Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices

Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the development of efficient algorithms for affine dynamical systems, available algorithms still lack scalability to ensure their wide adoption in the industrial setting. While modern linear algebra packages are efficient for matrices with tens of thousands of dimensions, set-based image computations are limited to a few hundred. We propose to decompose reach set computations such that set operations are performed in low dimensions, while matrix operations like exponentiation are carried out in the full dimension. Our method is applicable both in dense- and discrete-time settings. For a set of standard benchmarks, it shows a speed-up of up to two orders of magnitude compared to the respective state-of-the art tools, with only modest losses in accuracy. For the dense-time case, we show an experiment with more than 10.000 variables, roughly two orders of magnitude higher than possible with previous approaches

Bayesian Spatial Binary Regression for Label Fusion in Structural Neuroimaging

Many analyses of neuroimaging data involve studying one or more regions of interest (ROIs) in a brain image. In order to do so, each ROI must first be identified. Since every brain is unique, the location, size, and shape of each ROI varies across subjects. Thus, each ROI in a brain image must either be manually identified or (semi-) automatically delineated, a task referred to as segmentation. Automatic segmentation often involves mapping a previously manually segmented image to a new brain image and propagating the labels to obtain an estimate of where each ROI is located in the new image. A more recent approach to this problem is to propagate labels from multiple manually segmented atlases and combine the results using a process known as label fusion. To date, most label fusion algorithms either employ voting procedures or impose prior structure and subsequently find the maximum a posteriori estimator (i.e., the posterior mode) through optimization. We propose using a fully Bayesian spatial regression model for label fusion that facilitates direct incorporation of covariate information while making accessible the entire posterior distribution. We discuss the implementation of our model via Markov chain Monte Carlo and illustrate the procedure through both simulation and application to segmentation of the hippocampus, an anatomical structure known to be associated with Alzheimer's disease.Comment: 24 pages, 10 figure

A Survey on Deep Learning in Medical Image Registration: New Technologies, Uncertainty, Evaluation Metrics, and Beyond

Over the past decade, deep learning technologies have greatly advanced the field of medical image registration. The initial developments, such as ResNet-based and U-Net-based networks, laid the groundwork for deep learning-driven image registration. Subsequent progress has been made in various aspects of deep learning-based registration, including similarity measures, deformation regularizations, and uncertainty estimation. These advancements have not only enriched the field of deformable image registration but have also facilitated its application in a wide range of tasks, including atlas construction, multi-atlas segmentation, motion estimation, and 2D-3D registration. In this paper, we present a comprehensive overview of the most recent advancements in deep learning-based image registration. We begin with a concise introduction to the core concepts of deep learning-based image registration. Then, we delve into innovative network architectures, loss functions specific to registration, and methods for estimating registration uncertainty. Additionally, this paper explores appropriate evaluation metrics for assessing the performance of deep learning models in registration tasks. Finally, we highlight the practical applications of these novel techniques in medical imaging and discuss the future prospects of deep learning-based image registration

Trademark image retrieval by local features

The challenge of abstract trademark image retrieval as a test of machine vision algorithms has attracted considerable research interest in the past decade. Current operational trademark retrieval systems involve manual annotation of the images (the current ‘gold standard’). Accordingly, current systems require a substantial amount of time and labour to access, and are therefore expensive to operate. This thesis focuses on the development of algorithms that mimic aspects of human visual perception in order to retrieve similar abstract trademark images automatically. A significant category of trademark images are typically highly stylised, comprising a collection of distinctive graphical elements that often include geometric shapes. Therefore, in order to compare the similarity of such images the principal aim of this research has been to develop a method for solving the partial matching and shape perception problem. There are few useful techniques for partial shape matching in the context of trademark retrieval, because those existing techniques tend not to support multicomponent retrieval. When this work was initiated most trademark image retrieval systems represented images by means of global features, which are not suited to solving the partial matching problem. Instead, the author has investigated the use of local image features as a means to finding similarities between trademark images that only partially match in terms of their subcomponents. During the course of this work, it has been established that the Harris and Chabat detectors could potentially perform sufficiently well to serve as the basis for local feature extraction in trademark image retrieval. Early findings in this investigation indicated that the well established SIFT (Scale Invariant Feature Transform) local features, based on the Harris detector, could potentially serve as an adequate underlying local representation for matching trademark images. There are few researchers who have used mechanisms based on human perception for trademark image retrieval, implying that the shape representations utilised in the past to solve this problem do not necessarily reflect the shapes contained in these image, as characterised by human perception. In response, a ii practical approach to trademark image retrieval by perceptual grouping has been developed based on defining meta-features that are calculated from the spatial configurations of SIFT local image features. This new technique measures certain visual properties of the appearance of images containing multiple graphical elements and supports perceptual grouping by exploiting the non-accidental properties of their configuration. Our validation experiments indicated that we were indeed able to capture and quantify the differences in the global arrangement of sub-components evident when comparing stylised images in terms of their visual appearance properties. Such visual appearance properties, measured using 17 of the proposed metafeatures, include relative sub-component proximity, similarity, rotation and symmetry. Similar work on meta-features, based on the above Gestalt proximity, similarity, and simplicity groupings of local features, had not been reported in the current computer vision literature at the time of undertaking this work. We decided to adopted relevance feedback to allow the visual appearance properties of relevant and non-relevant images returned in response to a query to be determined by example. Since limited training data is available when constructing a relevance classifier by means of user supplied relevance feedback, the intrinsically non-parametric machine learning algorithm ID3 (Iterative Dichotomiser 3) was selected to construct decision trees by means of dynamic rule induction. We believe that the above approach to capturing high-level visual concepts, encoded by means of meta-features specified by example through relevance feedback and decision tree classification, to support flexible trademark image retrieval and to be wholly novel. The retrieval performance the above system was compared with two other state-of-the-art image trademark retrieval systems: Artisan developed by Eakins (Eakins et al., 1998) and a system developed by Jiang (Jiang et al., 2006). Using relevance feedback, our system achieves higher average normalised precision than either of the systems developed by Eakins’ or Jiang. However, while our trademark image query and database set is based on an image dataset used by Eakins, we employed different numbers of images. It was not possible to access to the same query set and image database used in the evaluation of Jiang’s trademark iii image retrieval system evaluation. Despite these differences in evaluation methodology, our approach would appear to have the potential to improve retrieval effectiveness