Use Of Correspondences Research Articles

Pose Estimation for General Cameras Using Lines.

In this paper, we address the problem of pose estimation under the framework of generalized camera models. We propose a solution based on the knowledge of the coordinates of 3-D straight lines (expressed in the world coordinate frame) and their corresponding image pixels. Previous approaches used the knowledge of the coordinates of 3-D points (zero dimensional elements) and their corresponding images (zero dimensional elements). In this paper, pixels belonging to the image of 3-D lines are used. There is no need to establish correspondences between pixels and 3-D points. Correspondences are established between 3-D lines and their images. There is no need to identify individual pixels. The use of correspondences between pixels (that belong to the images of the 3-D lines) and 3-D lines facilitates the correspondence problem when compared to the use of world and image points. This is one of the contributions of this paper. The approach is both evaluated and validated using synthetic data and also real images.

Two simple proofs of the feasibility of the linear tracing procedure

Theories of equilibrium selection in non-cooperative games, as well as the notion of risk dominance, depend heavily on the so-called linear tracing procedure. This is the first paper to give direct, simple proofs of the feasibility of the linear tracing procedure. The first proof utilizes a result that is related to Kakutani's fixed point theorem and that is an extension of Browder's fixed point theorem. The second proof shows that it is even possible to avoid the use of correspondences.

The Role of Parallelism in Strategies of Pronoun Comprehension

Two experiments investigated the role of parallelism in strategies of pronoun assignment and tested the proposition that a parallel function strategy and the subject assignment strategy jointly contribute to the interpretation of pronouns. The parallel function strategy interprets a pronoun as coreferential with a preceding noun phrase in the same grammatical role, while the subject assignment strategy interprets a pronoun as coreferential with a preceding subject noun phrase. The results of Experiment I showed that the subject assignment and parallel function strategies jointly constrained assignment. When both strategies yielded the same interpretation, as was the case for subject assignments with subject pronouns, subject assignment preferences were greater than when only the subject assignment strategy was available, as was the case with nonsubject pronouns in partially parallel sentences (i.e., sentences in which the pronoun and antecedent differed grammatically). When the two strategies yielded conflicting assignments, as was the case with nonsubject pronouns in fully parallel sentences, subject assignments were reduced even further and nonsubject assignments were preferred. Experiment 2 replicated the results of Experiment 1 in isolated sentences rather than in short texts and ruled out the idea that a third “parallel order” strategy might be used in partially parallel sentences. We suggest that the subject assignment strategy reflects the topic status of the subject noun phrase, while parallel function reflects the use of correspondences between sentence structures in comprehension. We also suggest that the joint operation of heuristic strategies implies a model of discourse processing in which a number of constraints compete in the interpretation of noun phrases.

Counting by Correspondence

How should mathematical objects be counted? Several quite distinct methods are popular including summation of finite series, use .of one-to-one correspondences, manipulation of generating functions, and application of the inclusion-exclusion principle, to name only the most common. Perhaps summation of finite series is the method used most widely, even though it tends to be a brute force approach relying on well-developed techniques of manipulation rather than on features which are inherent in the context of the particular problem. Its use reflects the viewpoint that the answer is of primary importance, while the way it is obtained is incidental: in other words, the end justifies the means. We are sure many besides ourselves have had the experience of solving a counting problem by summation of finite series and upon finding that the answer was relatively simple, have thought: There must be a more natural way to derive this solution! Our intention here is to show that the use of correspondences may provide more natural and more enlightening solutions to counting problems, by making use of inherent structural features. As a paradigm, we take the problem of counting all nondecreasing sequences of k natural numbers, none of which exceeds n: that is, the problem of determining the cardinality of the set