h1lambda = compute_source_index_and_lambda(height_scale, oh, in_h, out_h)
+            for ow in 0:out_w-1
+                iw0, iw1, w0lambda, w1lambda = compute_source_index_and_lambda(width_scale, ow, in_w, out_w)
+                output_offset = c * output_slice_size + oh * out_w + ow + 1
+                output[output_offset] =
+                    (h0lambda * w0lambda * input[idx(c, ih0, iw0)] + # h0 * w0 * i00
+                     h0lambda * w1lambda * input[idx(c, ih0, iw1)] + # h0 * w1 * i01
+                     h1lambda * w0lambda * input[idx(c, ih1, iw0)] + # h1 * w0 * i10
+                     h1lambda * w1lambda * input[idx(c, ih1, iw1)])  # h1 * w1 * i11
+            end
         end
-        # weight1 = cat(fill(kern1, n_chan)..., dims=(3,4)) # slow
-        dx[[1],:,:,:] .+= conv(Δ[1:nextras[1],:,:,:], weight1, pad=pad1, stride=stride1)
-        weight1 .= weight1[end:-1:1,:,:,:]
-        dx[[end],:,:,:] .+= conv(Δ[end-nextras[1]+1:end,:,:,:], weight1, pad=pad1, stride=stride1)
-    
-        ## Conv with views is not dispatched to CUDA.conv
-        # dx[[1],:,:,:] .+= conv(@view(Δ[1:nextras[1],:,:,:]), weight1, pad=pad1, stride=stride1)
-        # weight1 .= @view(weight1[end:-1:1,:,:,:])
-        # dx[[end],:,:,:] .+= conv(@view(Δ[end-nextras[1]+1:end,:,:,:]), weight1, pad=pad1, stride=stride1)
     end
+    return output
+end
 
-    # Second dimension edge-effect correction
-    if nextras[2] > 0
-        kern2 = kern[:,1:nextras[2]]
-        pad2 = (pad[1], 0)
-        stride2 = (stride[1], 1)
-        weight2 = similar(Δ, eltype(Δ), (size(kern2)..., n_chan, n_chan))
-        weight2 .= 0
-        for i in 1:n_chan
-            weight2[:,:,i,i] .= kern2
-        end
-        # weight2 = cat(fill(kern2, n_chan)..., dims=(3,4)) # slow
-    
-        yy = conv(Δ[:,1:nextras[2],:,:], weight2, pad=pad2, stride=stride2)
-        dx[:,[1],:,:] .+= conv(Δ[:,1:nextras[2],:,:], weight2, pad=pad2, stride=stride2)
-        weight2 .= weight2[:,end:-1:1,:,:]
-        dx[:,[end],:,:] .+= conv(Δ[:,end-nextras[2]+1:end,:,:], weight2, pad=pad2, stride=stride2)
+"""
+    ∇upsample_bilinear(Δ::AbstractArray{T,4}; size::NTuple{2,Integer}) where T
 
-        ## Conv with views is not dispatched to CUDA.conv
-        # yy = conv(@view(Δ[:,1:nextras[2],:,:]), weight2, pad=pad2, stride=stride2)
-        # dx[:,[1],:,:] .+= conv(@view(Δ[:,1:nextras[2],:,:]), weight2, pad=pad2, stride=stride2)
-        # weight2 .= @view(weight2[:,end:-1:1,:,:])
-        # dx[:,[end],:,:] .+= conv(@view(Δ[:,end-nextras[2]+1:end,:,:]), weight2, pad=pad2, stride=stride2)
-    end
+# Arguments
+- `Δ`: Incoming gradient array, backpropagated from downstream layers
+- `size`: Lateral (W,H) size of the image upsampled in the first place
 
-    ## Finally fix four corners if needed
-    n1, n2 = nextras
-    if (n1 > 0) & (n2 > 0)
-        dx[1,1,:,:] .+= sum(kern[1:n1,1:n2] .* @view(Δ[1:n1,1:n2,:,:]), dims=(1,2))[1,1,:,:]
-        dx[1,end,:,:] .+= sum(kern[1:n1,end-n2+1:end] .* @view(Δ[1:n1,end-n2+1:end,:,:]), dims=(1,2))[1,1,:,:]
-        dx[end,end,:,:] .+= sum(kern[end-n1+1:end,end-n2+1:end] .* @view(Δ[end-n1+1:end,end-n2+1:end,:,:]), dims=(1,2))[1,1,:,:]
-        dx[end,1,:,:] .+= sum(kern[end-n1+1:end,1:n2] .* @view(Δ[end-n1+1:end,1:n2,:,:]), dims=(1,2))[1,1,:,:]
+# Outputs
+- `dx`: Downsampled version of `Δ`
+"""
+function ∇upsample_bilinear(Δ::AbstractArray{T,4}; size::NTuple{2,Integer}) where T
+    w, h, c, n = Base.size(Δ)
+    out_w, out_h = size
+    if (w,h) == (out_w, out_h)
+        return Δ
     end
-
-    return dx
+    dx = zero(similar(Δ, T, out_w, out_h, c, n))
+    return ∇upsample_bilinear_whcn!(dx, Δ)
 end
 
-# `n` upsample factor for which a downsample kernel will be determined.
-# Δ is given in case of necessity of gpu conversion 
-function get_downsamplekernel(Δ, n::Int)
-    step = 1//n
-    if n % 2 == 0
-        start = step//2
-        upward = collect(start:step:1//1)
-        kernel = [upward; reverse(upward)]
-    else
-        start = step
-        upward = collect(start:step:1//1)
-        kernel = [upward; reverse(upward[1:end-1])]
+function ∇upsample_bilinear_whcn!(dx::AbstractArray{T,4}, Δ::AbstractArray{T,4}) where T
+    size(dx)[3:4] == size(Δ)[3:4] || error("Number of input and output channels and batches must match. Got input $(size(input)) and output $(size(output))")
+    in_w, in_h, channels, batches = size(dx)
+
+    # treat batch and channel dimension as one for better parallelization granularity
+    channels *= batches
+    out_w, out_h, _, _ = size(Δ)
+    output_slice_size = out_h * out_w
+
+    width_scale  = T((in_w - 1) // (out_w - 1))
+    height_scale = T((in_h - 1) // (out_h - 1))
+
+    @inline idx(c, h, w) = c * in_h * in_w + h * in_w + w + 1
+
+    @inbounds Threads.@threads for c in 0:channels-1
+        for oh in 0:out_h-1
+            ih0, ih1, h0lambda, h1lambda = compute_source_index_and_lambda(height_scale, oh, in_h, out_h)
+            for ow in 0:out_w-1
+                iw0, iw1, w0lambda, w1lambda = compute_source_index_and_lambda(width_scale, ow, in_w, out_w)
+                output_offset = c * output_slice_size + oh * out_w + ow + 1
+                Δ_value = Δ[output_offset]
+                dx[idx(c, ih0, iw0)] += h0lambda * w0lambda * Δ_value # i00
+                dx[idx(c, ih0, iw1)] += h0lambda * w1lambda * Δ_value # i01
+                dx[idx(c, ih1, iw0)] += h1lambda * w0lambda * Δ_value # i10
+                dx[idx(c, ih1, iw1)] += h1lambda * w1lambda * Δ_value # i11
+            end
+        end
     end
-    # TODO there must be a more convenient way to send to gpu 
-    kernel = convert(typeof(Δ), reshape(kernel, length(kernel), 1, 1, 1))
-    kernel = dropdims(kernel, dims=(2,3,4))
-    return kernel
+    return dx
 end
 
-function ChainRulesCore.rrule(::typeof(upsample_bilinear), x, k)
-    Ω = upsample_bilinear(x, k)
+function ChainRulesCore.rrule(::typeof(upsample_bilinear), x; size)
+    Ω = upsample_bilinear(x; size=size)
     function upsample_bilinear_pullback(Δ)
-        (NO_FIELDS, ∇upsample_bilinear(Δ, k), DoesNotExist())
+        (NO_FIELDS, ∇upsample_bilinear(Δ; size=(Base.size(x,1),Base.size(x,2))))
     end
     return Ω, upsample_bilinear_pullback
 end
 
-
 """
     pixel_shuffle(x, r)
-    
+
 Pixel shuffling operation. `r` is the upscale factor for shuffling.
 The operation converts an input of size [W,H,r²C,N] to size [rW,rH,C,N]
-Used extensively in super-resolution networks to upsample 
+Used extensively in super-resolution networks to upsample
 towards high resolution features.
 
 Reference : https://arxiv.org/pdf/1609.05158.pdf
@@ -301,7 +232,7 @@ function pixel_shuffle(x::AbstractArray, r::Integer)
     @assert ndims(x) > 2
     d = ndims(x) - 2
     sizein = size(x)[1:d]
-    cin, n = size(x, d+1), size(x, d+2) 
+    cin, n = size(x, d+1), size(x, d+2)
     @assert cin % r^d == 0
     cout = cin ÷ r^d
     # x = reshape(x, sizein..., fill(r, d)..., cout, n) # bug https://github.com/FluxML/Zygote.jl/issues/866