First-Class Object Sets

Abstract. Typically, objects are monolithic entities with a fixed interface. To increase the flexibility in this area, this paper presents first-class object sets as a language construct. An object set offers an interface which is a disjoint union of the interfaces of its member objects. It may also be used for a special kind of method invocation involving multipleobjects in a dynamic lookup process. With support for feature access and late-bound method calls object sets are similar to ordinary objects, only more flexible. The approach is made precise by means of a small calculus, and the soundness of its type system is shown by a mechanically checked proof in Coq

Discovering Class-Specific Pixels for Weakly-Supervised Semantic Segmentation

We propose an approach to discover class-specific pixels for the weakly-supervised semantic segmentation task. We show that properly combining saliency and attention maps allows us to obtain reliable cues capable of significantly boosting the performance. First, we propose a simple yet powerful hierarchical approach to discover the class-agnostic salient regions, obtained using a salient object detector, which otherwise would be ignored. Second, we use fully convolutional attention maps to reliably localize the class-specific regions in a given image. We combine these two cues to discover class-specific pixels which are then used as an approximate ground truth for training a CNN. While solving the weakly supervised semantic segmentation task, we ensure that the image-level classification task is also solved in order to enforce the CNN to assign at least one pixel to each object present in the image. Experimentally, on the PASCAL VOC12 val and test sets, we obtain the mIoU of 60.8% and 61.9%, achieving the performance gains of 5.1% and 5.2% compared to the published state-of-the-art results. The code is made publicly available

Adaptive imputation of missing values for incomplete pattern classification

In classification of incomplete pattern, the missing values can either play a crucial role in the class determination, or have only little influence (or eventually none) on the classification results according to the context. We propose a credal classification method for incomplete pattern with adaptive imputation of missing values based on belief function theory. At first, we try to classify the object (incomplete pattern) based only on the available attribute values. As underlying principle, we assume that the missing information is not crucial for the classification if a specific class for the object can be found using only the available information. In this case, the object is committed to this particular class. However, if the object cannot be classified without ambiguity, it means that the missing values play a main role for achieving an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and self-organizing map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is respectively classified according to each training class, and the classification results represented by basic belief assignments are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (which are particular disjunctions of several single classes). The credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets

MultiView : a methodology for supporting multiple view schemata in object-oriented databases

It has been widely recognized that object-oriented database (OODB) technology needs to be extended to provide a mechanism similar to views in relational database systems. We define an object-oriented view to be an arbitrarily complex virtual schema graph with possibly restructured generalization and decomposition hierarchies - rather than just one virtual class as has been proposed in the literature. In this paper, we propose a methodology, called MultiView, for supporting multiple such view schemata. MultiView breaks the schema design task into the following independent and well-defined subtasks: (1) the customization of type descriptions and object sets of existing classes by deriving virtual classes, (2) the integration of all derived classes into one consistent global schema graph, and (3) the definition of arbitrarily complex view schemata on this augmented global schema. For the first task of MultiView, we define a set of object algebra operators that can be used by the view definer for class customization. For the second task of MultiView, we propose an algorithm that automatically integrates these newly derived virtual classes into the global schema. We solve the third task of MultiView by first letting the view definer explicitly select the desired view classes from the global schema using a view definition language and then by automatically generating a view class hierarchy for these selected classes. In addition, we present algorithms that verify the closure property of a view and, if found to be incomplete, transform it into a closed, yet minimal, view. In this paper, we introduce the fundamental concept of view independence and show MultiView to be view independent. We also outline implementation techniques for realizing MultiView with existing OODB technology

On Algorithms and Complexity for Sets with Cardinality Constraints

Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate properties: relationships between the typestates of objects can be expressed as subset and disjointness relations on sets, and elements of sets can be represented as sets of cardinality one. Motivated by these applications, this paper presents new algorithms and new complexity results for constraints on sets and their cardinalities. We study several classes of constraints and demonstrate a trade-off between their expressive power and their complexity. Our first result concerns a quantifier-free fragment of Boolean Algebra with Presburger Arithmetic. We give a nondeterministic polynomial-time algorithm for reducing the satisfiability of sets with symbolic cardinalities to constraints on constant cardinalities, and give a polynomial-space algorithm for the resulting problem. In a quest for more efficient fragments, we identify several subclasses of sets with cardinality constraints whose satisfiability is NP-hard. Finally, we identify a class of constraints that has polynomial-time satisfiability and entailment problems and can serve as a foundation for efficient program analysis.Comment: 20 pages. 12 figure

Hallucinating optimal high-dimensional subspaces

Linear subspace representations of appearance variation are pervasive in computer vision. This paper addresses the problem of robustly matching such subspaces (computing the similarity between them) when they are used to describe the scope of variations within sets of images of different (possibly greatly so) scales. A naive solution of projecting the low-scale subspace into the high-scale image space is described first and subsequently shown to be inadequate, especially at large scale discrepancies. A successful approach is proposed instead. It consists of (i) an interpolated projection of the low-scale subspace into the high-scale space, which is followed by (ii) a rotation of this initial estimate within the bounds of the imposed ``downsampling constraint''. The optimal rotation is found in the closed-form which best aligns the high-scale reconstruction of the low-scale subspace with the reference it is compared to. The method is evaluated on the problem of matching sets of (i) face appearances under varying illumination and (ii) object appearances under varying viewpoint, using two large data sets. In comparison to the naive matching, the proposed algorithm is shown to greatly increase the separation of between-class and within-class similarities, as well as produce far more meaningful modes of common appearance on which the match score is based.Comment: Pattern Recognition, 201

A deductive and typed object-oriented language

In this paper we introduce a logical query language extended with object-oriented typing facilities. This language, called DTL (from DataTypeLog), can be seen as an extension of Datalog equipped with complex objects, object identities, and multiple inheritance based on Cardelli type theory. The language also incorporates a very general notion of sets as first-class objects. The paper offers a formal description of DTL, as well as a denotational semantics for DTL programs

Aftermath Of The Nothing

This article consists in two parts that are complementary and autonomous at the same time. In the first one, we develop some surprising consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. On a conceptual level, it allows to see sets in a new light and to give a legitimacy to the empty set. On a technical level, it leads to a relative resolution of the anomaly of the intersection of a family free of sets. In the second part, we show the interest of introducing an operator of potentiality into a standard set theory. Among other results, this operator allows to prove the existence of a hierarchy of empty sets and to propose a solution to the puzzle of "ubiquity" of the empty set. Both theories are presented with equi-consistency results (model and interpretation). Here is a declaration of intent : in each case, the starting point is a conceptual questionning; the technical tools come in a second time\\[0.4cm] \textbf{Keywords:} nothing, void, empty set, null-class, zero-order logic with quantifiers, potential, effective, empty set, ubiquity, hierarchy, equality, equality by the bottom, identity, identification

Initial Semantics for Reduction Rules

We give an algebraic characterization of the syntax and operational semantics of a class of simply-typed languages, such as the language PCF: we characterize simply-typed syntax with variable binding and equipped with reduction rules via a universal property, namely as the initial object of some category of models. For this purpose, we employ techniques developed in two previous works: in the first work we model syntactic translations between languages over different sets of types as initial morphisms in a category of models. In the second work we characterize untyped syntax with reduction rules as initial object in a category of models. In the present work, we combine the techniques used earlier in order to characterize simply-typed syntax with reduction rules as initial object in a category. The universal property yields an operator which allows to specify translations---that are semantically faithful by construction---between languages over possibly different sets of types. As an example, we upgrade a translation from PCF to the untyped lambda calculus, given in previous work, to account for reduction in the source and target. Specifically, we specify a reduction semantics in the source and target language through suitable rules. By equipping the untyped lambda calculus with the structure of a model of PCF, initiality yields a translation from PCF to the lambda calculus, that is faithful with respect to the reduction semantics specified by the rules. This paper is an extended version of an article published in the proceedings of WoLLIC 2012.Comment: Extended version of arXiv:1206.4547, proves a variant of a result of PhD thesis arXiv:1206.455