In 30 seconds
3Blue1Brown shows how a uniform 3×3 kernel averages color pixels to blur an image, and notes the rotation used in the formal definition of convolution.
- 1Average nine colorsEach output pixel combines a 3×3 neighborhood with equal weights.
- 2Blur the imageRepeating the average makes nearby colors blend.
- 3Rotate the kernelConvolution formally rotates the kernel by 180 degrees; this uniform kernel is unchanged.
Takeaways
- A 3×3 grid of 1/9 weights averages the nine corresponding color pixels.
- Applying the average across an image blends nearby colors and creates blur.
- Convolution uses a 180-degree rotated kernel; rotation has no effect on this uniform grid.
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A moving grid
Weight nine neighboring pixels equally.
Imagine a 3×3 grid sliding across an image. Each of its nine values is 1/9; multiply each value by the corresponding pixel beneath it.
A color pixel can be represented by a vector of red, green and blue values. Add the nine weighted pixel vectors, and you get their average: the color of one pixel in the output image.
From averages to convolution
Apply the operation across the image and consider kernel rotation.
Repeat this calculation across the image. Neighboring colors blend together, producing a blur. This operation is an example of convolving the image with a grid of numbers, or kernel.
Strictly speaking, convolution uses the grid rotated 180 degrees. Here every entry is identical, so rotating it changes nothing.
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