Bottom-Up Shape Analysis

Reliable banknote recognition is critical for detecting counterfeit banknotes in ATMs and help visual impaired people. To solve this problem, it was implemented a computer vision system that can recognize multiple banknotes in different perspective views and scales, even when they are within cluttered environments in which the lighting conditions may vary considerably. The system is also able to recognize banknotes that are partially visible, folded, wrinkled or even worn by usage. To accomplish this task, the system relies on computer vision algorithms, such as image preprocessing, feature detection, description and matching. To improve the confidence of the banknote recognition the feature matching results are used to compute the contour of the banknotes using an homography that later on is validated using shape analysis algorithms. The system successfully recognized all Euro banknotes in 80 test images even when there were several overlapping banknotes in the same test image.

As a dominant method in evidential reasoning, Bayesian network has been proved powerful in discrete fields. Although Bayesian network performs reliable in continuous variables and interval estimations, it relies on discretizing continuous variables or building an approximate model to conduct, which causes information loss and accuracy reduction. In order to bridge this gap, this paper introduces two inference rules combined with four inference rules proposed by other scholars. Then we propose a concept of uncertain inference network that consists of six basic structures matching inference rules to represent relationships and logic connection among the evidence. Evidence is represented by uncertain sets that can apply to continuous variables using membership functions to represent vague concepts. Furthermore, a numeric experiment for a forensic investigation of fire incidents is given to compare the results of uncertain inference network and Bayesian network. We found three merits in the case study. First, an uncertain inference network has simpler data access for each node because Bayesian network depends on conditional probability tables while uncertain inference network only relies on membership function. Second, an uncertain inference network has a more wide application because it can perform continuous variables with certain mathematical formulas without discretizing or approximating. Third, an uncertain inference network has a more accurate result because Bayesian network gives a point estimation with a 0–1 value while uncertain inference network conducts an interval estimation with a range value.

Algorithms for shape analysis are reviewed and classified under various criteria, whether they examine the boundary only or the whole area and whether they describe the original picture in terms of scalar measurements or through structural descriptions. The emphasis is on methodologies which have been popular during the last five years and among them, those which are information preserving.

Formal verification involves the use of logical and computational methods to establish claims that are expressed in precise mathematical terms. These can include ordinary mathematical theorems, as well as claims that pieces of hardware or software, network protocols, and mechanical and hybrid systems meet their specifications. In practice, there is not a sharp distinction between verifying a piece of mathematics and verifying the correctness of a system: formal verification requires describing hardware and software systems in mathematical terms, at which point establishing claims as to their correctness becomes a form of theorem proving. Conversely, the proof of a mathematical theorem may require a lengthy computation, in which case verifying the truth of the theorem requires verifying that the computation does what it is supposed to do. The gold standard for supporting a mathematical claim is to provide a proof, and twentieth-century developments in logic show most if not all conventional proof methods can be reduced to a small set of axioms and rules in any of a number of foundational systems. With this reduction, there are two ways that a computer can help establish a claim: it can help find a proof in the first place, and it can help verify that a purported proof is correct. Automated theorem proving focuses on the “finding” aspect. Resolution theorem provers, tableau theorem provers, fast satisfiability solvers, and so on provide means of establishing the validity of formulas in propositional and first-order logic. Other systems provide search procedures and decision procedures for specific languages and domains, such as linear or nonlinear expressions over the integers or the real numbers. Architectures like SMT (“satisfiability modulo theories”) combine domain-general search methods with domain-specific procedures. Computer algebra systems and specialized mathematical software packages provide means of carrying out mathematical computations, establishing mathematical bounds, or finding mathematical objects. A calculation can be viewed as a proof as well, and these systems, too, help establish mathematical claims. Automated reasoning systems strive for power and efficiency, often at the expense of guaranteed soundness. Such systems can have bugs, and it can be difficult to ensure that the results they deliver are correct. In contrast, interactive theorem proving focuses on the “verification” aspect of theorem proving, requiring that every claim is supported by a proof in a suitable axiomatic foundation. This sets a very high standard: every rule of inference and every step of a calculation has to be justified by appealing to prior definitions and theorems, all the way down to basic axioms and rules. In fact, most such systems provide fully elaborated “proof objects” that can be communicated to other systems and checked independently. Constructing such proofs typically requires much more input and interaction from users, but it allows us to obtain deeper and more complex proofs. The Lean Theorem Prover aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction of fully specified axiomatic proofs. The goal is to support both mathematical reasoning and reasoning about complex systems, and to verify claims in both domains.

Preface: Volume 58, Issue 2

Induction is a successful approach for verification of hardware and software systems. A common practice is to model a system using logical formulas, and then use a decision procedure to verify that some logical formula is an inductive safety invariant for the system. A key ingredient in this approach is coming up with the inductive invariant, which is known as invariant inference. This is a major difficulty, and it is often left for humans or addressed by sound but incomplete abstract interpretation. This paper is motivated by the problem of inductive invariants in shape analysis and in distributed protocols. This paper approaches the general problem of inferring first-order inductive invariants by restricting the language L of candidate invariants. Notice that the problem of invariant inference in a restricted language L differs from the safety problem, since a system may be safe and still not have any inductive invariant in L that proves safety. Clearly, if L is finite (and if testing an inductive invariant is decidable), then inferring invariants in L is decidable. This paper presents some interesting cases when inferring inductive invariants in L is decidable even when L is an infinite language of universal formulas. Decidability is obtained by restricting L and defining a suitable well-quasi-order on the state space. We also present some undecidability results that show that our restrictions are necessary. We further present a framework for systematically constructing infinite languages while keeping the invariant inference problem decidable. We illustrate our approach by showing the decidability of inferring invariants for programs manipulating linked-lists, and for distributed protocols.

Shape Analysis is concerned with determining invariants, i.e. structural properties of the heap, for programs that manipulate pointers and heap-allocated storage. Recently, very precise shape analysis algorithms have been developed that are able to prove the partial correctness of heap-manipulating programs. We explore the use of shape analysis to analyze abstract data types (ADTs). The ADT Set shall serve as an example, as it is widely used and can be found in most of the major data type libraries, like STL, the Java API, or LEDA. We formalize our notion of the ADT Set by algebraic specification. Two prototypical C set implementations are presented, one based on lists, the other on trees. We instantiate a parametric shape analysis framework to generate analyses that are able to prove the compliance of the two implementations to their specification.

Much software is written in industry standard programming languages, but these languages often have complex semantics making them hard to formalize. For example, the use of expressions with side effects is common in C programs. We present new inference rules for conditional (if) statements and looping constructs (while) with pre- and postevaluation side effects in their test expressions. These inference rules allow us to formally reason about the security properties of programs. We maintain that formal verification of secure programs written in common languages is feasible and can be worthwhile. To support our claim, we give an example of how our verification of a secure web server uncovered some previously unknown problems. Automated theorem proving assistants can help deal with complex inference rules, but many components must be brought together to make a broadly useful system. We propose elements of a formal verification system which could be widely useful.

Automatic verification of programs manipulating arrays relies on specialised decision procedures. A methodology to classify the theories handled by these procedures is introduced. It is based on decomposition theorems in the style of Feferman and Vaught. The method is applied to obtain an extension of combinatory array logic that is closed under propositional operations and Hoare triples. A classification according to expressiveness of six different fragments studied in the literature is given.

Algorithms for pulse shape analysis using silicon detectors

Stream-processing functions provide an excellent semantic model for the abstract representation of systems of nondeterministic concurrent communicating agents. Based on this model a formalism for the specification of such functions is suggested. This way a fully modular, compositional methodology for the specification and the design of distributed systems and their components is derived. Concepts of correctness are defined and rules of inference are discussed that help to transform such specifications into a network of communicating agents. A combinatorial (functional) notation for the sequential and parallel composition as well as feedback for those agents is introduced.

Diagnostic performance of McMaster, Wisconsin, and automated egg counting techniques for enumeration of equine strongyle eggs in fecal samples

I propose novel 3D shape analysis and modeling algorithm for active contours using variational scheme. The proposed algorithm utilizes an unknown surface of 3D shape by normal to 3D shape analysis and modeling. It would be used to get high quality reconstruction's results from many dimensions' data. I give it by utilizing continuous anisotropism weights would finish comparable ameliorate to surface reconstruction.

Gamma-ray imaging techniques, such as Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT), are becoming increasingly important for clinical diagnosis. As the power of these methods becomes more evident, the use of these techniques is becoming more widespread However, the performance of existing systems is restricted by the inherent properties of the scintillator detectors they are based on (e.g. poor energy resolution). The development of High Purity Germanium detectors has now reached the stage where they can be used as effective imaging devices. The electrical segmentation of the Germanium crystal coupled with digital signal processing electronics allows the measurement of energy, time, and position following the interaction of a gamma-ray. We propose to build a PET imaging system composed of two segmented planar HPGe detectors. The position and energy information are extracted following the digitisation of the detector charge signal, analysed using Pulse Shape Analysis (PSA) algorithms. Such a technique can potentially give a position resolution of about 1 mm/sup 3/ inside the detector volume. A prototype of a Compton camera has been built in order to test our pulse processing techniques and develop some gamma-ray tracking algorithms. The system is composed of a planar detector with 5mm strips in a 24/spl times/12 configuration, and a 16 segment coaxial Clover detector. Before being able to reconstruct the path of gamma-rays with the camera, it is necessary to calibrate the response of each detector as a function of the position. Several characterisation measurements have been made using an automated detector scanning systems. Preliminary results from the characterisation of the Clover will are presented in this paper.

Tracking subset relations between the contents containers on the heap is fundamental to modeling the semantics of many common programing idioms such as applying a function to a subset of objects and maintaining multiple views of the same set of objects. We introduce a relation, must reference sets, which subsumes the concept of must-aliasing and enables existing shape analysis techniques to efficiently and accurately model many types of containment properties without the use of explicit quantification or specialized logics for containers/sets. We extend an existing shape analysis to model the concept of reference sets. Reference sets allow the analysis to efficiently track a number of important relations (must-=, and must-⊆) between objects that are the targets of sets of references (variables or pointers). We show that shape analysis augmented with reference set information is able to precisely model sharing for a range of data structures in real programs that cannot be expressed using simple must-alias information. In contrast to more expressive proposals based on logic languages (e.g., extensions of first-order predicate logic with transitive closure or the use of a decision procedure for sets), reference sets can be efficiently tracked in a shape analyzer.