用于形状和图像分析的加权欧拉曲线变换
The Weighted Euler Curve Transform for Shape and Image Analysis
摘要：
Turner等人的欧拉曲线变换（ECT）是嵌入单纯复形的完全不变量，这是服从统计分析。我们推广的ECT提供了一个同样方便的表示加权单纯复形，自然产生的对象，例如，在某些医学成像应用。我们利用Ghrist等人的工作。欧拉积分证明这个不变量-被称为加权欧拉曲线变换（WECT）-也是完备的。我们解释了如何将灰度图像中的感兴趣的分割区域转换为加权单纯复形，然后转换为WECT表示。该WECT表示被应用于研究多形性胶质母细胞瘤脑肿瘤的形状和纹理数据。我们表明，WECT表示是有效的聚类肿瘤的定性形状和纹理特征的基础上，这种聚类与患者的生存时间。
英文摘要：
The Euler Curve Transform (ECT) of Turner et al.\ is a complete invariant of an embedded simplicial complex, which is amenable to statistical analysis. We generalize the ECT to provide a similarly convenient representation for weighted simplicial complexes, objects which arise naturally, for example, in certain medical imaging applications. We leverage work of Ghrist et al.\ on Euler integral calculus to prove that this invariant---dubbed the Weighted Euler Curve Transform (WECT)---is also complete. We explain how to transform a segmented region of interest in a grayscale image into a weighted simplicial complex and then into a WECT representation. This WECT representation is applied to study Glioblastoma Multiforme brain tumor shape and texture data. We show that the WECT representation is effective at clustering tumors based on qualitative shape and texture features and that this clustering correlates with patient survival time.
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