In this paper, we demonstrate that algebraic topology can be used to perform 2D+t object detection. After the construction of a topological complex for a 2D+t image sequence, we build a nested sequence of cell complexes on which relative persistent homology is computed. The relative homology adds to “absolute” homology the computation of classes related to the first and last frames of the sequence. By identifying 2D chains with large life spans, the most persistent classes are extracted. This allows for the identification of the interesting parts in a sequence and for the detection of the movement of objects despite continuous deformations in the image domain. The results obtained on a synthetic image and on two real biomedical images with moving vesicles recorded by a quantitative phase time‐lapse technique show the potential of this method. Comparing the method with a newly developed tracking tool proves that the strength of this method is its independence from prior parameters.

中文翻译：

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通过相对持久同源性进行 2D+t 轨迹检测

在本文中，我们证明了代数拓扑可用于执行 2D+t 对象检测。在为 2D+t 图像序列构建拓扑复合体之后，我们构建了一个嵌套的细胞复合体序列，在该序列上计算相对持久同源性。相对同源性将与序列的第一帧和最后一帧相关的类的计算添加到“绝对”同源性中。通过识别具有大生命周期的二维链，提取最持久的类。这允许在序列中识别有趣的部分，并允许在图像域中连续变形的情况下检测对象的运动。在合成图像和通过定量相位延时技术记录的具有移动囊泡的两个真实生物医学图像上获得的结果显示了该方法的潜力。