The conformal alpha shape filtration

Conformal alpha shapes are a new filtration of the Delaunay triangulation of a finite set of points in ℝ^d. In contrast to (ordinary) alpha shapes the new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha shapes. The local scale parameter conforms to the local geometry and is motivated from applications and previous algorithms in surface reconstruction. We show how conformal alpha shapes can be used for surface reconstruction of non-uniformly sampled surfaces, which is not possible with alpha shapes.     

Minimal Unroll Factor for Code Generation of Software Pipelining

We address the problem of generating compact code from software pipelined loops. Although software pipelining is a powerful technique to extract fine-grain parallelism, it generates lifetime intervals spanning multiple loop iterations. These intervals require periodic register allocation (also called variable expansion), which in turn yields a code generation challenge. We are looking for the minimal unrolling factor enabling the periodic register allocation of software pipelined kernels. This challenge is generally addressed through one of: (1) hardware support in the form of rotating register files, which solve the unrolling problem but are expensive in hardware; (2) register renaming by inserting register moves, which increase the number of operations in the loop, and may damage the schedule of the software pipeline and reduce throughput; (3) post-pass loop unrolling that does not compromise throughput but often leads to impractical code growth. The latter approach relies on the proof that MAXLIVE registers (maximal number of values simultaneously alive) are sufficient for periodic register allocation (Eisenbeis et al. in PACT ’95: Proceedings of the IFIP WG10.3 working conference on Parallel Architectures and Compilation Techniques, pages 264–267, Manchester, UK, 1995; Hendren et al. in CC ’92: Proceedings of the 4th International Conference on Compiler Construction, pages 176–191, London, UK, 1992). However, the best existing heuristic for controlling this code growth—modulo variable expansion (Lam in SIGPLAN Not 23(7):318–328, 1988)—may not apply the correct amount of loop unrolling to guarantee that MAXLIVE registers are enough, which may result in register spills Eisenbeis et al. in PACT ’95: Proceedings of the IFIP WG10.3 working conference on Parallel Architectures and Compilation Techniques, pages 264–267, Manchester, UK, 1995. This paper presents our research results on the open problem of minimal loop unrolling, allowing a software-only code generation that does not trade the optimality of the initiation interval (II) for the compactness of the generated code. Our novel idea is to use the remaining free registers after periodic register allocation to relax the constraints on register reuse. The problem of minimal loop unrolling arises either before or after software pipelining, either with a single or with multiple register types (classes). We provide a formal problem definition for each scenario, and we propose and study a dedicated algorithm for each problem. Our solutions are implemented within an industrial-strength compiler for a VLIW embedded processor from STMicroelectronics, and validated on multiple benchmarks suites.     

High-dimensional MRI data analysis using a large-scale manifold learning approach

A novel manifold learning approach is presented to efficiently identify low-dimensional structures embedded in high-dimensional MRI data sets. These low-dimensional structures, known as manifolds, are used in this study for predicting brain tumor progression. The data sets consist of a series of high-dimensional MRI scans for four patients with tumor and progressed regions identified. We attempt to classify tumor, progressed and normal tissues in low-dimensional space. We also attempt to verify if a progression manifold exists—the bridge between tumor and normal manifolds. By identifying and mapping the bridge manifold back to MRI image space, this method has the potential to predict tumor progression. This could be greatly beneficial for patient management. Preliminary results have supported our hypothesis: normal and tumor manifolds are well separated in a low-dimensional space. Also, the progressed manifold is found to lie roughly between the normal and tumor manifolds.     

Fast Minor Testing in Planar Graphs

Minor Containment is a fundamental problem in Algorithmic Graph Theory used as a subroutine in numerous graph algorithms. A model of a graph H in a graph G is a set of disjoint connected subgraphs of G indexed by the vertices of H, such that if {u,v} is an edge of H, then there is an edge of G between components C _u and C _v . A graph H is a minor of G if G contains a model of H as a subgraph. We give an algorithm that, given a planar n-vertex graph G and an h-vertex graph H, either finds in time $\mathcal{O}(2^{\mathcal{O}(h)} \cdot n +n^{2}\cdot\log n)$ a model of H in G, or correctly concludes that G does not contain H as a minor. Our algorithm is the first single-exponential algorithm for this problem and improves all previous minor testing algorithms in planar graphs. Our technique is based on a novel approach called partially embedded dynamic programming.     

From Images to Shape Models for Object Detection

We present an object class detection approach which fully integrates the complementary strengths offered by shape matchers. Like an object detector, it can learn class models directly from images, and can localize novel instances in the presence of intra-class variations, clutter, and scale changes. Like a shape matcher, it finds the boundaries of objects, rather than just their bounding-boxes. This is achieved by a novel technique for learning a shape model of an object class given images of example instances. Furthermore, we also integrate Hough-style voting with a non-rigid point matching algorithm to localize the model in cluttered images. As demonstrated by an extensive evaluation, our method can localize object boundaries accurately and does not need segmented examples for training (only bounding-boxes).     

DanVideo: an MPEG-7 authoring and retrieval system for dance videos

A well-annotated dance media is an essential part of a nation’s identity, transcending cultural and language barriers. Many dance video archives suffer from problems concerning authoring and access, because of the complex spatio-temporal relationships that exist between the dancers in terms of movements of their body parts and the emotions expressed by them in a dance. This paper presents a system named DanVideo for semi-automatic authoring and access to dance archives. DanVideo provides methods of annotation and authoring and retrieval tools for choreographers, dancers, and students. We demonstrate how dance media can be semantically annotated and how this information can be used for the retrieval of the dance video semantics. In particular, DanVideo offers an MPEG-7 based semi-automatic authoring tool that takes dance video annotations generated by dance experts and produces MPEG-7 metadata. DanVideo also has a search engine that takes users’ queries and retrieves dance semantics from metadata arranged using tree-embedding technique and based on spatial, temporal and spatio-temporal features of dancers. The search engine also leverages a domain-specific ontology to process knowledge-based queries. We have assessed the dance-video queries and semantic annotations in terms of precision, recall, and fidelity.     

Quantum Complexity of Testing Group Commutativity

We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is in . The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of , we give a reduction from a special case of Element Distinctness to our problem. Along the way, we prove the optimality of the algorithm of Pak for the randomized model.     

The medial scaffold of 3D unorganized point clouds

We introduce the notion of the medial scaffold, a hierarchical organization of the medial axis of a 3D shape in the form of a graph constructed from special medial curves connecting special medial points. A key advantage of the scaffold is that it captures the qualitative aspects of shape in a hierarchical and tightly condensed representation. We propose an efficient and exact method for computing the medial scaffold based on a notion of propagation along the scaffold itself, starting from initial sources of the flow and constructing the scaffold during the propagation. We examine this method specifically in the context of an unorganized cloud of points in 3D, e.g., as obtained from laser range finders, which typically involve hundreds of thousands of points, but the ideas are generalizable to data arising from geometrically described surface patches. The computational bottleneck in the propagation-based scheme is in finding the initial sources of the flow. We thus present several ideas to avoid the unnecessary consideration of pairs of points which cannot possibly form a medial point source, such as the "visibility of a point from another given a third point and the interaction of clusters of points. An application of using the medial scaffold for the representation of point samplings of real-life objects is also illustrated     

EOQ Model: The Case in Which the Placing of Orders Is Rewarded

The first models of optimization of inventory management costs have undergone few changes since they were developed at the beginning of the last century. It is only with the passage of time that new scenarios have appeared with the introduction of new systems of production, and consequently of new strategies in the logistics chain. In this article, we analyze and propose a revision of the basic inventory model of economic order quantity first defined by Harris in 1913 for a scenario in which the owner of the stock receives a bonus or reward each time he replenishes his stock. This situation arises when the supplier receives a benefit (which he then shares with the customer) when managing his stock replenishment. An array of nested models is shown to illustrate this scenario, from which the constraints of previous scenarios have been removed. The model provides insights into the negotiation of batch size between supplier and buyer in a win‐win environment in the specific situation in which the supplier gives a bonus to the buyer at each stock replenishment. © 2011 Wiley Periodicals, Inc.     

Project preparedness and the emergence of implementation problems in ERP projects

The problems that organizations face in implementing an enterprise-wide ERP project are linked to their level of understanding of what is involved in such an endeavor and how it influences their initial preparations. We sought to demonstrate empirically the causal relationship between the organization's preparedness and the emergence of implementation problems. We examined four case studies to extract insight into the criticality of certain factors and the type of problems created when no moderating measures were taken by project managers. Consequently, we developed a predictor-outcome model mapping a lack of preparedness with implementation problems.