研究图像超分辨与配准中的舍入误差和高斯模糊影响，提出新方法精准定位边缘点。
On Round-Off Errors and Gaussian Blur in Superresolution and in Image Registration
- 构建依赖信号的测量矩阵，统一建模高斯模糊与舍入误差
- 在特定条件下，能正确对齐两组数据并定位断点后首点
- 适用于需高精度边缘检测的图像配准与超分辨任务
超分辨理论与技术旨在从受模糊和噪声影响的采样中恢复信号。离散图像配准可用来融合同一信号的不同采样集信息。空间域量化误差是数字图像固有属性。本文研究一维空间有限的分段常数函数，在高斯或高斯混合模糊及舍入误差下的超分辨与离散图像配准问题。提出一种信号依赖的测量矩阵，同时刻画两类效应。在无其他噪声情况下，仍难以确定断点位置。若存在统计噪声，则需对数据序列进行对齐与分段，以有效推断幅值和断点。在模糊、噪声及断点间距满足一定条件时，证明基于动态规划的方法可正确对齐两组数据，并准确确定每个断点后的首样本。
原文摘要 · Abstract (English)
Superresolution theory and techniques seek to recover signals from samples in the presence of blur and noise. Discrete image registration can be an approach to fuse information from different sets of samples of the same signal. Quantization errors in the spatial domain are inherent to digital images. We consider superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions which are subject to blur which is Gaussian or a mixture of Gaussians as well as to round-off errors. We describe a signal-dependent measurement matrix which captures both types of effects. For this setting we show that the difficulties in determining the discontinuity points from two sets of samples even in the absence of other types of noise. If the samples are also subject to statistical noise, then it is necessary to align and segment the data sequences to make the most effective inferences about the amplitudes and discontinuity points. Under some conditions on the blur, the noise, and the distance between discontinuity points, we prove that we can correctly align and determine the first samples following each discontinuity point in two data sequences with an approach based on dynamic programming.
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