局部参数化形状的统计分析
Statistical analysis of locally parameterized shapes
AI总结：
本文提出基于局部坐标系的分层形状参数化方法，以解决传统Procrustes对齐可能引入虚假形状差异的问题，并在模拟数据与帕金森病海马体数据上验证了其有效性。
摘要：
形状对齐一直是统计形状分析中的关键步骤，例如在计算平均形状、检测两个形状总体之间的位置差异以及进行分类时。Procrustes对齐是最常用的方法，也是当前最先进的方法。在本工作中，我们发现对齐可能会严重影响统计分析。例如，对齐可能诱发虚假的形状差异，并导致误导性的结果和解释。我们提出了一种基于局部坐标系的新型分层形状参数化方法。局部参数化形状具有平移和旋转不变性。因此，使用这种参数化方法可以避免常用的全局坐标系形状表示所固有的对齐问题。这种新参数化方法在形状变形和模拟方面也更具优势。该方法的能力在模拟数据的假设检验以及帕金森病患者与对照组的左侧海马体上得到了验证。
英文摘要：
The alignment of shapes has been a crucial step in statistical shape analysis, for example, in calculating mean shape, detecting locational differences between two shape populations, and classification. Procrustes alignment is the most commonly used method and state of the art. In this work, we uncover that alignment might seriously affect the statistical analysis. For example, alignment can induce false shape differences and lead to misleading results and interpretations. We propose a novel hierarchical shape parameterization based on local coordinate systems. The local parameterized shapes are translation and rotation invariant. Thus, the inherent alignment problems from the commonly used global coordinate system for shape representation can be avoided using this parameterization. The new parameterization is also superior for shape deformation and simulation. The method's power is demonstrated on the hypothesis testing of simulated data as well as the left hippocampi of patients with Parkinson's disease and controls.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
