论文标题
加权欧拉曲线变换进行形状和图像分析
The Weighted Euler Curve Transform for Shape and Image Analysis
论文作者
论文摘要
Turner等人的Euler曲线变换（ECT）是嵌入式简单复合物的完全不变，这是统计分析的。我们将ECT概括为为加权简单复合物提供类似方便的表示，例如在某些医学成像应用中自然出现的对象。我们利用Ghrist等人在Euler积分上的工作来证明这种不变的 - 称为加权的Euler曲线变换（Wect）---也是完整的。我们解释了如何将灰度图像中感兴趣的分段区域转换为加权的简单复合物，然后转变为wect表示。该wect表示用于研究多形脑肿瘤形状和纹理数据的胶质母细胞瘤。我们表明，根据定性形状和纹理特征，wect表示可有效地聚类肿瘤，并且该聚类与患者的生存时间相关。
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.
