Using machine learning on new feature sets extracted from three-dimensional models of broken animal bones to classify fragments according to break agent.

Distinguishing agents of bone modification at paleoanthropological sites is an important means of understanding early hominin evolution. Fracture pattern analysis is used to help determine site formation processes, including whether hominins were hunting or scavenging for animal food resources. Determination of how these behaviors manifested in ancient human sites has major implications for our biological and behavioral evolution, including social and cognitive abilities, dietary impacts of having access to in-bone nutrients like marrow, and cultural variation in butchering and food processing practices. Nevertheless, previous analyses remain inconclusive, often suffering from lack of replicability, misuse of mathematical methods, and/or failure to overcome equifinality. In this paper, we present a new approach aimed at distinguishing bone fragments resulting from hominin and carnivore breakage. Our analysis is founded on a large collection of scanned three-dimensional models of fragmentary bone broken by known agents, to which we apply state of the art machine learning algorithms. Our classification of fragments achieves an average mean accuracy of 77% across tests, thus demonstrating notable, but not overwhelming, success for distinguishing the agent of breakage. We note that, while previous research applying such algorithms has claimed higher success rates, fundamental errors in the application of machine learning protocols suggest that the reported accuracies are unjustified and unreliable. The systematic, fully documented, and proper application of machine learning algorithms leads to an inherent reproducibility of our study, and therefore our methods hold great potential for deciphering when and where hominins first began exploiting marrow and meat, and clarifying their importance and influence on human evolution.

Accelerated Variational PDEs for Efficient Solution of Regularized Inversion Problems.

We further develop a new framework, called PDE acceleration, by applying it to calculus of variation problems defined for general functions on ℝ n , obtaining efficient numerical algorithms to solve the resulting class of optimization problems based on simple discretizations of their corresponding accelerated PDEs. While the resulting family of PDEs and numerical schemes are quite general, we give special attention to their application for regularized inversion problems, with particular illustrative examples on some popular image processing applications. The method is a generalization of momentum, or accelerated, gradient descent to the PDE setting. For elliptic problems, the descent equations are a nonlinear damped wave equation, instead of a diffusion equation, and the acceleration is realized as an improvement in the CFL condition from Δt ~ Δx 2 (for diffusion) to Δt ~ Δx (for wave equations). We work out several explicit as well as a semi-implicit numerical scheme, together with their necessary stability constraints, and include recursive update formulations which allow minimal-effort adaptation of existing gradient descent PDE codes into the accelerated PDE framework. We explore these schemes more carefully for a broad class of regularized inversion applications, with special attention to quadratic, Beltrami, and total variation regularization, where the accelerated PDE takes the form of a nonlinear wave equation. Experimental examples demonstrate the application of these schemes for image denoising, deblurring, and inpainting, including comparisons against primal-dual, split Bregman, and ADMM algorithms.

Robust variational segmentation of 3D bone CT data with thin cartilage interfaces.

We present a two-stage variational approach for segmenting 3D bone CT data that performs robustly with respect to thin cartilage interfaces. In the first stage, we minimize a flux-augmented Chan-Vese model that accurately segments well-separated regions. In the second stage, we apply a new phase-field fracture inspired model that reliably eliminates spurious bridges across thin cartilage interfaces, resulting in an accurate segmentation topology, from which each bone object can be identified. Its mathematical formulation is based on the phase-field approach to variational fracture, which naturally blends with the variational approach to segmentation. We successfully test and validate our methodology for the segmentation of 3D femur and vertebra bones, which feature thin cartilage regions in the hip joint, the intervertebral disks, and synovial joints of the spinous processes. The major strength of the new methodology is its potential for full automation and seamless integration with downstream predictive bone simulation in a common finite element framework.

Multicriteria Similarity-Based Anomaly Detection Using Pareto Depth Analysis.

We consider the problem of identifying patterns in a data set that exhibits anomalous behavior, often referred to as anomaly detection. Similarity-based anomaly detection algorithms detect abnormally large amounts of similarity or dissimilarity, e.g., as measured by the nearest neighbor Euclidean distances between a test sample and the training samples. In many application domains, there may not exist a single dissimilarity measure that captures all possible anomalous patterns. In such cases, multiple dissimilarity measures can be defined, including nonmetric measures, and one can test for anomalies by scalarizing using a nonnegative linear combination of them. If the relative importance of the different dissimilarity measures are not known in advance, as in many anomaly detection applications, the anomaly detection algorithm may need to be executed multiple times with different choices of weights in the linear combination. In this paper, we propose a method for similarity-based anomaly detection using a novel multicriteria dissimilarity measure, the Pareto depth. The proposed Pareto depth analysis (PDA) anomaly detection algorithm uses the concept of Pareto optimality to detect anomalies under multiple criteria without having to run an algorithm multiple times with different choices of weights. The proposed PDA approach is provably better than using linear combinations of the criteria, and shows superior performance on experiments with synthetic and real data sets.

Pareto-depth for multiple-query image retrieval.

Most content-based image retrieval systems consider either one single query, or multiple queries that include the same object or represent the same semantic information. In this paper, we consider the content-based image retrieval problem for multiple query images corresponding to different image semantics. We propose a novel multiple-query information retrieval algorithm that combines the Pareto front method with efficient manifold ranking. We show that our proposed algorithm outperforms state of the art multiple-query retrieval algorithms on real-world image databases. We attribute this performance improvement to concavity properties of the Pareto fronts, and prove a theoretical result that characterizes the asymptotic concavity of the fronts.

Optimal real-time Q-ball imaging using regularized Kalman filtering with incremental orientation sets.

Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation. Since its inception, Diffusion MRI has expanded considerably to include a number of variations such as diffusion tensor imaging (DTI), diffusion spectrum imaging (DSI) and Q-ball imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real-time during the repetition time (TR) of the acquisition sequence. In this article, we first revisit and thoroughly analyze this approach and show it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the standard offline processing techniques and outperforms the existing solution. Last, we propose a fast algorithm to recursively compute gradient orientation sets whose partial subsets are almost uniform and show that it can also be applied to the problem of efficiently ordering an existing point-set of any size. This work enables a clinician to start an acquisition with just the minimum number of gradient directions and an initial estimate of the orientation distribution functions (ODF) and then the next gradient directions and ODF estimates can be recursively and optimally determined, allowing the acquisition to be stopped as soon as desired or at any iteration with the optimal ODF estimates. This opens new and interesting opportunities for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion orientation sets and real-time fiber tracking and connectivity mapping.