Feature volume — a conv layer's output shape

Background

A conv layer turns an (H, W, C_in) volume into an (H', W', F) volume: the spatial size shrinks per the convolution formula, and the depth becomes the number of filters F (each filter makes one feature map). Per spatial dim:

$$H' = \left\lfloor \frac{H + 2P - K}{S}\right\rfloor + 1$$

Problem statement

Implement conv_block_shape(H, W, kernel, stride, padding, filters) returning the output volume shape (H', W', filters).

Input

• H, W — input height and width.
• kernel, stride, padding — conv hyperparameters.
• filters — number of conv filters F.

Output

Returns a tuple (H', W', filters).

Examples

Example 1 — the lesson's first conv (16 filters)

Input:  H = 32, W = 32, kernel = 3, stride = 1, padding = 0, filters = 16
Output: (30, 30, 16)

Example 2 — same padding keeps H, W

Input:  H = 28, W = 28, kernel = 3, stride = 1, padding = 1, filters = 64
Output: (28, 28, 64)

Constraints

• Spatial size uses $\lfloor (N + 2P - K)/S\rfloor + 1$ for each of H and W.
• The output depth is filters.
• Return a tuple of ints.

Notes

• Stacking blocks, depth tends to grow (more filters) while H and W shrink (stride / pooling) — the "feature volume" getting deeper and smaller as you go.