Optimal embedding for shape indexing in medical image databases

Abstract

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.

Explicit shape descriptors: Novel morphologic features for histopathology classification

“…Researchers have recently begun using non-linear DR (NLDR) schemes in conjunction with shape descriptors (Bai et al, 2010; Egozi et al, 2010; Qian et al, 2010). Such methods extract a small set of features which describe the variation in morphology between different objects.…”

“…A k -nearest neighbor approach to finding object similarity in the high dimensional shape space was presented in Egozi et al (2010). Qian et al (2010) presented a NLDR scheme to determine relevant morphologic differences between vertebrae, exploiting the definition of the Procrustes shape space. However, their methodology is only applicable to objects represented by PDMs.…”

“…Nasreddine et al (2010) utilized a geodesic distance function to distinguish between contours for pairs of objects. The use of NLDR schemes typically improves the ability to measure similarity in object morphology compared to the Euclidean distance in CBIR applications (Bai et al, 2010; Egozi et al, 2010; Qian et al, 2010). …”

SPIRS: A Web-based image retrieval system for large biomedical databases

“…After indexing, every shape was used as queries and the k-nearest neighbor vertebral images were retrieved using the Euclidean shape distance. Retrieval using a kD-tree consistently outperformed that of the metric tree, but both approaches were sublinear in complexity [26]. …”

A medical image retrieval scheme through a medical social network

“…A number of papers (Antani et al 2004;Iakovidis et al 2009;Antani et al 2003;Lee et al 2003;Xu et al 2008;Hsu et al 2009;Lee et al 2009;Qian et al 2010) have described investigations into every component of CBIR for spine X-ray retrieval, including feature extraction Lee et al 2003;Qian et al 2010), indexing (Qian et al 2010), similarity measurement (Xu et al 2008;Qian et al 2010), and visualization and refinement (Hsu et al 2009). …”