Fast Gaussian Filter Approximations Comparison on SIMD Computing Platforms

Abstract

Gaussian filtering, being a convolution with a Gaussian kernel, is a widespread technique in image analysis and computer vision applications. It is the traditional approach for noise reduction. In some cases, performing the exact convolution can be computationally expensive and time-consuming. To address this problem, approximations of the convolution are often used to achieve a balance between accuracy and computational efficiency, such as with running sums, Bell blur, Deriche approximation, etc. At the same time, modern computing devices support data parallelism (vectorization) via Single Instruction Multiple Data (SIMD) and can process integer numbers faster than floating-point approaches. In this paper, we describe several methods for approximating a Gaussian filter, implement the SIMD and quantized versions, and compare them in terms of speed and accuracy. The experiments were performed on central processing units with a x86_64 architecture using a family of SSE SIMD extensions and an ARMv8 architecture using the NEON SIMD extension. All the optimized approximations demonstrated 10–20× speedup while maintaining the accuracy in the range of 1 × 10−5 or higher. The fastest method is a trivial Stack blur with a relatively high error, so we recommend using the second-order Vliet–Young–Verbeek filter and quantized Bell blur and running sums as more accurate and still computationally efficient alternatives.

Keywords

• approximations
• computational efficiency
• Gaussian smoothing
• image filtering
• impulse response
• quantization