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Abstract: An algorithm for polygonal approximation based on dominant point (DP) deletion is presented in this paper. The algorithm selects an initial set of DPs and starts eliminating them one by one depending upon the error associated with each DP. The associated error value is based on global measure. A local optimization of few neighboring points is performed after each deletion. Although the algorithm does not guarantee an optimal solution, the combination of local and global optimization is expected to produce optimal results. The algorithm is extensively tested on various shapes with varying number of DPs and error threshold. In general, optimal results were observed for about 96% of the times. A good comparative study is also presented in this paper [Copyright &y& Elsevier]

Abstract: This paper proposes an efficient algorithm for inexact graph matching based on spectral embedding with missing value. We commence by building an association graph model based on initial matching algorithm. Then, by dot product representation of graph with missing value, a new embedding method (co-embedding), where the correspondences between unmatched nodes are treated as missing data in an association graph, is presented. At last, a new graph matching algorithm which alternates between the co-embedding and point pattern matching is proposed. Convictive experimental results on both synthetic and real-world data demonstrate the effectiveness of the proposed graph matching algorithm. [Copyright &y& Elsevier]

Abstract: This paper presents an iterated region merging-based graph cuts algorithm which is a novel extension of the standard graph cuts algorithm. Graph cuts addresses segmentation in an optimization framework and finds a globally optimal solution to a wide class of energy functions. However, the extraction of objects in a complex background often requires a lot of user interaction. The proposed algorithm starts from the user labeled sub-graph and works iteratively to label the surrounding un-segmented regions. In each iteration, only the local neighboring regions to the labeled regions are involved in the optimization so that much interference from the far unknown regions can be significantly reduced. Meanwhile, the data models of the object and background are updated iteratively based on high confident labeled regions. The sub-graph requires less user guidance for segmentation and thus better results can be obtained under the same amount of user interaction. Experiments on benchmark datasets validated that our method yields much better segmentation results than the standard graph cuts and the Grabcut methods in either qualitative or quantitative evaluation. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a general learning framework based on local and global regularization. In the local regularization part, our algorithm constructs a regularized classifier for each data point using its neighborhood, while the global regularization part adopts a Laplacian regularizer to smooth the data labels predicted by those local classifiers. We show that such a learning framework can easily be incorporated into either unsupervised learning, semi-supervised learning, and supervised learning paradigm. Moreover, many existing learning algorithms can be derived from our framework. Finally we present some experimental results to show the effectiveness of our method. [Copyright &y& Elsevier]

Abstract: In many applied sciences the problem of revealing the underlying (crisp or fuzzy) structure (partitions or covers) in a collection of objects to be represented in non-temporal situations, measures, observations, phenomena, etc., is an essential task. Motivated by the independent use of some different partitions criteria and the theoretical and empirical analysis of some of its properties, in this paper, we introduce an incremental nested partition method which combines these partitions criteria for finding the inner structure of static and dynamic datasets. For this, we proved that there are relationships of nesting between partitions obtained, respectively, from these partition criteria, and besides that the sensitivity when a new object arrives to the dataset is rigorously studied. Our algorithm exploits all of these mathematical properties for obtaining the hierarchy of clusterings. Moreover, we realize a theoretical and experimental comparative study of our method with classical hierarchical clustering methods such as single-link and complete-link and other more recently introduced methods. The experimental results over databases of UCI repository and the AFP and TDT2 news collections show the usefulness and capability of our method to reveal different levels of information hidden in datasets. [Copyright &y& Elsevier]

Abstract: This paper explores the problem of multi-view feature matching from an unordered set of widely separated views. A set of local invariant features is extracted independently from each view. First we propose a new view-ordering algorithm that organizes all the unordered views into clusters of related (i.e. the same scene) views by efficiently computing the view-similarity values of all view pairs by reasonably selecting part of extracted features to match. Second a robust two-view matching algorithm is developed to find initial matches, then detect the outliers and finally incrementally find more reliable feature matches under the epipolar constraint between two views from dense to sparse based on an assumption that changes of both motion and feature characteristics of one match are consistent with those of neighbors. Third we establish the reliable multi-view matches across related views by reconstructing missing matches in a neighboring triple of views and efficiently determining the states of matches between view pairs. Finally, the reliable multi-view matches thus obtained are used to automatically track all the views by using a self-calibration method. The proposed methods were tested on several sets of real images. Experimental results show that it is efficient and can track a large set of multi-view feature matches across multiple widely separated views. [Copyright &y& Elsevier]

Abstract: This paper presents an algorithm to model volumetric data and other one for non-rigid registration of such models using spheres formulated in the geometric algebra framework. The proposed algorithm for modeling, as opposite to the Union of Spheres method, reduces the number of entities (spheres) used to model 3D data. Our proposal is based in marching cubes idea using, however, spheres, while the Union of Spheres uses Delaunay tetrahedrization. The non-rigid registration is accomplished in a deterministic annealing scheme. At the preprocessing stage we segment the objects of interest by a segmentation method based on texture information. This method is embedded in a region growing scheme. As our final application, we present a scheme for surgical object tracking using again geometric algebra techniques. [Copyright &y& Elsevier]

This paper introduces a new and simple criterion for rigid registration based on Gaussian fields. The criterion is always differentiable and convex in a large neighborhood of the alignment parameters; allowing for the use of well-proven optimization techniques. Using this method we can extend the size of the region of convergence so that no close initialization is needed, thus overcoming local convergence problems of Iterative Closest Point algorithms. Furthermore, the Gaussian energy function can be evaluated with linear complexity using the fast Gauss transform, which permits efficient implementation of the registration algorithm. Experimental analysis on real-world data sets shows the usefulness and points the limits of the approach. [Copyright &y& Elsevier]

This paper presents a table structure understanding algorithm designed using optimization methods. The algorithm is probability based, where the probabilities are estimated from geometric measurements made on the various entities in a large training set. The methodology includes a global parameter optimization scheme, a novel automatic table ground truth generation system and a table structure understanding performance evaluation protocol. With a document data set having 518 table and 10,934 cell entities, it performed at the 96.76% accuracy rate on the cell level and 98.32% accuracy rate on the table level. [Copyright &y& Elsevier]