Estimating the Number of Peaks in a Random Field Using the Hadwiger Characteristic of Excursion Sets, with Applications to Medical Images
利用超水平集的 Hadwiger 特征估计随机场峰值数：医学图像应用AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究随机场几何和医学图像热点计数，没有所列经济计量细分方向的直接依据。
反馈分类问题正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
利用超水平集的 Hadwiger 特征估计随机场峰值数：医学图像应用
- 研究问题
- 医学与天体物理图像中的热点如何计数？研究关注超水平集接触观测区域边界时，几何特征能否仍反映峰值数量。
- 方法与思路
- 作者研究超水平集的 Hadwiger 特征，利用其旋转不变性及对边界连通区域的计数能力，在各向同性平稳随机场下求期望。
- 材料陈述的贡献
- 摘要称，作者给出二维、三维及嵌入三维空间的光滑曲面上该特征期望的简洁表达，并应用于疼痛和词语识别的 PET 研究。
- 阅读关注点
- 应核对随机场的光滑性与分布条件、区域边界处理，以及高阈值下几何特征近似峰值数的依据和实际适用范围。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；具体公式及条件未提供，不能判断峰值计数误差，也不能推断其他版本变化。
原文摘要
Certain three-dimensional images arising in medicine and astrophysics are modelled as a smooth random field, and experimenters are interested in the number of peaks or "hot-spots" present in such an image. This paper studies the Hadwiger characteristic of the excursion set of a random field. The excursion set is the set of points where the image exceeds a fixed threshold, and the Hadwiger characteristic, like the Euler characteristic, counts the number of connected components in the excursion set minus the number of "holes." For high thresholds the Hadwiger characteristic is a measure of the number of peaks. The geometry of excursion sets has been studied by Adler, who defined the IG (integral geometry) characteristic of excursion sets as a multidimensional analogue of the number of "upcrossings" of the threshold by a unidimensional process. The IG characteristic equals the Euler characteristic of an excursion set provided that the set does not touch the boundary of the volume, and Adler found the expected IG characteristic for a stationary random field inside a fixed volume. Worsley, Evans, Marrett and Neelin used the IG characteristic as an estimator of the number of regions of activation of positron emission tomography (PET) images of blood flow in the brain. Unfortunately the IG characteristic is only defined on intervals: it is not invariant under rotations and it can fail to count connected regions that touch the boundary. This is important since activation often occurs in the cortical regions near the boundary of the brain. In this paper we study the Hadwiger characteristic, which is defined on arbitrary sets, is invariant under rotations and does count connected regions whether they touch the boundary or not. Our main result is a simple expression for the expected Hadwiger characteristic for an isotropic stationary random field in two and three dimensions and on a smooth surface embedded in three dimensions. Results are applied to PET studies of pain perception and word recognition.