학술논문
Scattering and Gathering for Spatially Varying Blurs
Document Type
Periodical
Author
Source
IEEE Transactions on Signal Processing IEEE Trans. Signal Process. Signal Processing, IEEE Transactions on. 72:1507-1517 2024
Subject
Language
ISSN
1053-587X
1941-0476
1941-0476
Abstract
A spatially varying blur kernel $h(\mathbf{x},\mathbf{u})$ is specified by an input coordinate $\mathbf{u} \mathbf{\in} \mathbb{R}^{2}$ and an output coordinate $\mathbf{x} \mathbf{\in} \mathbb{R}^{2}$. For computational efficiency, we sometimes write $h(\mathbf{x},\mathbf{u})$ as a linear combination of spatially invariant basis functions. The associated pixelwise coefficients, however, can be indexed by either the input coordinate or the output coordinate. While appearing subtle, the two indexing schemes will lead to two different forms of convolutions known as scattering and gathering , respectively. We discuss the origin of the operations. We discuss conditions under which the two operations are identical. We show that scattering is more suitable for simulating how light propagates and gathering is more suitable for image filtering such as denoising.