Convolutional Neural Network CNN: Which Pixels Affect the Circled Pixel in a CNN Convolution Operation?

Learn how convolution operations in CNNs work, focusing on which input pixels influence specific output pixels. Understand stride, filters, and receptive fields.

Question

The following image depicts the result of a convolution at the right when using a stride of 1 and the filter is shown right next.

On which pixels does the circled pixel of the activation at the right depend?

A. It depends on the pixels enclosed by the blue square.
B. It depends on the pixels enclosed by the red square.
C. It depends on all the pixels of the image on the left.
D. It depends on the pixels enclosed by the green square.

Answer

D. It depends on the pixels enclosed by the green square.

Explanation

In convolutional neural networks (CNNs), the output of a convolution operation is determined by applying a filter (kernel) to a specific region of the input matrix. This region is referred to as the receptive field. Here’s how this applies to the given problem:

Filter and Input Matrix:

• The filter is a 3×3 matrix.
• The input matrix is a 5×5 grid filled with values of 10 in the top-left and zeros elsewhere.

Stride:

• The stride is 1, meaning the filter moves one pixel at a time across the input matrix.

Output Calculation:

• The circled pixel in the output corresponds to the center position of the second row and second column of the output matrix.
• To compute this value, the filter is applied to a 3×3 region of the input matrix. This region is highlighted by the green square in the image.

Receptive Field:

• The circled pixel depends only on the values within this 3×3 receptive field, as these are the pixels that interact with the filter during computation.

Why Not Other Options?

Blue Square (Option A): This corresponds to a different region of the input matrix, influencing another output pixel.
Red Square (Option B): Similarly, this region affects a different output pixel.
Entire Input Matrix (Option C): Only a localized 3×3 area contributes to each output pixel due to the size of the filter and stride.

Thus, Option D is correct because it accurately identifies the specific region of input pixels that determine the value of the circled pixel in the output.

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