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引用次数: 7
摘要
许多图像处理操作都是成对存在的:正向映射版本和反向映射版本[Wolberg 94, Wolberg et al. 00]。在本文中,我们证明了空间变化卷积滤波器的正向和反向版本是彼此的转置。然后,我们将展示如何将对一组变量进行线性操作的函数的实现转换为其转置函数的实现。这给出了一个将反向空间变化卷积转换为正向卷积的机械过程,反之亦然。虽然这种方法是通用的,但我们专注于一种特殊类型的应用:将这种转换应用于基于运行和或求和面积表的反向卷积的快速算法[Lewis 95, Crow 84],从而产生新的快速正向卷积算法。对于许多实际应用,例如模拟景深和运动模糊,前向卷积通常可以产生更具视觉吸引力的结果,而反向映射算法传统上更容易实现。
Two Tricks for the Price of One: Linear Filters and Their Transposes
Many image processing operations exist in pairs: a forward-mapping version and a reverse-mapping version [Wolberg 94, Wolberg et al. 00]. In this paper, we show that the forward and reverse versions of spatially-varying convolution filters are transposes of each other. We will then show how an implementation of a function that operates linearly on a set of variables may be transformed into an implementation of its transpose function. This gives a mechanical procedure to convert a reverse spatially-varying convolution into a forward one and vice versa. Although this approach is general-purpose, we focus on one particular type of application: applying this transformation to fast algorithms for reverse convolution based on running sums or summed-area tables [Lewis 95, Crow 84] yielding novel fast algorithms for forward convolution. For many practical applications, such as simulating depth of field and motion blur, the forward convolution can often yield more visually appealing results while the reverse-mapping algorithm has traditionally been more straightforward to implement.