Towards Reliable and Accurate Global Structure-from-Motion

Reconstruction of objects or scenes from sparse point detections across multiple views is one of the most tackled problems in computer vision. Given the coordinates of 2D points tracked in multiple images, the problem consists of estimating the corresponding 3D points and cameras\u27 calibrations (intrinsic and pose), and can be solved by minimizing reprojection errors using bundle adjustment. However, given bundle adjustment\u27s nonlinear objective function and iterative nature, a good starting guess is required to converge to global minima. Global and Incremental Structure-from-Motion methods appear as ways to provide good initializations to bundle adjustment, each with different properties. While Global Structure-from-Motion has been shown to result in more accurate reconstructions compared to Incremental Structure-from-Motion, the latter has better scalability by starting with a small subset of images and sequentially adding new views, allowing reconstruction of sequences with millions of images. Additionally, both Global and Incremental Structure-from-Motion methods rely on accurate models of the scene or object, and under noisy conditions or high model uncertainty might result in poor initializations for bundle adjustment. Recently pOSE, a class of matrix factorization methods, has been proposed as an alternative to conventional Global SfM methods. These methods use VarPro - a second-order optimization method - to minimize a linear combination of an approximation of reprojection errors and a regularization term based on an affine camera model, and have been shown to converge to global minima with a high rate even when starting from random camera calibration estimations.This thesis aims at improving the reliability and accuracy of global SfM through different approaches. First, by studying conditions for global optimality of point set registration, a point cloud averaging method that can be used when (incomplete) 3D point clouds of the same scene in different coordinate systems are available. Second, by extending pOSE methods to different Structure-from-Motion problem instances, such as Non-Rigid SfM or radial distortion invariant SfM. Third and finally, by replacing the regularization term of pOSE methods with an exponential regularization on the projective depth of the 3D point estimations, resulting in a loss that achieves reconstructions with accuracy close to bundle adjustment

A preliminary investigation into the effects of nonlinear response modification within coupled oscillators

This thesis provides an account of an investigation into possible dynamic interactions between two coupled nonlinear sub-systems, each possessing opposing nonlinear overhang characteristics in the frequency domain in terms of positive and negative cubic stiffnesses. This system is a two degree-of-freedom Duffing oscillator coupled in series in which certain nonlinear effects can be advantageously neutralised under specific conditions. This theoretical vehicle has been used as a preliminary methodology for understanding the interactive behaviour within typical industrial ultrasonic cutting components. Ultrasonic energy is generated within a piezoelectric exciter, which is inherently nonlinear, and which is coupled to a bar-horn or block-horn to one, or more, material cutting blades, for example. The horn/blade configurations are also nonlinear, and within the whole system there are response features which are strongly reminiscent of positive and negative cubic stiffness effects. The two degree-of-freedom model is analysed and it is shown that a practically useful mitigating effect on the overall nonlinear response of the system can be created under certain conditions when one of the cubic stiffnesses is varied. It has also bfeen shown experimentally that coupling of ultrasonic components with different nonlinear characteristics can strongly influence the performance of the system and that the general behaviour of the hypothetical theoretical model is indeed borne out in practice

Towards the Formal Verification of Model Transformations: An Application to Kermeta

Model-Driven Engineering (MDE) is becoming a popular engineering methodology for developing large-scale software applications, using models and transformations as primary principles. MDE is now being successfully applied to domain-specific languages (DSLs), which target a narrow subject domain like process management, telecommunication, product lines, smartphone applications among others, providing experts high-level and intuitive notations very close to their problem domain. More recently, MDE has been applied to safety-critical applications, where failure may have dramatic consequences, either in terms of economic, ecologic or human losses. These recent application domains call for more robust and more practical approaches for ensuring the correctness of models and model transformations. Testing is the most common technique used in MDE for ensuring the correctness of model transformations, a recurrent, yet unsolved problem in MDE. But testing suffers from the so-called coverage problem, which is unacceptable when safety is at stake. Rather, exhaustive coverage is required in this application domain, which means that transformation designers need to use formal analysis methods and tools to meet this requirement. Unfortunately, two factors seem to limit the use of such methods in an engineer’s daily life. First, a methodological factor, because MDE engineers rarely possess the effective knowledge for deploying formal analysis techniques in their daily life developments. Second, a practical factor, because DSLs do not necessarily have a formal explicit semantics, which is a necessary enabler for exhaustive analysis. In this thesis, we contribute to the problem of formal analysis of model transformations regarding each perspective. On the conceptual side, we propose a methodological framework for engineering verified model transformations based on current best practices. For that purpose, we identify three important dimensions: (i) the transformation being built; (ii) the properties of interest ensuring the transformation’s correctness; and finally, (iii) the verification technique that allows proving these properties with minimal effort. Finding which techniques are better suited for which kind of properties is the concern of the Computer-Aided Verification community. Consequently in this thesis, we focus on studying the relationship between transformations and properties. Our methodological framework introduces two novel notions. A transformation intent gathers all transformations sharing the same purpose, abstracting from the way the transformation is expressed. A property class captures under the same denomination all properties sharing the same form, abstracting away from their underlying property languages. The framework consists of mapping each intent with its characteristic set of property classes, meaning that for proving the correctness of a particular transformation obeying this intent, one has to prove properties of these specific classes. We illustrate the use and utility of our framework through the detailed description of five common intents in MDE, and their application to a case study drawn from the automative software domain, consisting of a chain of more than thirty transformations. On a more practical side, we study the problem of verifying DSLs whose behaviour is expressed with Kermeta. Kermeta is an object-oriented transformation framework aligned with Object Management Group standard specification MOF (Meta-Object Facility). It can be used for defining metamodels and models, as well as their behaviour. Kermeta lacks a formal semantics: we first specify such a semantics, and then choose an appropriate verification domain for handling the analysis one is interested in. Since the semantics is defined at the level of Kermeta’s transformation language itself, our work presents two interesting features: first, any DSL whose behaviour is defined using Kermeta (more precisely, any transformation defined with Kermeta) enjoys a de facto formal underground for free; second, it is easier to define appropriate abstractions for targeting specific analysis for this full-fledged semantics than defining specific semantics for each possible kind of analysis. To illustrate this point, we have selected Maude, a powerful rewriting system based on algebraic specifications equipped with model-checking and theorem-proving capabilities. Maude was chosen because its underlying formalism is close to the mathematical tools we use for specifying the formal semantics, reducing the implementation gap and consequently limiting the possible implementation mistakes. We validate our approach by illustrating behavioural properties of small, yet representative DSLs from the literature

CALF: Categorical Automata Learning Framework

Automata learning is a popular technique used to automatically construct an automaton model from queries, and much research has gone into devising specific adaptations of such algorithms for different types of automata. This thesis presents a unifying approach to many existing algorithms using category theory, which eases correctness proofs and guides the design of new automata learning algorithms. We provide a categorical automata learning framework---CALF---that at its core includes an abstract version of the popular L* algorithm. Using this abstract algorithm we derive several concrete ones. We instantiate the framework to a large class of Set functors, by which we recover for the first time a tree automata learning algorithm from an abstract framework, which moreover is the first to cover also algebras of quotiented polynomial functors. We further develop a general algorithm to learn weighted automata over a semiring. On the one hand, we identify a class of semirings, principal ideal domains, for which this algorithm terminates and for which no learning algorithm previously existed; on the other hand, we show that it does not terminate over the natural numbers. Finally, we develop an algorithm to learn automata with side-effects determined by a monad and provide several optimisations, as well as an implementation with experimental evaluation. This allows us to improve existing algorithms and opens the door to learning a wide range of automata