I knew the theory well enough but actually coding it cleanly under pressure is a different thing.
Start by clarifying the requirements (e.g., kernel size, sigma, boundary handling, performance constraints) and then explain the mathematical basis of Gaussian filtering. Outline a step-by-step implementation plan, covering kernel generation, convolution, and optimizations like separability, while discussing trade-offs between accuracy and efficiency.
Pro tip: Demonstrate awareness of practical issues: mention that for large sigma, truncating the kernel or using separable convolution is essential, and that boundary handling (e.g., zero-padding vs. reflect) can significantly affect results. Also, note that in ML pipelines, Gaussian filtering is often used for anti-aliasing before downsampling, so aligning with that use case shows maturity.
Ask about kernel size, sigma, input format (e.g., grayscale or RGB), boundary conditions, and performance expectations (e.g., real-time vs. offline). This ensures the implementation meets the specific needs.
Describe how to compute a 2D Gaussian kernel using the formula, including normalization to sum to 1. Mention that the kernel size is typically 6*sigma+1 to cover 99.7% of the distribution.
Outline the convolution operation: for each pixel, multiply the kernel with the neighborhood and sum. Discuss handling boundaries (e.g., zero-padding, reflect, replicate) and potential edge effects.
Explain that the 2D Gaussian is separable into two 1D convolutions (horizontal and vertical), reducing complexity from O(k^2) to O(2k) per pixel. This is crucial for large kernels.
Compare naive convolution vs. separable convolution vs. using FFT or integral images. Mention trade-offs in accuracy, speed, and memory, and when to use each (e.g., small sigma vs. large sigma).
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