Learning from image structure

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Beginner explanation

An image is a grid of numbers. A convolutional network looks for patterns across small regions using reusable filters. The same learned filter can detect a pattern in several parts of the image.

Intermediate explanation

Convolutions share weights across spatial positions, reducing parameters relative to a fully connected treatment of every pixel. Stride and pooling change resolution. Translation equivariance is not the same as complete invariance to position, scale or rotation.

Advanced explanation

Output size for one spatial dimension is floor((n + 2p − k)/s) + 1 with input n, padding p, kernel k and stride s, for unit dilation. Padding, sampling and boundary effects influence behavior. Data augmentation does not guarantee robustness to every transformation.

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A worked example

For a 5×5 image, a 3×3 filter with stride 1 and no padding produces a 3×3 output. The filter is applied at nine positions with the same weights. The output is a feature map, not a smaller photograph by necessity.

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Practice the idea

Calculate the output width for a 7-pixel-wide input, a 3-pixel filter, stride 2 and no padding.

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floor((7 − 3)/2) + 1 = 3. The filter starts at positions 0, 2 and 4. This calculation assumes unit dilation and ordinary valid convolution.

Go further: advanced challenge

Describe how a dataset with identical backgrounds for each class can produce high test scores but poor results in new locations.

An open-ended discussion task. Explain your assumptions and evidence; there may be more than one defensible answer.

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