Machine learning -- based diffractive imaging with subwavelength resolution

Far-field characterization of small objects is severely constrained by the diffraction limit. Existing tools achieving sub-diffraction resolution often utilize point-by-point image reconstruction via scanning or labelling. Here, we present a new imaging technique capable of fast and accurate characterization of two-dimensional structures with at least wavelength/25 resolution, based on a single far-field intensity measurement. Experimentally, we realized this technique resolving the smallest-available to us 180-nm-scale features with 532-nm laser light. A comprehensive analysis of machine learning algorithms was performed to gain insight into the learning process and to understand the flow of subwavelength information through the system. Image parameterization, suitable for diffractive configurations and highly tolerant to random noise was developed. The proposed technique can be applied to new characterization tools with high spatial resolution, fast data acquisition, and artificial intelligence, such as high-speed nanoscale metrology and quality control, and can be further developed to high-resolution spectroscop

An output-sensitive algorithm for the minimization of 2-dimensional String Covers

String covers are a powerful tool for analyzing the quasi-periodicity of 1-dimensional data and find applications in automata theory, computational biology, coding and the analysis of transactional data. A \emph{cover} of a string $T$ is a string $C$ for which every letter of $T$ lies within some occurrence of $C$. String covers have been generalized in many ways, leading to \emph{k-covers}, \emph{$\lambda$-covers}, \emph{approximate covers} and were studied in different contexts such as \emph{indeterminate strings}. In this paper we generalize string covers to the context of 2-dimensional data, such as images. We show how they can be used for the extraction of textures from images and identification of primitive cells in lattice data. This has interesting applications in image compression, procedural terrain generation and crystallography

An elementary algorithm for digital arc segmentation

International audienceThis paper concerns the digital circle recognition problem, especially in the form of the circular separation problem. General fundamentals, based on classical tools, as well as algorithmic details are given (the latter by providing pseudo-code for major steps of the algorithm). After recalling the geometrical meaning of the separating circle problem, we present an incremental algorithm to segment a discrete curve into digital arcs

Temporal shape super-resolution by intra-frame motion encoding using high-fps structured light

One of the solutions of depth imaging of moving scene is to project a static pattern on the object and use just a single image for reconstruction. However, if the motion of the object is too fast with respect to the exposure time of the image sensor, patterns on the captured image are blurred and reconstruction fails. In this paper, we impose multiple projection patterns into each single captured image to realize temporal super resolution of the depth image sequences. With our method, multiple patterns are projected onto the object with higher fps than possible with a camera. In this case, the observed pattern varies depending on the depth and motion of the object, so we can extract temporal information of the scene from each single image. The decoding process is realized using a learning-based approach where no geometric calibration is needed. Experiments confirm the effectiveness of our method where sequential shapes are reconstructed from a single image. Both quantitative evaluations and comparisons with recent techniques were also conducted.Comment: 9 pages, Published at the International Conference on Computer Vision (ICCV 2017

Data compression techniques applied to high resolution high frame rate video technology

An investigation is presented of video data compression applied to microgravity space experiments using High Resolution High Frame Rate Video Technology (HHVT). An extensive survey of methods of video data compression, described in the open literature, was conducted. The survey examines compression methods employing digital computing. The results of the survey are presented. They include a description of each method and assessment of image degradation and video data parameters. An assessment is made of present and near term future technology for implementation of video data compression in high speed imaging system. Results of the assessment are discussed and summarized. The results of a study of a baseline HHVT video system, and approaches for implementation of video data compression, are presented. Case studies of three microgravity experiments are presented and specific compression techniques and implementations are recommended

Robust convex optimisation techniques for autonomous vehicle vision-based navigation

This thesis investigates new convex optimisation techniques for motion and pose estimation. Numerous computer vision problems can be formulated as optimisation problems. These optimisation problems are generally solved via linear techniques using the singular value decomposition or iterative methods under an L2 norm minimisation. Linear techniques have the advantage of offering a closed-form solution that is simple to implement. The quantity being minimised is, however, not geometrically or statistically meaningful. Conversely, L2 algorithms rely on iterative estimation, where a cost function is minimised using algorithms such as Levenberg-Marquardt, Gauss-Newton, gradient descent or conjugate gradient. The cost functions involved are geometrically interpretable and can statistically be optimal under an assumption of Gaussian noise. However, in addition to their sensitivity to initial conditions, these algorithms are often slow and bear a high probability of getting trapped in a local minimum or producing infeasible solutions, even for small noise levels. In light of the above, in this thesis we focus on developing new techniques for finding solutions via a convex optimisation framework that are globally optimal. Presently convex optimisation techniques in motion estimation have revealed enormous advantages. Indeed, convex optimisation ensures getting a global minimum, and the cost function is geometrically meaningful. Moreover, robust optimisation is a recent approach for optimisation under uncertain data. In recent years the need to cope with uncertain data has become especially acute, particularly where real-world applications are concerned. In such circumstances, robust optimisation aims to recover an optimal solution whose feasibility must be guaranteed for any realisation of the uncertain data. Although many researchers avoid uncertainty due to the added complexity in constructing a robust optimisation model and to lack of knowledge as to the nature of these uncertainties, and especially their propagation, in this thesis robust convex optimisation, while estimating the uncertainties at every step is investigated for the motion estimation problem. First, a solution using convex optimisation coupled to the recursive least squares (RLS) algorithm and the robust H filter is developed for motion estimation. In another solution, uncertainties and their propagation are incorporated in a robust L convex optimisation framework for monocular visual motion estimation. In this solution, robust least squares is combined with a second order cone program (SOCP). A technique to improve the accuracy and the robustness of the fundamental matrix is also investigated in this thesis. This technique uses the covariance intersection approach to fuse feature location uncertainties, which leads to more consistent motion estimates. Loop-closure detection is crucial in improving the robustness of navigation algorithms. In practice, after long navigation in an unknown environment, detecting that a vehicle is in a location it has previously visited gives the opportunity to increase the accuracy and consistency of the estimate. In this context, we have developed an efficient appearance-based method for visual loop-closure detection based on the combination of a Gaussian mixture model with the KD-tree data structure. Deploying this technique for loop-closure detection, a robust L convex posegraph optimisation solution for unmanned aerial vehicle (UAVs) monocular motion estimation is introduced as well. In the literature, most proposed solutions formulate the pose-graph optimisation as a least-squares problem by minimising a cost function using iterative methods. In this work, robust convex optimisation under the L norm is adopted, which efficiently corrects the UAV’s pose after loop-closure detection. To round out the work in this thesis, a system for cooperative monocular visual motion estimation with multiple aerial vehicles is proposed. The cooperative motion estimation employs state-of-the-art approaches for optimisation, individual motion estimation and registration. Three-view geometry algorithms in a convex optimisation framework are deployed on board the monocular vision system for each vehicle. In addition, vehicle-to-vehicle relative pose estimation is performed with a novel robust registration solution in a global optimisation framework. In parallel, and as a complementary solution for the relative pose, a robust non-linear H solution is designed as well to fuse measurements from the UAVs’ on-board inertial sensors with the visual estimates. The suggested contributions have been exhaustively evaluated over a number of real-image data experiments in the laboratory using monocular vision systems and range imaging devices. In this thesis, we propose several solutions towards the goal of robust visual motion estimation using convex optimisation. We show that the convex optimisation framework may be extended to include uncertainty information, to achieve robust and optimal solutions. We observed that convex optimisation is a practical and very appealing alternative to linear techniques and iterative methods