Abstract-Defining the support (or frequency) of a subgraph is trivial when a database of graphs is given: it is simply the number of graphs in the database that contain the subgraph. However, if the input is one large graph, an appropriate support definition is much more difficult to find. In this paper we study the core problem, namely overlapping embeddings of the subgraph, in detail and suggest a definition that relies on the non-existence of equivalent ancestor embeddings in order to guarantee that the resulting support is anti-monotone. We prove this property and describe a method to compute the support defined in this way.

Evaluating the success of prediction and retrieval systems depends upon a reliable reference standard, a ground truth. The ideal gold standard is expected to result from the marking, labeling, and rating of domain experts of the image of interest. However experts often disagree and this lack of agreement challenges the development and evaluation of image-based feature prediction of expert-defined "truth." This paper addresses the success and limitations in bridging the semantic gap between CT-based pulmonary nodule image features and the ratings of diagnostic characteristics recorded by expert pulmonary radiologists. The prediction of diagnostic characteristics promises to automatically annotate medical images with medically meaningful descriptions directly usable for indexing and retrieving in content-based image retrieval (CBIR) and assisting in computer aided diagnosis (CADx). Successful results in predicting texture characteristics will be contrasted with less successful results for boundary shapes. The two primary differences in agreement between radiologists will be discussed; the first concerns agreement about the existence of a nodule, while the second considers the variability in diagnostic ratings among radiologists who agree on the presence of a nodule.

Using computer-calculated features to characterize the shape of suspicious lesions aims to assist the diagnosis of pulmonary nodules; moreover, these computerized features have to be in agreement with radiologists' ratings measuring their human perception of the nodules' shape. In the Lung Image Database Consortium (LIDC), there exists strong disagreement among the radiologists on the ratings of the shape diagnostic characteristics as well as on their drawn outlines of the extent of the nodules. Since shape is often considered a property of the object boundary and the manual boundaries are not consistent among radiologists, new methods are necessary to, first, define regionbased boundaries that use radiologists' outlines as guides and, second, adapt computer-based shape measurements to use regions rather than the traditional nodule segmentation outlines. This paper introduces a method for defining a boundary region of interest by combining radiologist-drawn outlines (the pixel-set difference between the union and intersection of all radiologist-drawn outlines for a specific nodule), then adapts a radial gradient indexing method for use within image regions, and lastly predicts several composite ratings of sets of radiologists for shape-based characteristics: spiculation, lobulation, and sphericity. The prediction of the majority (mode) rating significantly outperforms earlier work on predicting the ratings of individual radiologists. The prediction of spiculation improves to 53% from 41%, lobulation increases to 44% from 38%, and sphericity improves to 58% from 43%. A binary version of the rating has high accuracy but poor Kappa agreement for all three shape characteristics.

Computer-aided diagnostic characterization (CADc) aims to support medical imaging decision making by objectively rating the radiologists' subjective, perceptual opinions of visual diagnostic characteristics of suspicious lesions. This research uses the publicly available Lung Image Database Consortium (LIDC) collection of radiologists' outlines of nodules and ratings of boundary and shape characteristics: spiculation, margin, lobulation, and sphericity. The approach attempts to reduce the observed disagreement between radiologists on the extent of nodules by combining their spatial opinion using probability maps to create regions of interest (ROIs). From these ROIs, images features are extracted and combined using machine learning models to predict a combined opinion, the median rating and a thresholded, binary version of their diagnostic characteristics. The results show slight to fair agreement-linear-weighted Kappa-between the CADc models and median radiologist opinion for the full scale five-level rating and fair to moderate agreement using a binary version of the median radiologist opinion.

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