# chainer.functions.depthwise_convolution_2d¶

chainer.functions.depthwise_convolution_2d(x, W, b=None, stride=1, pad=0)[source]

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 b.

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.

Parameters
Returns

Output variable. Its shape is $$(n, c_I * c_M, h_O, w_O)$$.

Return type

Variable

Like Convolution2D, DepthwiseConvolution2D function computes correlations between filters and patches of size $$(k_H, k_W)$$ in x. But unlike Convolution2D, DepthwiseConvolution2D does 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 Convolution2D.

If the bias vector is given, then it is added to all spatial locations of the output of convolution.

Example

>>> 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)