799 research outputs found

    Lipschitz gradients for global optimization in a one-point-based partitioning scheme

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    A global optimization problem is studied where the objective function f(x)f(x) is a multidimensional black-box function and its gradient f(x)f'(x) satisfies the Lipschitz condition over a hyperinterval with an unknown Lipschitz constant KK. Different methods for solving this problem by using an a priori given estimate of KK, its adaptive estimates, and adaptive estimates of local Lipschitz constants are known in the literature. Recently, the authors have proposed a one-dimensional algorithm working with multiple estimates of the Lipschitz constant for f(x)f'(x) (the existence of such an algorithm was a challenge for 15 years). In this paper, a new multidimensional geometric method evolving the ideas of this one-dimensional scheme and using an efficient one-point-based partitioning strategy is proposed. Numerical experiments executed on 800 multidimensional test functions demonstrate quite a promising performance in comparison with popular DIRECT-based methods.Comment: 25 pages, 4 figures, 5 tables. arXiv admin note: text overlap with arXiv:1103.205

    Multidimensional bisection: a dual viewpoint

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    AbstractThis paper provides an alternative viewpoint of multidimensional bisection global optimization methods of Wood. A dual coordinate representation of convex bodies is introduced which leads to an easy implementation and eliminates the need to see the geometry of intersecting simplexes. Although developed in the context of global optimization, the techniques deal more generally with regions represented as the union of convex bodies. With this dual framework the algorithm can be implemented efficiently using any multiattribute index data structure that allows for quick range queries. A C version using a “multi-key double linked skip list” based on Pugh's skip list has been implemented

    MoSculp: Interactive Visualization of Shape and Time

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    We present a system that allows users to visualize complex human motion via 3D motion sculptures---a representation that conveys the 3D structure swept by a human body as it moves through space. Given an input video, our system computes the motion sculptures and provides a user interface for rendering it in different styles, including the options to insert the sculpture back into the original video, render it in a synthetic scene or physically print it. To provide this end-to-end workflow, we introduce an algorithm that estimates that human's 3D geometry over time from a set of 2D images and develop a 3D-aware image-based rendering approach that embeds the sculpture back into the scene. By automating the process, our system takes motion sculpture creation out of the realm of professional artists, and makes it applicable to a wide range of existing video material. By providing viewers with 3D information, motion sculptures reveal space-time motion information that is difficult to perceive with the naked eye, and allow viewers to interpret how different parts of the object interact over time. We validate the effectiveness of this approach with user studies, finding that our motion sculpture visualizations are significantly more informative about motion than existing stroboscopic and space-time visualization methods.Comment: UIST 2018. Project page: http://mosculp.csail.mit.edu

    PointMCD: Boosting Deep Point Cloud Encoders via Multi-view Cross-modal Distillation for 3D Shape Recognition

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    As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era, remarkable progress in processing such two data modalities has been achieved through respectively customizing compatible 3D and 2D network architectures. However, unlike multi-view image-based 2D visual modeling paradigms, which have shown leading performance in several common 3D shape recognition benchmarks, point cloud-based 3D geometric modeling paradigms are still highly limited by insufficient learning capacity, due to the difficulty of extracting discriminative features from irregular geometric signals. In this paper, we explore the possibility of boosting deep 3D point cloud encoders by transferring visual knowledge extracted from deep 2D image encoders under a standard teacher-student distillation workflow. Generally, we propose PointMCD, a unified multi-view cross-modal distillation architecture, including a pretrained deep image encoder as the teacher and a deep point encoder as the student. To perform heterogeneous feature alignment between 2D visual and 3D geometric domains, we further investigate visibility-aware feature projection (VAFP), by which point-wise embeddings are reasonably aggregated into view-specific geometric descriptors. By pair-wisely aligning multi-view visual and geometric descriptors, we can obtain more powerful deep point encoders without exhausting and complicated network modification. Experiments on 3D shape classification, part segmentation, and unsupervised learning strongly validate the effectiveness of our method. The code and data will be publicly available at https://github.com/keeganhk/PointMCD

    On parallel Branch and Bound frameworks for Global Optimization

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    Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity

    A study of free-form shape rationalization using biomimicry as inspiration

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    Bridging the gap between the material and geometrical aspects of a structure is critical in lightweight construction. Throughout the history of structural development, shape rationalization has been of prime focus for designers and architects, with biological forms being a major source of inspiration. In this work, an attempt is made to integrate different phases of design, construction, and fabrication under a single framework of parametric modeling with the help of visual programming. The idea is to offer a novel free-form shape rationalization process that can be realized with unidirectional materials. Taking inspiration from the growth of a plant, we established a relationship between form and force, which can be translated into different shapes using mathematical operators. Different prototypes of generated shapes were constructed using a combination of existing manufacturing processes to test the validity of the concept in both isotropic and anisotropic material domains. Moreover, for each material/manufacturing combination, generated geometrical shapes were compared with other equivalent and more conventional geometrical constructions, with compressive load-test results being the qualitative measure for each use case. Eventually, a 6-axis robot emulator was integrated with the setup, and corresponding adjustments were made such that a true free-form geometry could be visualized in a 3D space, thus closing the loop of digital fabrication

    Learning and Searching Methods for Robust, Real-Time Visual Odometry.

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    Accurate position estimation provides a critical foundation for mobile robot perception and control. While well-studied, it remains difficult to provide timely, precise, and robust position estimates for applications that operate in uncontrolled environments, such as robotic exploration and autonomous driving. Continuous, high-rate egomotion estimation is possible using cameras and Visual Odometry (VO), which tracks the movement of sparse scene content known as image keypoints or features. However, high update rates, often 30~Hz or greater, leave little computation time per frame, while variability in scene content stresses robustness. Due to these challenges, implementing an accurate and robust visual odometry system remains difficult. This thesis investigates fundamental improvements throughout all stages of a visual odometry system, and has three primary contributions: The first contribution is a machine learning method for feature detector design. This method considers end-to-end motion estimation accuracy during learning. Consequently, accuracy and robustness are improved across multiple challenging datasets in comparison to state of the art alternatives. The second contribution is a proposed feature descriptor, TailoredBRIEF, that builds upon recent advances in the field in fast, low-memory descriptor extraction and matching. TailoredBRIEF is an in-situ descriptor learning method that improves feature matching accuracy by efficiently customizing descriptor structures on a per-feature basis. Further, a common asymmetry in vision system design between reference and query images is described and exploited, enabling approaches that would otherwise exceed runtime constraints. The final contribution is a new algorithm for visual motion estimation: Perspective Alignment Search~(PAS). Many vision systems depend on the unique appearance of features during matching, despite a large quantity of non-unique features in otherwise barren environments. A search-based method, PAS, is proposed to employ features that lack unique appearance through descriptorless matching. This method simplifies visual odometry pipelines, defining one method that subsumes feature matching, outlier rejection, and motion estimation. Throughout this work, evaluations of the proposed methods and systems are carried out on ground-truth datasets, often generated with custom experimental platforms in challenging environments. Particular focus is placed on preserving runtimes compatible with real-time operation, as is necessary for deployment in the field.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113365/1/chardson_1.pd

    An analytical surver on customization at modular systems in the context of industrial design

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    Thesis (Master)--Izmir Institute of Technology, Industrial Design, Izmir, 2006Includes bibliographical references (leaves: 96-99)Text in English; Abstract: Turkish and Englishxi, 99 leavesEnterprises in all branches of industry are being required to become more user focused, yet, at the same time, increasing competitive pressure dictates that costs must also continue to decrease. Mass customization and modularity are strategies developed to address this challenge by producing goods and services meeting individual customer's needs with near mass production efficiency. However, while mass customization and modular systems have already been discussed in the literature, reports on practical implementation of the principles of mass customization in businesses can be found only within the last years. It is a challenge of manufacturing to produce variety of products with limited resources. As corporations strive to rationalize their manufacturing facilities and to produce a large variety of products at lower cost, modularity is becoming a focus of attention. Modular products and reconfigurable processes are crucial to agile manufacturing and provide a way to produce a variety of products that satisfy various customer requirements in time. This modular approach promises the benefits of high volume production (that arises from producing standard modules) and at the same time, the ability to produce a wide variety of products that are customized for individual customers. Such modular product design has been stated as being a goal of good design. Mass Customization target is the transformation of knowledge into "new" products or services, thus customizing and adapting first knowledge then the product itself. Customizing knowledge happens through instantiation and adaptation of design prototypes of the products or the component to fit the individual needs of the customer. This thesis. emphasis is placed on mass customization and modularity which can be seen as key strategies for making firms more customer centric. Furthermore, provide an introduction into principles, concepts, and demarcations, for mass customization and modularity. As the case study Aye Birsel.s resolve model for Herman Miller is a very good example for the relationship between mass customization and modularity
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