Adding For-Loops to First-Order Logic

We study the query language BQL: the extension of the relational algebra with for-loops. We also study FO(FOR): the extension of first-order logic with a for-loop variant of the partial fixpoint operator. In contrast to the known situation with query languages, which include while-loops instead of for-loops, BQL and FO(FOR) are not equivalent. Among the topics we investigate are: the precise relationship between BQL and FO(FOR); inflationary versus noninflationary iteration; the relationship with logics that have the ability to count; and nested versus unnested loops.     

Clausal Logic and Logic Programming in Algebraic Domains

We introduce a domain-theoretic foundation for disjunctive logic programming. This foundation is built on clausal logic, a representation of the Smyth powerdomain of any coherent algebraic dcpo. We establish the completeness of a resolution rule for inference in such a clausal logic; we introduce a natural declarative semantics and a fixed-point semantics for disjunctive logic programs, and prove their equivalence; finally, we apply our results to give both a syntax and semantics for default logic in any coherent algebraic dcpo.     

Tarskian Set Constraints

We investigate set constraints over set expressions with Tarskian functional and relational operations. Unlike the Herbrand constructor symbols used in recent set constraint formalisms, the meaning of a Tarskian function symbol is interpreted in an arbitrary first order structure. We show that satisfiability of Tarskian set constraints is decidable in nondeterministic doubly exponential time. We also give complexity results and open problems for various extensions and restrictions of the language.     

A Monadic Second-Order Definition of the Structure of Convex Hypergraphs

We consider finite hypergraphs with hyperedges defined as sets of vertices of unbounded cardinality. Each such hypergraph has a unique modular decomposition, which is a tree, the nodes of which correspond to certain subhypergraphs (induced by certain sets of vertices called strong modules) of the considered hypergraph. One can define this decomposition by monadic second-order (MS) logical formulas. Such a hypergraph is convex if the vertices are linearly ordered in such a way that the hyperedges form intervals. Our main result says that the unique linear order witnessing the convexity of a prime hypergraph (i.e., of one, the modular decomposition of which is trivial) can be defined in MS logic. As a consequence, we obtain that if a set of bipartite graphs that correspond (in the usual way) to convex hypergraphs has a decidable monadic second-order theory (which means that one can decide whether a given MS formula is satisfied in some graph of the set) then it has bounded clique-width. This yields a new case of validity of a conjecture which is still open.     

The Undecidability of the First-Order Theories of One Step Rewriting in Linear Canonical Systems

By reduction from the halting problem for Minsky's two-register machines we prove that there is no algorithm capable of deciding the -theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixed such system with undecidable *-theory of one step rewriting (strong undecidability). This improves over all previously known results of the same kind.     

Nonerasing, Counting, and Majority over the Linear Time Hierarchy

In this paper, we investigate several extensions of the linear time hierarchy (denoted by LTH). We first prove that it is not necessary to erase the oracle tape between two successive oracle calls, thereby lifting a common restriction on LTH machines. We also define a natural counting extension of LTH and show that it corresponds to a robust notion of counting bounded arithmetic predicates. Finally, we show that the computational power of the majority operator is equivalent to that of the exact counting operator in both contexts.     

A Real-Time Approach to the Spotting, Representation, and Recognition of Hand Gestures for Human–Computer Interaction

Aiming at the use of hand gestures for human–computer interaction, this paper presents a real-time approach to the spotting, representation, and recognition of hand gestures from a video stream. The approach exploits multiple cues including skin color, hand motion, and shape. Skin color analysis and coarse image motion detection are joined to perform reliable hand gesture spotting. At a higher level, a compact spatiotemporal representation is proposed for modeling appearance changes in image sequences containing hand gestures. The representation is extracted by combining robust parameterized image motion regression and shape features of a segmented hand. For efficient recognition of gestures made at varying rates, a linear resampling technique for eliminating the temporal variation (time normalization) while maintaining the essential information of the original gesture representations is developed. The gesture is then classified according to a training set of gestures. In experiments with a library of 12 gestures, the recognition rate was over 90%. Through the development of a prototype gesture-controlled panoramic map browser, we demonstrate that a vocabulary of predefined hand gestures can be used to interact successfully with applications running on an off-the-shelf personal computer equipped with a home video camera.     

Assigning Types to Processes

In wide area distributed systems it is now common for higher-order code to be transferred from one domain to another; the receiving host may initialise parameters and then execute the code in its local environment. In this paper we propose a fine-grained typing system for a higher-order π-calculus which can be used to control the effect of such migrating code on local environments. Processes may be assigned different types depending on their intended use. This is in contrast to most of the previous work on typing processes where all processes are typed by a unique constant type, indicating essentially that they are well typed relative to a particular environment. Our fine-grained typing facilitates the management of access rights and provides host protection from potentially malicious behaviour. Our process type takes the form of an interface limiting the resources to which it has access and the types at which they may be used. Allowing resource names to appear both in process types and process terms, as interaction ports, complicates the typing system considerably. For the development of a coherent typing system, we use a kinding technique, similar to that used by the subtyping of the system F, and order-theoretic properties of our subtyping relation. Various examples of this paper illustrate the usage of our fine-grained process types in distributed systems.     

3D Articulated Models and Multiview Tracking with Physical Forces

We present a method for automatically estimating the motion of an articulated object filmed by two or more fixed cameras. We focus our work on the case where the quality of the images is poor, and where only an approximation of a geometric model of the tracked object is available. Our technique uses physical forces applied to each rigid part of a kinematic 3D model of the object we are tracking. These forces guide the minimization of the differences between the pose of the 3D model and the pose of the real object in the video images. We use a fast recursive algorithm to solve the dynamical equations of motion of any 3D articulated model. We explain the key parts of our algorithms: how relevant information is extracted from the images, how the forces are created, and how the dynamical equations of motion are solved. A study of what kind of information should be extracted in the images and of when our algorithms fail is also presented. Finally we present some results about the tracking of a person. We also show the application of our method to the tracking of a hand in sequences of images, showing that the kind of information to extract from the images depends on their quality and of the configuration of the cameras.     

Specularities on Surfaces with Tangential Hairs or Grooves

Specularities on surfaces with tangential hairs or grooves are readily observable in nature. Examples of such phenomena are the arched or looped highlights observed on horses and human heads and the linear or curved specularities observed on parts of industrial machinery that have tangential grooves. We investigate the geometry of curvilinear specularities on surfaces of different curvature with tangential hairs or grooves of different orientations under controlled lighting and viewing conditions. First the nature of these specularities is investigated qualitatively. Then specularities on parametric surfaces and hair or groove orientations are calculated for some specific cases. Explicit calculations of specularities on some special surfaces, cylinders, cones, and spheres, are verified by photographs of the reflections. Aspects of the work are applicable to computer graphics and can be utilized for the image interpretation of surface specularities.     

Cooperative Stereo–Motion: Matching and Reconstruction

One of the most interesting goals of computer vision is the 3D structure recovery of scenes. Traditionally, two cues are used: structure from motion and structure from stereo, two subfields with complementary sets of assumptions and techniques. This paper introduces a new general framework of cooperation between stereo and motion. This framework combines the advantages of both cues: (i) easy correspondence from motion and (ii) accurate 3D reconstruction from stereo. First, we show how the stereo matching can be recovered from motion correspondences using only geometric constraints. Second, we propose a method of 3D reconstruction of both binocular and monocular features using all stereo pairs in the case of a calibrated stereo rig. Third, we perform an analysis of the performance of the proposed framework as well as a comparison with an affine method. Experiments involving real and synthetic stereo pairs indicate that rich and reliable information can be derived from the proposed framework. They also indicate that robust 3D reconstruction can be obtained even with short image sequences.     

Mobile Objects as Mobile Processes

Obliq is a lexically scoped, distributed, object-based programming language. In Obliq, the migration of an object is proposed as creating a clone of the object at the target site, whereafter the original object is turned into an alias for the clone. Obliq has only an informal semantics, so there is no proof that this style of migration is safe, i.e., transparent to object clients. In previous work, we introduced Ø, an abstraction of Obliq, where, by lexical scoping, sites have been abstracted away. We used Ø in order to exhibit how the semantics behind Obliq's implementation renders migration unsafe. We also suggested a modified semantics that we conjectured instead to be safe. In this paper, we rewrite our modified semantics of Ø in terms of the π-calculus, and we use it to formally prove the correctness of object surrogation, the abstraction of object migration in Ø.     

Token-Passing Nets: Call-by-Need for Free

Recently, encodings in interaction nets of the call-by-name and call-by-value strategies of the λ-calculus have been proposed. The purpose of these encodings was to bridge the gap between interaction nets and traditional abstract machines, which are both used to provide lower-level specifications of strategies of the λ-calculus, but in radically different ways. The strength of these encodings is their simplicity, which comes from the simple idea of introducing an explicit syntactic object to represent the flow of evaluation. In particular, no artifact to represent boxes is needed. However, these encodings purposefully follow as closely as possible the implemented strategies, call-by-name and call-by-value, hence do not benefit from the ability of interaction nets to easily represent sharing. The aim of this note is to show that sharing can indeed be achieved without adding any structure. We thus present the call-by-need strategy following the same philosophy, which is indeed not any more complicated than call-by-name. This continues the task of bridging the gap between interaction nets and abstract machines, thus pushing forward a more uniform framework for implementations of the λ-calculus.     

Working with ARMs: Complexity Results on Atomic Representations of Herbrand Models

An atomic representation of a Herbrand model (ARM) is a finite set of (not necessarily ground) atoms over a given Herbrand universe. Each ARM represents a possibly infinite Herbrand interpretation. This concept has emerged independently in different branches of computer science as a natural and useful generalization of the concept of finite Herbrand interpretation. It was shown that several recursively decidable problems on finite Herbrand models (or interpretations) remain decidable on ARMs.The following problems are essential when working with ARMs: Deciding the equivalence of two ARMs, deciding subsumption between ARMs, and evaluating clauses over ARMs. These problems were shown to be decidable, but their computational complexity has remained obscure so far. The previously published decision algorithms require exponential space. In this paper, we prove that all mentioned problems are coNP-complete.     

Novel Techniques for Robust Voxelization and Visualization of Implicit Surfaces

Voxelization is the transformation of geometric surfaces into voxels. Up to date this process has been done essentially using incremental algorithms. Incremental algorithms have the reputation of being efficient but they lack an important property: robustness. The voxelized representation should envelop its continuous model. However, without robust methods this cannot be guaranteed. This article describes novel techniques of robust voxelization and visualization of implicit surfaces. First of all our recursive subdivision voxelization algorithm is reviewed. This algorithm was initially inspired by Duff's image space subdivision method. Then, we explain the algorithm to voxelize implicit surfaces defined in spherical or cylindrical coordinates. Next, we show a new technique to produce infinite replications of implicit objects and their voxelization method. Afterward, we comment on the parallelization of our voxelization procedure. Finally we present our voxel visualization algorithm based on point display. Our voxelization algorithms can be used with any data structure, thanks to the fact that a voxel is only stored once the last subdivision level is reached. We emphasize the use of the octree, though, because it is a convenient way to store the discrete model hierarchically. In a hierarchy the discrete model refinement is simple and possible from any previous voxelized scene thanks to the fact that the voxelization algorithms are robust.     

Interaction in Time and Space

Distributed π-calculus and ambient calculus are extended with timers which may trigger timeout recovery processes. Timers provide a useful notion of relative time with respect to the interaction in a distributed system. The rather flat notion of space in timed distributed π-calculus is improved by considering a hierarchical representation of space in timed mobile ambients. Some basic results are proven, making sound both formal approaches. An easily understood example is used for both extensions, showing how it is possible to describe a non-monotonic behaviour and use a decentralized control to coordinate the interacting components in time and space.     

3-D Reconstruction of Urban Scenes from Aerial Stereo Imagery: A Focusing Strategy

A contribution to the automatic 3-D reconstruction of complex urban scenes from aerial stereo pairs is proposed. It consists of segmenting the scene into two different kinds of components: the ground and the above-ground objects. The above-ground objects are classified either as buildings or as vegetation. The idea is to define appropriate regions of interest in order to achieve a relevant 3-D reconstruction. For that purpose, a digital elevation model of the scene is first computed and segmented into above-ground regions using a Markov random field model. Then a radiometric analysis is used to classify above-ground regions as building or vegetation, leading to the determination of the final above-ground objects. The originality of the method is its ability to cope with extended above-ground areas, even in case of a sloping ground surface. This characteristic is necessary in a urban environment. Results are very robust to image and scene variability, and they enable the utilization of appropriate local 3-D reconstruction algorithms.     

Building Detection from Multiple Aerial Images in Dense Urban Areas

In this paper we present a novel approach for building detection from multiple aerial images in dense urban areas. The approach is based on accurate surface reconstruction, followed by extraction of building façades that are used as a main cue for building detection. For the façade detection, a simple but nevertheless flexible and robust algorithm is proposed. It is based on the observation that building façades correspond to the accumulation of 3D data, available from different views, in object space. Knowledge-driven thresholding of 3D data accumulators followed by Hough transform-based segment detection results in the extraction of façade positions. Three-dimensional planar regions resulting from surface reconstruction procedure and bounded by the extracted façades are detected as building hypotheses through testing a set of spatial criteria. Then, a set of verification criteria is proposed for the hypothesis confirmation.     

An Algebra of Discrete Channels That Involve Combinations of Three Basic Error Types

Recently, the author introduced a nonprobabilistic mathematical model of discrete channels, the BEE channels, that involve the error-types substitution, insertion, and deletion. This paper defines an important class of BEE channels, the SID channels, which include channels that permit a bounded number of scattered errors and, possibly at the same time, a bounded burst of errors in any segment of predefined length of a message. A formal syntax is defined for generating channel expressions, and appropriate semantics is provided for interpreting a given channel expression as a communication channel (SID channel) that permits combinations of substitutions, insertions, and deletions of symbols. Our framework permits one to generalize notions such as error correction and unique decodability, and express statements of the form “The code K can correct all errors of type ξ” and “it is decidable whether the code K is uniquely decodable for the channel described by ξ”, where ξ is any SID channel expression.