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首页> 外文期刊>Pattern Analysis and Machine Intelligence, IEEE Transactions on >Discrete Mereotopology for Spatial Reasoning in Automated Histological Image Analysis
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Discrete Mereotopology for Spatial Reasoning in Automated Histological Image Analysis

机译：自动化组织学图像分析中空间推理的离散超拓扑学

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摘要

Discrete mereotopology (DM) is a first-order spatial logic that fuses together mereology (the theory of parthood relations) and topology to model discrete space. We show how a set of quasitopological functions defined within DM can be mapped to specific operators defined in mathematical morphology (MM) and easily implemented in scientific image processing programs. These functions provide the means to model topological properties of individual regions and spatial relations between them such as contact, overlap, and the relation of part to whole. DM not only extends the expressive power of image processing applications where mathematical morphology is used, but by functioning as a logic it also supplies the formal basis with which to prove the correctness of implemented algorithms as well as providing the computational basis to mechanically reason about segmented digital images using automated reasoning programs. In particular, we show how DM can supply a model-based and algorithmic context to the otherwise blind pixel-based image processing routines still dominating conventional imaging approaches. A number of worked examples drawn from the histological domain are given, including segmentation of cells in culture, identifying basal cell layers from stratified epithelia sections, and cell sorting in blood smears.
机译：离散层状拓扑（DM）是一阶空间逻辑，将层状性（部分性关系理论）和拓扑融合在一起，以对离散空间进行建模。我们展示了如何将DM中定义的一组拟拓扑函数映射到数学形态学（MM）中定义的特定算符，并在科学图像处理程序中轻松实现。这些功能提供了对单个区域的拓扑属性及其之间的空间关系（例如接触，重叠以及零件与整体之间的关系）进行建模的方法。 DM不仅扩展了使用数学形态学的图像处理应用程序的表达能力，而且还通过充当逻辑功能提供了形式基础，以证明已实现算法的正确性，并为基于机械原理的分段算法提供了计算基础。使用自动推理程序的数字图像。特别是，我们展示了DM如何为仍然主导传统成像方法的基于盲点的图像处理例程提供基于模型和算法的上下文。给出了许多从组织学领域得出的工作实例，包括培养细胞的分段，从分层上皮切片中识别基底细胞层以及血涂片中的细胞分选。

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