Gu Kelvin, Pati Debdeep, Dunson David B
Department of Statistics, Stanford University, Department of Statistics, Florida State University, Department of Statistical Science, Duke University.
J Am Stat Assoc. 2014 Oct;109(508):1481-1494. doi: 10.1080/01621459.2014.934825.
Modeling object boundaries based on image or point cloud data is frequently necessary in medical and scientific applications ranging from detecting tumor contours for targeted radiation therapy, to the classification of organisms based on their structural information. In low-contrast images or sparse and noisy point clouds, there is often insufficient data to recover local segments of the boundary in isolation. Thus, it becomes critical to model the entire boundary in the form of a closed curve. To achieve this, we develop a Bayesian hierarchical model that expresses highly diverse 2D objects in the form of closed curves. The model is based on a novel multiscale deformation process. By relating multiple objects through a hierarchical formulation, we can successfully recover missing boundaries by borrowing structural information from similar objects at the appropriate scale. Furthermore, the model's latent parameters help interpret the population, indicating dimensions of significant structural variability and also specifying a 'central curve' that summarizes the collection. Theoretical properties of our prior are studied in specific cases and efficient Markov chain Monte Carlo methods are developed, evaluated through simulation examples and applied to panorex teeth images for modeling teeth contours and also to a brain tumor contour detection problem.
在医学和科学应用中，基于图像或点云数据对物体边界进行建模通常是必要的，这些应用范围从检测用于靶向放射治疗的肿瘤轮廓，到根据生物体的结构信息对其进行分类。在低对比度图像或稀疏且有噪声的点云中，往往没有足够的数据来单独恢复边界的局部片段。因此，以封闭曲线的形式对整个边界进行建模变得至关重要。为了实现这一点，我们开发了一种贝叶斯层次模型，该模型以封闭曲线的形式表示高度多样的二维物体。该模型基于一种新颖的多尺度变形过程。通过分层公式将多个物体联系起来，我们可以通过在适当尺度上借用相似物体的结构信息来成功恢复缺失的边界。此外，模型的潜在参数有助于解释总体，表明显著结构变异性的维度，并指定一条“中心曲线”来概括该集合。我们在特定情况下研究了先验的理论性质，并开发了高效的马尔可夫链蒙特卡罗方法，通过模拟示例进行评估，并应用于全景牙齿图像以对牙齿轮廓进行建模，还应用于脑肿瘤轮廓检测问题。
