揭示图像配准中信号重构精度受断点参考点影响的理论反例
A Counterexample in Image Registration
- 通过理想无噪采样重建分段常数信号，研究误差能量与断点位置关系
- 发现信号估计误差随参考断点选择而变化，最大误差达理论上限
- 为图像配准的理论极限提供关键反例，适合研究配准算法边界的人参考
图像配准是广泛存在的问题，通过图像变换或相似性模型对同一场景的离散图像进行对齐。然而，即使在一维数据情况下，其准确性的理论极限仍不明确。正如奈奎斯特采样定理规定了从采样中完美重构信号的条件，对于在无额外假设下从理想无噪采样中重现量化函数的情况，也存在质量限制。本文研究从两组或更多无噪采样模式中估计空间受限的分段常数信号。重点分析误差函数的能量，发现信号断点位置的不确定性依赖于所选的参考断点。因此，信号估计的准确性取决于该信号的参考点选择。
原文摘要 · Abstract (English)
Image registration is a widespread problem which applies models about image transformation or image similarity to align discrete images of the same scene. Nevertheless, the theoretical limits on its accuracy are not understood even in the case of one-dimensional data. Just as Nyquist's sampling theorem states conditions for the perfect reconstruction of signals from samples, there are bounds to the quality of reproductions of quantized functions from sets of ideal, noiseless samples in the absence of additional assumptions. In this work we estimate spatially-limited piecewise constant signals from two or more sets of noiseless sampling patterns. We mainly focus on the energy of the error function and find that the uncertainties of the positions of the discontinuity points of the function depend on the discontinuity point selected as the reference point of the signal. As a consequence, the accuracy of the estimate of the signal depends on the reference point of that signal.
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