How Dilated Convolutions Preserve Image Size While Expanding Receptive Field

1. Concept of Dilated Convolution

Dilated convolutions, also called atrous convolutions, introduce a dilation rate parameter that expands the kernel without increasing the number of parameters, thereby enlarging the receptive field.

2. Diagram

Examples:

Standard convolution, dilation=1, receptive field 3×3=9

Dilated convolution, dilation=2, receptive field 7×7=49

Dilated convolution, dilation=4, receptive field 16×16=256

3. Receptive Field Concept

The receptive field of a layer is the region of the original image that influences a single output pixel.

Key Formula

The effective kernel size after dilation is calculated as:

Dilated kernel size = dilation × (kernel_size‑1) + 1

PyTorch Example

In PyTorch there is no padding='SAME' option; padding must be set manually. The output size follows the same rule as TensorFlow's VALID padding:

Output = (W‑F+2P)/S + 1

For a 19×19 input, a 3×3 kernel, stride = 1, and dilation = 6, the dilated kernel size becomes 13. Solving (19‑13+2P)/1 + 1 = 19 yields P = 6 , which keeps the spatial dimensions unchanged.

4. Advantages of Dilated Convolution

It expands the receptive field without increasing the number of parameters, allowing the network to capture broader context while preserving computational cost.

5. Application Areas

Typical uses include image inpainting, semantic segmentation, and speech synthesis.