Depth-wise Convolution and Depth-wise Separable Convolution

Depth-wise convolution

In this convolution, we apply a 2-d depth filter at each depth level of input tensor. Lets understand this through an example. Suppose our input tensor is 3* 8 *8 (input_channels*width* height). Filter is 3*3*3. In a standard convolution we would directly convolve in depth dimension as well (fig 1).

Fig 1. Normal convolution
Fig 2. Depth-wise convolution. Filters and image have been broken into three different channels and then convolved separately and stacked thereafter

Depth-wise Separable Convolution

This convolution originated from the idea that depth and spatial dimension of a filter can be separated- thus the name separable. Let us take the example of Sobel filter, used in image processing to detect edges. You can separate the height and width dimension of these filters. Gx filter (see fig 3) can be viewed as matrix product of [1 2 1] transpose with [-1 0 1]. We notice

Fig 3. Sobel Filter. Gx for vertical edge, Gy for horzontal edge detection
Fig 4. Depth-wise separable convolution

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