How many models/atlases are needed as priors for capturing anatomic population variations?

Many medical image processing and analysis operations can benefit a great deal from prior information encoded in the form of models/atlases to capture variations over a population in form, shape, anatomic layout, and image appearance of objects. However, two fundamental questions have not been addressed in the literature: "How many models/atlases are needed for optimally encoding prior information to address the differing body habitus factor in that population?" and "Images of how many subjects in the given population are needed to optimally harness prior information?" We propose a method to seek answers to these questions. We assume that there is a well-defined body region of interest and a subject population under consideration, and that we are given a set of representative images of the body region for the population. After images are trimmed to the exact body region, a hierarchical agglomerative clustering algorithm partitions the set of images into a specified number of groups by using pairwise image (dis)similarity as a cost function. Optionally the images may be pre-registered among themselves prior to this partitioning operation. We define a measure called Residual Dissimilarity (RD) to determine the goodness of each partition. We then ascertain how RD varies as a function of the number of elements in the partition for finding the optimum number(s) of groups. Breakpoints in this function are taken as the recommended number of groups/models/atlases. Our results from analysis of sizeable CT data sets of adult patients from two body regions - thorax (346) and head and neck (298) - can be summarized as follows. (1) A minimum of 5 to 8 groups (or models/atlases) seems essential to properly capture information about differing anatomic forms and body habitus. (2) A minimum of 150 images from different subjects in a population seems essential to cover the anatomical variations for a given body region. (3) In grouping, body habitus variations seem to override differences due to other factors such as gender, with/without contrast enhancement in image acquisition, and presence of moderate pathology. This method may be helpful for constructing high quality models/atlases from a sufficiently large population of images and in optimally selecting the training image sets needed in deep learning strategies.