Supervised learning has been very successful for automatic segmentation of images from a single scanner. However, several papers report deteriorated performances when using classifiers trained on images from one scanner to segment images from other scanners. We propose a transfer learning classifier that adapts to differences between training and test images. This method uses a weighted ensemble of classifiers trained on individual images. The weight of each classifier is determined by the similarity between its training image and the test image. We examine three unsupervised similarity measures, which can be used in scenarios where no labeled data from a newly introduced scanner or scanning protocol is available. The measures are based on a divergence, a bag distance, and on estimating the labels with a clustering procedure. These measures are asymmetric. We study whether the asymmetry can improve classification. Out of the three similarity measures, the bag similarity measure is the most robust across different studies and achieves excellent results on four brain tissue segmentation datasets and three white matter lesion segmentation datasets, acquired at different centers and with different scanners and scanning protocols. We show that the asymmetry can indeed be informative, and that computing the similarity from the test image to the training images is more appropriate than the opposite direction.
Chronic obstructive pulmonary disease (COPD) is a lung disease where early detection benefits the survival rate. COPD can be quantified by classifying patches of computed tomography images, and combining patch labels into an overall diagnosis for the image. As labeled patches are often not available, image labels are propagated to the patches, incorrectly labeling healthy patches in COPD patients as being affected by the disease. We approach quantification of COPD from lung images as a multiple instance learning (MIL) problem, which is more suitable for such weakly labeled data. We investigate various MIL assumptions in the context of COPD and show that although a concept region with COPD-related disease patterns is present, considering the whole distribution of lung tissue patches improves the performance. The best method is based on averaging instances and obtains an AUC of 0.742, which is higher than the previously reported best of 0.713 on the same dataset. Using the full training set further increases performance to 0.776, which is significantly higher (DeLong test) than previous results.
Knowledge of airway tree morphology has important clinical applications in diagnosis of chronic obstructive pulmonary disease. We present an automatic tree extraction method based on multiple hypothesis tracking and template matching for this purpose and evaluate its performance on chest CT images. The method is adapted from a semi-automatic method devised for vessel segmentation. Idealized tubular templates are constructed that match airway probability obtained from a trained classifier and ranked based on their relative significance. Several such regularly spaced templates form the local hypotheses used in constructing a multiple hypothesis tree, which is then traversed to reach decisions. The proposed modifications remove the need for local thresholding of hypotheses as decisions are made entirely based on statistical comparisons involving the hypothesis tree. The results show improvements in performance when compared to the original method and region growing on intensity images. We also compare the method with region growing on the probability images, where the presented method does not show substantial improvement, but we expect it to be less sensitive to local anomalies in the data.
Methodological contributions: This paper introduces a family of kernels for analyzing (anatomical) trees endowed with vector valued measurements made along the tree. While state-of-the-art graph and tree kernels use combinatorial tree/graph structure with discrete node and edge labels, the kernels presented in this paper can include geometric information such as branch shape, branch radius or other vector valued properties. In addition to being flexible in their ability to model different types of attributes, the presented kernels are computationally efficient and some of them can easily be computed for large datasets (N of the order 10.000) of trees with 30-600 branches. Combining the kernels with standard machine learning tools enables us to analyze the relation between disease and anatomical tree structure and geometry. Experimental results: The kernels are used to compare airway trees segmented from low-dose CT, endowed with branch shape descriptors and airway wall area percentage measurements made along the tree. Using kernelized hypothesis testing we show that the geometric airway trees are significantly differently distributed in patients with Chronic Obstructive Pulmonary Disease (COPD) than in healthy individuals. The geometric tree kernels also give a significant increase in the classification accuracy of COPD from geometric tree structure endowed with airway wall thickness measurements in comparison with state-of-the-art methods, giving further insight into the relationship between airway wall thickness and COPD. Software: Software for computing kernels and statistical tests is available at http://image.diku.dk/aasa/software.php.
In order to develop statistical methods for shapes with a tree-structure, we construct a shape space framework for tree-like shapes and study metrics on the shape space. This shape space has singularities, corresponding to topological transitions in the represented trees. We study two closely related metrics on the shape space, TED and QED. QED is a quotient Euclidean distance arising naturally from the shape space formulation, while TED is the classical tree edit distance. Using Gromov's metric geometry we gain new insight into the geometries defined by TED and QED. We show that the new metric QED has nice geometric properties which facilitate statistical analysis, such as existence and local uniqueness of geodesics and averages. TED, on the other hand, does not share the geometric advantages of QED, but has nice algorithmic properties. We provide a theoretical framework and experimental results on synthetic data trees as well as airway trees from pulmonary CT scans. This way, we effectively illustrate that our framework has both the theoretical and qualitative properties necessary to build a theory of statistical tree-shape analysis.