depthwise_convolution_2d(x, W, b=None, stride=1, pad=0)¶
Two-dimensional depthwise convolution function.
This is an implementation of two-dimensional depthwise convolution. It takes two or three variables: the input image
x, the filter weight
W, and optionally, the bias vector
Notation: here is a notation for dimensionalities.
- \(n\) is the batch size.
- \(c_I\) is the number of the input.
- \(c_M\) is the channel multiplier.
- \(h\) and \(w\) are the height and width of the input image, respectively.
- \(h_O\) and \(w_O\) are the height and width of the output image, respectively.
- \(k_H\) and \(k_W\) are the height and width of the filters, respectively.
- x (
Variableor N-dimensional array) – Input variable of shape \((n, c_I, h, w)\).
- W (
Variableor N-dimensional array) – Weight variable of shape \((c_M, c_I, k_H, k_W)\).
- b (
Variableor N-dimensional array) – Bias variable of length \(c_M * c_I\) (optional).
- stride (int or pair of ints) – Stride of filter applications.
stride=(s, s)are equivalent.
- pad (int or pair of ints) – Spatial padding width for input arrays.
pad=(p, p)are equivalent.
Output variable. Its shape is \((n, c_I * c_M, h_O, w_O)\).
DepthwiseConvolution2Dfunction computes correlations between filters and patches of size \((k_H, k_W)\) in
x. But unlike
DepthwiseConvolution2Ddoes not add up input channels of filters but concatenates them. For that reason, the shape of outputs of depthwise convolution are \((n, c_I * c_M, h_O, w_O)\), \(c_M\) is called channel_multiplier.
\((h_O, w_O)\) is determined by the equivalent equation of
If the bias vector is given, then it is added to all spatial locations of the output of convolution.
>>> x = np.random.uniform(0, 1, (2, 3, 4, 7)) >>> W = np.random.uniform(0, 1, (2, 3, 3, 3)) >>> b = np.random.uniform(0, 1, (6,)) >>> y = F.depthwise_convolution_2d(x, W, b) >>> y.shape (2, 6, 2, 5)