VL_NNCONVT - CNN convolution transpose.

Y = VL_NNCONVT(X, F, B) computes the transposed convolution of the image stack X with the filter bank F and biases B. If B is the empty matrix, then no biases are added.

X is a SINGLE array of dimension H x W x D x N where (H,W) are the height and width of the image stack, D is the image depth (number of feature channels) and N the number of of images in the stack.

F is a SINGLE array of dimension FW x FH x K x FD where (FH,FW) are the filter height and width, K the number of filters in the bank, and FD the depth of a filter (the same as the depth of image X). Filter k is givenby elements F(:,:,k,:); this differ from VL_NNCONV() where a filter is given by elements F(:,:,:,k). FD must be the same as the input depth D.

B is a SINGLE array with 1 x 1 x K elements (B can in fact be of any shape provided that it has K elements).

[DZDX, DZDF, DZDB] = VL_NNCONVT(X, F, B, DZDY) computes the derivatives of the block projected onto DZDY. DZDX, DZDF, DZDB, and DZDY have the same dimensions as X, F, B, and Y respectively. In particular, if B is the empty matrix, then DZDB is also empty.

VL_NNCONVT(..., 'option', value, ...) takes the following options:

• Upsample [1]

  The input stride (upsampling factor). Passing [UPY UPX] allows specifying different upsampling factors for the vertical and horizontal directions.

• Crop [0]

  The amount of output cropping. [TOP BOTTOM LEFT RIGHT] pixels around the output image are dropped. Passing a scalar applies the same amount of crop to all borders.

• NumGroups [1]

  The number of filter groups. This parameter allows using filter groups in the same way as defined by VL_NNCONV(). NUMGROUPS must divide the filter bank depth FD. In this case, filters are divided in NUMGROUPS different groups, each operating on a equal number of contiguous dimensions of the input. FILTERS is then interpreted as containing K * NUMGROUPS different filters, each of depth FD / NUMGROUPS.

About the convolution transpose operator

The convolution transpose operator is defined as follows. Let U = VL_NNCONV(V, F, []). Since this is a linear operation, there is a matrix M such that U(:) = M V(:). The convolution transpose is the linear convolution operator that results in Y(:) = M' X(:). See the PDF manual for further detials.

There are two main uses for this operator. As a sort of 'reverse' of convolution, useful for example in a deconvolutional network, and as an interpolating filter (instead of a decimating one).

The output a is a SINGLE array of dimension YH x YW x K x N of N images with K channels and size:

  YH = UPH (XH - 1) + FH - CROPTOP - CROPBOTTOM,
  YW = UPW (XW - 1) + FW - CROPLEFT - CROPRIGHT.

CUDNN SUPPORT

If compiled in, the function will use cuDNN convolution routines (with the exception of asymmetric left-right or top-bottom padding and a few corner cases such as 1x1 filters in Linux that trigger current bugs in cuDNN). You can use the 'NoCuDNN' option to disable cuDNN or 'cuDNN' to activate it back again (the choice sticks until MATLAB purges the MEX files for any reason).

Some CuDNN algorithms may use a very large amount of memory on the GPU (workspace). MatConvNet requests CuDNN to use at most 512MB of GPU memory for the workspace. To change this behaviour, use the CudnnWorskpaceLimit option to specify the maximum size of the workspace in bytes. Set this parameter +inf to remove the limit and use the Verbose flag to check how much memory is being used.