Dept. of Electrical Engineering, Yale University, New Haven, CT 06520, United States.
Med Image Anal. 2010 Jun;14(3):243-54. doi: 10.1016/j.media.2010.01.001. Epub 2010 Jan 20.
This paper addresses the problem of indexing shapes in medical image databases. Shapes of organs are often indicative of disease, making shape similarity queries important in medical image databases. Mathematically, shapes with landmarks belong to shape spaces which are curved manifolds with a well defined metric. The challenge in shape indexing is to index data in such curved spaces. One natural indexing scheme is to use metric trees, but metric trees are prone to inefficiency. This paper proposes a more efficient alternative. We show that it is possible to optimally embed finite sets of shapes in shape space into a Euclidean space. After embedding, classical coordinate-based trees can be used for efficient shape retrieval. The embedding proposed in the paper is optimal in the sense that it least distorts the partial Procrustes shape distance. The proposed indexing technique is used to retrieve images by vertebral shape from the NHANES II database of cervical and lumbar spine X-ray images maintained at the National Library of Medicine. Vertebral shape strongly correlates with the presence of osteophytes, and shape similarity retrieval is proposed as a tool for retrieval by osteophyte presence and severity. Experimental results included in the paper evaluate (1) the usefulness of shape similarity as a proxy for osteophytes, (2) the computational and disk access efficiency of the new indexing scheme, (3) the relative performance of indexing with embedding to the performance of indexing without embedding, and (4) the computational cost of indexing using the proposed embedding versus the cost of an alternate embedding. The experimental results clearly show the relevance of shape indexing and the advantage of using the proposed embedding.
本文探讨了医学图像数据库中形状索引的问题。器官的形状通常是疾病的指征，因此形状相似性查询在医学图像数据库中非常重要。从数学角度来看，带有地标（landmarks）的形状属于形状空间（shape spaces），它是具有明确定义度量的弯曲流形。形状索引的挑战在于在这些弯曲的空间中进行索引数据。一种自然的索引方案是使用度量树（metric trees），但度量树容易效率低下。本文提出了一种更有效的替代方案。我们表明，将形状空间中的有限形状集最优地嵌入到欧几里得空间中是可能的。嵌入后，可以使用经典的基于坐标的树进行有效的形状检索。本文提出的嵌入方法在最小化偏 Procrustes 形状距离的意义上是最优的。所提出的索引技术用于从国家医学图书馆维护的 NHANES II 颈椎和腰椎 X 射线图像数据库中通过椎骨形状检索图像。椎骨形状与骨赘的存在强烈相关，形状相似性检索被提议作为一种通过骨赘存在和严重程度进行检索的工具。本文包含的实验结果评估了：1）形状相似性作为骨赘的代理的有用性；2）新索引方案的计算和磁盘访问效率；3）嵌入索引与不嵌入索引的相对性能；4）使用所提出的嵌入进行索引的计算成本与替代嵌入的成本。实验结果清楚地表明了形状索引的相关性和使用所提出的嵌入的优势。
