This paper presents two approaches to quantifying and visualizing variation in datasets of trees. The first approach localizes subtrees in which significant population differences are found through hypothesis testing and sparse classifiers on subtree features. The second approach visualizes the global metric structure of datasets through low-distortion embedding into hyperbolic planes in the style of multidimensional scaling. A case study is made on a dataset of airway trees in relation to Chronic Obstructive Pulmonary Disease.
Many data types represent entities which can be decomposed into parts or regions. Examples are graph-structured data @cite_9 @cite_26 , anatomical data which can be segmented into different organs @cite_14 @cite_1 or even single anatomical organs where additional spatial information is relevant; for instance, in the framework of shape analysis @cite_18 @cite_15 where local analysis is made on correspondence points on biomedical shape surfaces. A typical problem when studying such data is : A classifier will often only predict a certain diagnosis or class, but in order to understand the cause of the result (and, e.g. in diagnostic settings, react on it) one also desires to know which parts of the collection caused a certain classification outcome.
@cite_18 @cite_14 @cite_26 @cite_9 @cite_1 @cite_15
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Incorporation of prior knowledge about organ shape and location is key to improve performance of image analysis approaches. In particular, priors can be useful in cases where images are corrupted and contain artefacts due to limitations in image acquisition. The highly constrained nature of anatomical objects can be well captured with learning-based techniques. However, in most recent and promising techniques such as CNN-based segmentation it is not obvious how to incorporate such prior knowledge. State-of-the-art methods operate as pixel-wise classifiers where the training objectives do not incorporate the structure and inter-dependencies of the output. To overcome this limitation, we propose a generic training strategy that incorporates anatomical prior knowledge into CNNs through a new regularisation model, which is trained end-to-end. The new framework encourages models to follow the global anatomical properties of the underlying anatomy ( e.g. shape, label structure) via learnt non-linear representations of the shape. We show that the proposed approach can be easily adapted to different analysis tasks ( e.g. image enhancement, segmentation) and improve the prediction accuracy of the state-of-the-art models. The applicability of our approach is shown on multi-modal cardiac data sets and public benchmarks. In addition, we demonstrate how the learnt deep models of 3-D shapes can be interpreted and used as biomarkers for classification of cardiac pathologies. An important goal of statistical shape analysis is the discrimination between populations of objects, exploring group differences in morphology not explained by standard volumetric analysis. Certain applications additionally require analysis of objects in their embedding context by joint statistical analysis of sets of interrelated objects. In this paper, we present a framework for discriminant analysis of populations of 3-D multi-object sets. In view of the driving medical applications, a skelet al object parametrization of shape is chosen since it naturally encodes thickening, bending and twisting. In a multi-object setting, we not only consider a joint analysis of sets of shapes but also must take into account differences in pose. Statistics on features of medial descriptions and pose parameters, which include rotational frames and distances, uses a Riemannian symmetric space instead of the standard Euclidean metric. Our choice of discriminant method is the distance weighted discriminant (DWD) because of its generalization ability in high dimensional, low sample size settings. Joint analysis of 10 subcortical brain structures in a pediatric autism study demonstrates that multi-object analysis of shape results in a better group discrimination than pose, and that the combination of pose and shape performs better than shape alone. Finally, given a discriminating axis of shape and pose, we can visualize the differences between the populations. We present a new local descriptor for 3D shapes, directly applicable to a wide range of shape analysis problems such as point correspondences, semantic segmentation, affordance prediction, and shape-to-scan matching. The descriptor is produced by a convolutional network that is trained to embed geometrically and semantically similar points close to one another in descriptor space. The network processes surface neighborhoods around points on a shape that are captured at multiple scales by a succession of progressively zoomed-out views, taken from carefully selected camera positions. We leverage two extremely large sources of data to train our network. First, since our network processes rendered views in the form of 2D images, we repurpose architectures pretrained on massive image datasets. Second, we automatically generate a synthetic dense point correspondence dataset by nonrigid alignment of corresponding shape parts in a large collection of segmented 3D models. As a result of these design choices, our network effectively encodes multiscale local context and fine-grained surface detail. Our network can be trained to produce either category-specific descriptors or more generic descriptors by learning from multiple shape categories. Once trained, at test time, the network extracts local descriptors for shapes without requiring any part segmentation as input. Our method can produce effective local descriptors even for shapes whose category is unknown or different from the ones used while training. We demonstrate through several experiments that our learned local descriptors are more discriminative compared to state-of-the-art alternatives and are effective in a variety of shape analysis applications. This work addresses the challenging problem of simultaneously segmenting multiple anatomical structures in highly varied CT scans. We propose the entangled decision forest (EDF) as a new discriminative classifier which augments the state of the art decision forest, resulting in higher prediction accuracy and shortened decision time. Our main contribution is two-fold. First, we propose entangling the binary tests applied at each tree node in the forest, such that the test result can depend on the result of tests applied earlier in the same tree and at image points offset from the voxel to be classified. This is demonstrated to improve accuracy and capture long-range semantic context. Second, during training, we propose injecting randomness in a guided way, in which node feature types and parameters are randomly drawn from a learned (non-uniform) distribution. This further improves classification accuracy. We assess our probabilistic anatomy segmentation technique using a labeled database of CT image volumes of 250 different patients from various scan protocols and scanner vendors. In each volume, 12 anatomical structures have been manually segmented. The database comprises highly varied body shapes and sizes, a wide array of pathologies, scan resolutions, and diverse contrast agents. Quantitative comparisons with state of the art algorithms demonstrate both superior test accuracy and computational efficiency.