The core operation of every CNN

Convolution kernel lab

A kernel is nine numbers. Slide it over an image, multiply, add up — that is the whole operation, and it is the operation a convolutional network learns the numbers for. Edit the nine values below and watch what they detect. Then press step to walk the window across the image one position at a time and see the arithmetic.

The kernel —
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Input and feature map click the source to move the inspector
Input —
Output —

The output is drawn at the same scale as the input, so when padding or stride shrink it, it really does occupy less of the panel.

One position at a time —
Pixels under the window
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Kernel
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Products
8/s

This is the equation from the notes, drawn out: Output(i,j) = Σm Σn km,n · pi+m−2, j+n−2. Nine multiplications and eight additions, repeated once per output pixel. A 300×225 feature map costs about 600,000 multiply-adds — for one filter, and a real layer has dozens.

Sum of weights
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Learnable parameters
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Multiply-adds for this map
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Output range
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The sum of the weights tells you what the filter does to brightness. If it sums to 1, average brightness survives — that is every blur and every sharpen. If it sums to 0, flat regions produce exactly zero and only changes survive: that is every edge detector, and it is why the Sobel and Laplacian presets return a mostly-black image with the outlines glowing. Nothing in a flat region differs from its neighbours, so there is nothing for a zero-sum kernel to report.

Try Sobel X on the brick scene, then Sobel Y. One finds the vertical mortar lines and is nearly blind to the horizontal ones; the other does the opposite. Neither was told what a brick is. This is the entire premise of a convolutional layer: a small stack of filters like these, applied everywhere, turns raw pixels into a map of where the interesting structure is — and because a network learns the nine numbers rather than being given them, it discovers whichever detectors the task actually rewards.

Nine numbers, reused everywhere. A fully connected layer reading a 300×225 image needs 67,500 weights per neuron. This kernel needs nine, and it applies them at every position. That reuse — weight sharing — is why CNNs made image processing tractable, and it is the answer to the parameter explosion the notes raise just before this section.