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Acceleration of Gaussian Filter with Short Window Length Using DCT-1

机译：使用DCT-1加速短窗高斯滤波器

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摘要

This paper presents an accelerated constant-time Gaussian filter (O(1) GF) specialized in short window length where constant-time (O(1)) means that computational complexity per pixel does not depend on filter window length. Our method is extensively designed based on the idea of O(1) GF based on Discrete Cosine Transform (DCT). This framework approximates a Gaussian kernel by a linear sum of cosine terms and then convolves each cosine term in O(1) per pixel using sliding transform. Importantly, if window length is short, DCT-1 consists of easily-computable cosine values such as 0, ±[1/2] and ±1. This behavior is not satisfied in other DCT types. From this fact, our method accelerates the sliding transform by employing DCT-1 focusing on short window length. Experiments show that our method overcomes naive Gaussian convolution and existing O(1) GF in terms of computational time. Interestingly, the results also reveal that, without truncating negligible terms, our method runs faster than convolution.
机译：本文提出了一种专门针对短窗口长度的加速恒定时间高斯滤波器（O（1）GF），其中恒定时间（O（1））意味着每个像素的计算复杂度不取决于滤波器窗口长度。我们的方法是基于基于离散余弦变换（DCT）的O（1）GF的思想进行广泛设计的。该框架通过余弦项的线性和近似高斯核，然后使用滑动变换将每个余弦项以每个像素O（1）进行卷积。重要的是，如果窗口长度很短，则DCT-1由易于计算的余弦值组成，例如0，±1/2和±1。在其他DCT类型中，不能满足此行为。基于这个事实，我们的方法通过采用关注短窗口长度的DCT-1来加速滑动变换。实验表明，我们的方法在计算时间上克服了朴素的高斯卷积和现有的O（1）GF。有趣的是，结果还表明，在不删节可忽略术语的情况下，我们的方法比卷积运行得更快。

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