Background

In the context of signal analysis and pattern matching, alignment of 1D signals for the comparison of signal morphologies is an important problem. For image processing and computer vision, 2D optical flow (OF) methods find wide application for motion analysis and image registration and variational OF methods have been continuously improved over the past decades.

New method

We propose a variational method for the alignment and displacement estimation of 1D signals. We pose the estimation of non-flat displacements as an optimization problem with a similarity and smoothness term similar to variational OF estimation. To this end, we can make use of efficient optimization strategies that allow real-time applications on consumer grade hardware.

Results

We apply our method to two applications from functional neuroimaging: The alignment of 2-photon imaging line scan recordings and the denoising of evoked and event-related potentials in single trial matrices. We can report state of the art results in terms of alignment quality and computing speeds.

Existing methods

Existing methods for 1D alignment target mostly constant displacements, do not allow native subsample precision or precise control over regularization or are slower than the proposed method.

Conclusions

Our method is implemented as a MATLAB toolbox and is online available. It is suitable for 1D alignment problems, where high accuracy and high speed is needed and non-constant displacements occur.

中文翻译：

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非平面一维位移的快速变分对准在神经成像中的应用

背景

在信号分析和模式匹配的背景下，一维信号的对齐以比较信号形态是一个重要的问题。对于图像处理和计算机视觉，二维光流（OF）方法在运动分析中得到了广泛的应用，并且在过去的几十年中，图像配准和变化型OF方法得到了不断改进。

新方法

我们提出了一种变分方法，用于一维信号的对准和位移估计。我们将非平坦位移的估计作为具有相似性和平滑度项的优化问题，类似于变分OF估计。为此，我们可以利用有效的优化策略，允许在消费级硬件上进行实时应用。

结果

我们将我们的方法应用于功能性神经成像的两个应用：2光子成像线扫描记录的对齐以及单个试验矩阵中诱发电位和事件相关电位的去噪。我们可以根据对齐质量和计算速度报告最新的结果。

现有方法

现有的用于一维对齐的方法主要目标是恒定位移，不允许自然的子样本精度或对正则化的精确控制，或者比拟议的方法慢。

结论

我们的方法被实现为MATLAB工具箱，并且可以在线获取。它适用于需要高精度和高速度且发生非恒定位移的一维对齐问题。