Dimension-independent simplification and refinement of Morse complexes

Ascending and descending Morse complexes, determined by a scalar field f defined over a manifold M, induce a subdivision of M into regions associated with critical points of f, and compactly represent the topology of M. We define two simplification operators on Morse complexes, which work in arbitrary dimensions, and we define their inverse refinement operators. We describe how simplification and refinement operators affect Morse complexes on M, and we show that these operators form a complete set of atomic operators to create and update Morse complexes on M. Thus, any operator that modifies Morse complexes on M can be expressed as a suitable sequence of the atomic simplification and refinement operators we have defined. The simplification and refinement operators also provide a suitable basis for the construction of a multi-resolution representation of Morse complexes.     

Road intersection detection and classification using hierarchical SVM classifier

In this paper, a hierarchical multi-classification approach using support vector machines (SVM) has been proposed for road intersection detection and classification. Our method has two main steps. The first involves the road detection. For this purpose, an edge-based approach has been developed using the bird’s eye view image which is mapped from the perspective view of the road scene. Then, the concept of vertical spoke has been introduced for road boundary form extraction. The second step deals with the problem of road intersection detection and classification. It consists on building a hierarchical SVM classifier of the extracted road forms using the unbalanced decision tree architecture. Many measures are incorporated for good evaluation of the proposed solution. The obtained results are compared to those of Choi et al. (2007).     

Regional scale hierarchical classification of temporal series of AVHRR vegetation index

In this paper a hierarchical approach is taken to classify temporal sequences of images of the Normalized Difference Vegetation Index (NDVI) from the Advanced Very High Resolution Radiometer (AVHRR), using Iberia as an example. Iberia is a convenient area of study because it has a high environmental diversity and very strong environmental gradients, and yet a reduced size at the spatial resolution of current global data-sets. An Iberian subset of a global temporal series of AVHRR-NDVI images facilitates test and validation of different approaches while producing results that are likely to be valid over much larger areas. Our hierarchical clustering approach yields maps with nested legends. We compare these maps to a digitized map of potential natural vegetation, which reveals a clear bioclimatic control. The highest level of the hierarchical classification separates vegetation with a Summer peak of NDVI from vegetation with a Spring peak of NDVI. Such a discontinuity corresponds to the discontinuity between Atlantic and Submediterranean vegetation in the vegetation map. Lower levels in the hierarchical classification produce maps of increasing complexity but that keep a high degree of spatial continuity. A correspondence analysis between a 16-classes NDVI map and the digitized map of potential vegetation produces an ordination that is bioclimatically coherent. According to the known characteristics of the potential vegetation units, the two first correspondence axes can be interpreted, respectively, as water availability and temperature. These results are a consequence of the temporal NDVI series being an accurate signal of vegetative phenology, which in turn is a fundamental vegetation property. A comparison of our results with several global land cover digital maps by means of the Wilk's ratio indicates that the global maps do not produce an appropriate partition of the region in terms of the NDVI temporal course. We conclude that the analysis of temporal series of NDVI yield relevant ecological information at finer scales and with more detailed legends that had not been attempted until now, and, therefore, are suitable for regional scale applications. Our results also indicate the interest of a bioclimatic analysis and modeling of the NDVI signatures for their correct ecological understanding. Maps at a global scale can be produced based on such an understanding.     

Multidimensional hierarchical classification

Hierarchical classification can be seen as a multidimensional classification problem where the objective is to predict a class, or set of classes, according to a taxonomy. There have been different proposals for hierarchical classification, including local and global approaches. Local approaches can suffer from the inconsistency problem, that is, if a local classifier has a wrong prediction, the error propagates down the hierarchy. Global approaches tend to produce more complex models. In this paper, we propose an alternative approach inspired in multidimensional classification. It starts by building a multi-class classifier per each parent node in the hierarchy. In the classification phase, all the local classifiers are applied simultaneously to each instance, providing a probability for each class in the taxonomy. Then the probability of the subset of classes, for each path in the hierarchy, is obtained by combining the local classifiers results. The path with highest probability is returned as the result for all the levels in the hierarchy. As an extension of the proposal method, we also developed a new technique, based on information gain, to classifies at different levels in the hierarchy. The proposed method was tested on different hierarchical classification data sets and was compared against state-of-the-art methods, resulting in superior predictive performance and/or efficiency to the other approaches in all the datasets.     

Estimating 3D hand pose using hierarchical multi-label classification

This paper presents an analysis of the design of classifiers for use in a hierarchical object recognition approach. In this approach, a cascade of classifiers is arranged in a tree in order to recognize multiple object classes. We are interested in the problem of recognizing multiple patterns as it is closely related to the problem of locating an articulated object. Each different pattern class corresponds to the hand in a different pose, or set of poses. For this problem obtaining labelled training data of the hand in a given pose can be problematic. Given a parametric 3D model, generating training data in the form of example images is cheap, and we demonstrate that it can be used to design classifiers almost as good as those trained using non-synthetic data. We compare a variety of different template-based classifiers and discuss their merits.     

Mixture of experts classification using a hierarchical mixture model

A three-level hierarchical mixture model for classification is presented that models the following data generation process: (1) the data are generated by a finite number of sources (clusters), and (2) the generation mechanism of each source assumes the existence of individual internal class-labeled sources (subclusters of the external cluster). The model estimates the posterior probability of class membership similar to a mixture of experts classifier. In order to learn the parameters of the model, we have developed a general training approach based on maximum likelihood that results in two efficient training algorithms. Compared to other classification mixture models, the proposed hierarchical model exhibits several advantages and provides improved classification performance as indicated by the experimental results.     

An effective non-cooperative iris recognition system using hierarchical collaborative representation-based classification

The Journal of Supercomputing - In recent years, non-cooperative iris recognition has gained a major role in biometric authentication system. However, owing to images captured in non-cooperative...     

Dynamic surfel set refinement for high-quality rendering

Splatting-based rendering techniques are currently the best choice for efficient high-quality rendering of point-based geometries. However, such techniques are not suitable for large magnification, especially when the object is under-sampled. This paper improves the rendering quality of pure splatting techniques using a fast dynamic up-sampling algorithm for point-based geometry. Our algorithm is inspired by interpolatory subdivision surfaces where the geometry is refined iteratively. At each step the refined geometry is that from the previous step enriched by a new set of points. The point insertion procedure uses three operators: a local neighborhood selection operator, a refinement operator (adding new points) and a smoothing operator. Even though our insertion procedure makes the analysis of the limit surface complicated and it does not guarantee its G¹ continuity, it remains very efficient for high-quality real-time point rendering. Indeed, while providing an increased rendering quality, especially for large magnification, our algorithm needs no other preprocessing nor any additional information beyond that used by any splatting technique. This extended version (Real-time point cloud refinement, in: Proceedings of Eurographics Symposium on Point-Based Graphic, 2004, pp. 41.) contains details on creases handling and more comparison to other smoothing operators.     

A distance based classification method using an incomplete training set

This paper describes two distance based methods for classification when all the classes are not known. The first method is parametric, based on Gaussian assumption; the second one is nonparametric, based on the membership function concept.     

Parallelization of structured,hierarchical adaptive mesh refinement algorithms

We describe an approach to parallelization of structured adaptive mesh refinement algorithms. This type of adaptive methodology is based on the use of local grids superimposed on a coarse grid to achieve sufficient resolution in the solution. The key elements of the approach to parallelization are a dynamic load-balancing technique to distribute work to processors and a software methodology for managing data distribution and communications. The methodology is based on a message-passing model that exploits the coarse-grained parallelism inherent in the algorithms. The approach is illustrated for an adaptive algorithm for hyperbolic systems of conservation laws in three space dimensions. A numerical example computing the interaction of a shock with a helium bubble is presented. We give timings to illustrate the performance of the method. Received: 28 April 1999 / Accepted: 25 November 1999     

Fingerprint classification by a hierarchical classifier

Fingerprint classification is still a challenging problem due to large intra-class variability, small inter-class variability and the presence of noise. To deal with these difficulties, we propose a regularized orientation diffusion model for fingerprint orientation extraction and a hierarchical classifier for fingerprint classification in this paper. The proposed classification algorithm is composed of five cascading stages. The first stage rapidly distinguishes a majority of Arch by using complex filter responses. The second stage distinguishes a majority of Whorl by using core points and ridge line flow classifier. In the third stage, K-NN classifier finds the top two categories by using orientation field and complex filter responses. In the fourth stage, ridge line flow classifier is used to distinguish Loop from other classes except Whorl. SVM is adopted to make the final classification in the last stage. The regularized orientation diffusion model has been evaluated on a web-based automated evaluation system FVC-onGoing, and a promising result is obtained. The classification method has been evaluated on the NIST SD 4. It achieved a classification accuracy of 95.9% for five-class classification and 97.2% for four-class classification without rejection.     

Decision trees for hierarchical multi-label classification

Hierarchical multi-label classification (HMC) is a variant of classification where instances may belong to multiple classes at the same time and these classes are organized in a hierarchy. This article presents several approaches to the induction of decision trees for HMC, as well as an empirical study of their use in functional genomics. We compare learning a single HMC tree (which makes predictions for all classes together) to two approaches that learn a set of regular classification trees (one for each class). The first approach defines an independent single-label classification task for each class (SC). Obviously, the hierarchy introduces dependencies between the classes. While they are ignored by the first approach, they are exploited by the second approach, named hierarchical single-label classification (HSC). Depending on the application at hand, the hierarchy of classes can be such that each class has at most one parent (tree structure) or such that classes may have multiple parents (DAG structure). The latter case has not been considered before and we show how the HMC and HSC approaches can be modified to support this setting. We compare the three approaches on 24 yeast data sets using as classification schemes MIPS’s FunCat (tree structure) and the Gene Ontology (DAG structure). We show that HMC trees outperform HSC and SC trees along three dimensions: predictive accuracy, model size, and induction time. We conclude that HMC trees should definitely be considered in HMC tasks where interpretable models are desired.     

A new hierarchical packet classification algorithm

Packet classification is one of the most challenging functions in Internet routers since it involves a multi-dimensional search that should be performed at wire-speed. Hierarchical packet classification is an effective solution which reduces the search space significantly whenever a field search is completed. However, the hierarchical approach using binary tries has two intrinsic problems: back-tracking and empty internal nodes. To avoid back-tracking, the hierarchical set-pruning trie applies rule copy, and the grid-of-tries uses pre-computed switch pointers. However, none of the known hierarchical algorithms simultaneously avoids empty internal nodes and back-tracking. This paper describes various packet classification algorithms and proposes a new efficient packet classification algorithm using the hierarchical approach. In the proposed algorithm, a hierarchical binary search tree, which does not involve empty internal nodes, is constructed for the pruned set of rules. Hence, both back-tracking and empty internal nodes are avoided in the proposed algorithm. Two refinement techniques are also proposed; one for reducing the rule copy caused by the set-pruning and the other for avoiding rule copy. Simulation results show that the proposed algorithm provides an improvement in search performance without increasing the memory requirement compared with other existing hierarchical algorithms.     

Array-based,parallel hierarchical mesh refinement algorithms for unstructured meshes

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE’s using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in-memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework “Mesh Oriented dAtaBase” (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. We also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.     

A hierarchical approach to adaptive local refinement in isogeometric analysis

Adaptive local refinement is one of the key issues in isogeometric analysis. In this article we present an adaptive local refinement technique for isogeometric analysis based on extensions of hierarchical B-splines. We investigate the theoretical properties of the spline space to ensure fundamental properties like linear independence and partition of unity. Furthermore, we use concepts well-established in finite element analysis to fully integrate hierarchical spline spaces into the isogeometric setting. This also allows us to access a posteriori error estimation techniques. Numerical results for several different examples are given and they turn out to be very promising.     

Feature correspondences using Morse Smale complex

Establishing corresponding features on two non-rigidly deformed 3D surfaces is a challenging and well-studied problem in computer graphics. Unlike previous approaches that constrain the matching between feature pairs using isometry-invariant distance metrics, we constrain the matching using a discrete connectivity graph derived from the Morse–Smale complex of the Auto Diffusion Function. We observed that the graph remains stable even for surfaces differing by topology or by significant deformation. This algorithm is simple to implement and efficient to run. When tested on a range of examples, our algorithm produces comparable results with state-of-art methods on surfaces with strong isometry but with greatly improved efficiency, and often gets better correspondences on surfaces with larger shape variances.     

Proving refinement using transduction

Summary. When designing distributed systems, one is faced with the problem of verifying a refinement between two specifications, given at different levels of abstraction. Suggested verification techniques in the literature include refinement mappings and various forms of simulation. We present a verification method, in which refinement between two systems is proven by constructing a transducer that inputs a computation of a concrete system and outputs a matching computation of the abstract system. The transducer uses a FIFO queue that holds segments of the concrete computation that have not been matched yet. This allows a finite delay between the occurrence of a concrete event and the determination of the corresponding abstract event. This delay often makes the use of prophecy variables or backward simulation unnecessary. An important generalization of the method is to prove refinement modulo some transformation on the observed sequences of events. The method is adapted by replacing the FIFO queue by a component that allows the appropriate transformation on sequences of events. A particular case is partial-order refinement, i.e., refinement that preserves only a subset of the orderings between events of a system. Examples are sequential consistency and serializability. The case of sequential consistency is illustrated on a proof of sequential consistency of a cache protocol.     

Covering-based rough set classification system

Medical data classification is applied in intelligent medical decision support system to classify diseases into different categories. Several classification methods are commonly used in various healthcare settings. These techniques are fit for enhancing the nature of prediction, initial identification of sicknesses and disease classification. The categorization complexities in healthcare area are focused around the consequence of healthcare data investigation or depiction of medicine by the healthcare professions. This study concentrates on applying uncertainty (i.e. rough set)-based pattern classification techniques for UCI healthcare data for the diagnosis of diseases from different patients. In this study, covering-based rough set classification (i.e. proposed pattern classification approach) is applied for UCI healthcare data. Proposed CRS gives effective results than delicate pattern classifier model. The results of applying the CRS classification method to UCI healthcare data analysis are based upon a variety of disease diagnoses. The execution of the proposed covering-based rough set classification is contrasted with other approaches, such as rough set (RS)-based classification methods, Kth nearest neighbour, improved bijective soft set, support vector machine, modified soft rough set and back propagation neural network methodologies using different evaluating measures.