Fast Algorithms for Uniform Semi-Unification We present a fast algorithm for uniform semi-uni cation based on adapting the Huet unication closure method for standard uni cation. It solves the following decision problem in O(n 2 (n) 2 ), where n is the size of the two terms, and is the functional inverse of Ackermann's function: Given two terms s and t, do there exist two substitutions and such that ( (s)) = (t)? In the a rmative case, a solution can be constructed within the same time bound. However, if a principal solution (analogous to an mgu) is required, some modi cations to the algorithm must be made, and the upper bound increases to O(n 2 log 2 (n (n)) (n) 2 ). Semiuni cation is a combination of matching and uni cation on rst-order terms that has applications in term rewriting, type checking for programming languages, proof theory, and computational linguistics; although it can be de ned simply (see following section), it has proved remarkably difcult to analyze precisely. In its general form the problem has been shown to be undecidable 5], with an exceedingly di cult proof. The uniform case is decidable, and various authors have given algorithms (some incorrect), however, a careful analysis of its asymptotic complexity has not as yet been performed.. In this paper we present an algorithm with a time complexity in O(n 2 (n) 2 ). Our algorithm is based on the Huet uni cation algorithm, using a graph representation of the terms. It can generate solutions, although they may not be principal. An algorithm that can nd principal solutions in O(n 2 log 2 (n (n)) (n) 2 ) is also presented. Full details are found in the thesis of the rst author.. 2 Basic De nitions Let = ff 1 ; f 2 ; : : : ; f k g; k 1 be a rst order signature. Let X a countably in nite set of variables, and let T ;X be the set of all rst order terms over and X.. De nition 1 A substitution is a function : X ! T ;X such that (x) 2 X for almost all x 2 X. The set of variables x such that (x) 6 2 X is called Dom( ). A substitution can be extended naturally to a function : T ;X ! T ;X . An injective substitution is called a variable renaming i for all x 2 X; (x) 2 X.. De nition 2 If is a substitution and V X then j V , the restriction of to V is de ned as De nition 3 If 1 and 2 are substitution then we say that 1 2 i there is a substitution such that 2 = 1 , where denotes functional composition.. De nition 4 If t; u 2 T ;X then we say that t u i there is a substitution such that (t) = u.. De nition 5 A Semi-Uni cation Instance consists of a pair of terms denoted ft ? ug. We say that a semi-uni cation instance ft ? ug has a solution i is a substitution such that (t) (u).. De nition 6 A substitution is the principal solution of a semi-uni cation instance i for any other solution ;. .. De nition 7 Given a set of terms ft 1 ; : : : ; t n g, the set of all variables occurring in t 1 ; : : : ; t n is denoted by V (t 1 ; : : : ; t n ).. De nition 8 If V X is a set of variables then:

O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


The use of sensitivity analysis and genetic algorithms for the management of catalyst emissions from oil refineries Abstract: Excessive catalyst emissions from Fluidized Catalytic Cracking Units (FCCU) during start up situations are common, and have been deemed 'normal' with little research conducted on determining their causes. A simplistic model found to predict trends in emission rates under normal conditions has been expanded to better represent the actual processes inside an FCCU. First and second order sensitivity analysis techniques are used to assess the interactions between various operational parameters, with a genetic algorithm used to optimize the operating conditions to minimise air emissions. These 'key' parameters may then be altered to help manage both normal and start up emissions through operational changes. It was also found that significant scale up issues arise with the use of the attrition models found in the literature. The petroleum industry currently employs Fluidizing Catalytic Cracking Units (FCCU's) as the major tool in producing gasoline from crude oil. FCCU's typically consist of a rising main where the chemical reactions between catalyst and hydrocarbons occur, a reactor to separate the product and catalyst, and a regenerator to re-charge the used catalyst. The regenerator is a fluidized bed used to combust coke from the used catalyst, with cyclones to remove particles from the flue gas stream before venting to the atmosphere. The recharged catalyst then re-circulates through the rising main and the process is repeated (Kunii and Levenspiel 1991) .. In recent years, fine particle emissions from industry have been identified as important contributors to poor environmental and health standards across the United States (Johnson 2001) . With increasing demands for cleaner air, catalyst emissions from FCCU's have the potential to impact significantly on the environmental efficiency of the overall refining operation (Rucker and Strieter 1992) .. Currently, FCCU's are designed and operated in such a way as to maximise output and profitability of the refinery (Lin 1993) . With the lack of literature dealing with FCCU emissions, there is a need for the relationships between current operational strategies and air pollution to be better understood. The updated model has shown that fine particles, gas velocity and particle density are the most important operational parameters in terms of minimising particle emissions from a FCCU. Overall the model was found to significantly over estimate the true nature of emissions from an FCCU. It was concluded that this error was due to scale up issues arising from the attrition terms used. Optimization of the model supported the hypothesis that it is the attrition terms, and in particular the cyclone attrition coefficient, which is responsible of the over estimation of particle emissions. It appears that cyclone attrition is substantially less in larger systems than found in smaller laboratory based cyclones. Optimisation of the model with a more realistic attrition term showed that even at high gas velocities emission levels could be minimised. This work has supported earlier studies identifying particle size, density and gas velocity as the main parameters which should be controlled to minimise particle emissions from FCCUs. Further work is needed to develop better attrition models for use in large scale systems, so more accurate emission models can be developed. MATLAB was used to extend a simplistic model, already developed and tested on FCCU emissions (Whitcombe et al. 2001 and . The model comprised the essential processes inside the FCCU including fluidization, elutriation, entrainment and attrition, with model equations sourced from the literature.. The aim of this paper is to further develop the model into a more realistic package, for use in modelling industrial emissions. This will provide a simulation package of the FCCU, where the simulated emission can be studied in terms of system parameters. Emission results are then compared with observations from an operating FCCU, where the FCCU particle emissions during a start up period were identified. Thus allowing the complete range of emission to be seen .

O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Evaluating large-scale distributed vertical search Aggregating search results from a variety of distributed heterogeneous sources, i.e. so-called verticals, such as news, image, video and blog, into a single interface has become a popular paradigm in large-scale web search. As various distributed vertical search techniques (also as known as aggregated search) have been proposed, it is crucial that we need to be able to properly evaluate those systems on a large-scale standard test set. A test collection for aggregated search requires a number of verticals, each populated by items (e.g. documents, images, etc) of that vertical type, a set of topics expressing information needs relating to one or more verticals, and relevance assessments, indicating the relevance of the items and their associated verticals to each of the topics. Building a large-scale test collection for aggregate search is costly in terms of time and resources. In this paper, we propose a methodology to build such a test collection reusing existing test collections, which allows the investigation of aggregated search approaches. We report on experiments, based on twelve simulated aggregated search systems, that show the impact of misclassification of items into verticals to the evaluation of systems. Increasingly diverse content is available on the web, in terms of media (e.g. text, image, video, audio), and genre Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. LSDS-IR'11, October 28, 2011, Glasgow, Scotland, UK. Copyright 2011 ACM 978-1-4503-0959-2/11/10 ...$10.00.. (e.g. reference/wiki, FAQs, news, blogs). Until recently each type of content was dealt with in a separate way through so-called search verticals, and users switched between verticals to access information of a given type. Now, there is a growing tendency to "aggregate" search results from those different large-scale distributed verticals into one single interface. This is referred to as aggregated search [10] , and is implemented by most major search engines.. In order to properly evaluate those various large-scale distributed vertical search systems, there is a need for a test collection for research into the various stages involved in aggregated research. This is the main focus of this paper. A test collection for aggregated search requires verticals, each populated by items of that vertical type, a set of topics expressing information needs relating to one or more verticals, and relevance assessments, indicating the relevance of the items and their associated verticals to each topic. Constructing such a large-scale test collection from scratch is very time-consuming. Therefore, for aggregated search, there is the need to re-use existing (and emerging) collections to allow for evaluation in a timely fashion and with the required focus. In this way, as new, more focused verticals become available, they can be seamlessly integrated into the existing collection. It should be noted that our focus is not to replace the test collection creation methodology used in TREC, but rather utilise a similar methodology to create a practically useful, reliable, and consistent large-scale test collection for the aggregated search community. The contribution of this paper is three-fold:. • We outline the process and methodology of reuse to construct a test collection for aggregated search from existing test collections (Section 3).. • We build a practical test collection for aggregated search by using a SVM classifier to classify items into various types (Section 4).. • We investigate the impact of misclassification (of items into verticals) to the evaluation of systems, by experimenting with twelve large-scale distributed vertical search systems on simulated test collections with various misclassification rate (Section 5).. The remainder of the paper is as follows: Section 2 provides some background. Section 3 describes our methodology and introduces some important concepts. Section 4 describes the stages and design decisions involved in building the test collection. Section 5 details experiments carried out to investigate the consistency of the constructed test collection. Finally, Section 6 outlines our conclusions and future work. We describe a method for creating a large-scale aggregated search test collections by reusing existing test collections. We have demonstrated that by identifying topics from existing test collections, a sufficient number (320) of topics with multiple vertical intents can be collected. In addition, through simulation we have showed that aggregated search approaches can be properly evaluated even if there are inherent misclassification within the verticals. Future work includes rigorous testing of evaluation measures that incorporate many aspects of aggregated search system performance. We ran the 12 systems on the the collections with various levels of misclassification (with five iterations for each level). We used a subset of topics that had at least two vertical intents. The average Spearman rank correlation between the performance of the systems on the different collections is shown in Table 7 . We can see that in general there is a high correlation between the systems even if misclassification increases to 30%. A random classification of documents (not shown in Table 7 ) leads to a moderate correlation of 0.573. In this section we discuss research that is related to both aggregated search and test collection design. In this section, we describe the methodology of reuse adopted herein to construct an aggregated search test collection. The methodology can be categorized into several steps:. 1. First, we define the verticals that we want to investigate (Section 3.1). 4. Furthermore, we discuss how existing relevance assessments can be used correctly so that the aggregated collection remains reliable. We used a classifier to assign documents to verticals and, therefore, some documents may be incorrectly assigned to a vertical. We need to assess the impact of this. We now describe an experiment carried out to evaluate the effect that document misclassification has on our newly created test collection. We create different versions of the test collection, 9 These were preliminary experiments and a full evaluation of this process is planned. 10 16 common verticals include News, Image, Video, Blog, Discussions, Answer, Reference, Maps, Books, Updates, Scholar, Shopping, Financial, Local Listings, Weather, Web. where the only difference is that we intentionally mis-classify a certain percentage of the documents. Then, having created these modified collections, we investigate whether the ordering (based on an effectiveness metric) of a number of different aggregated search systems is preserved (or at least correlated) when run on these different versions of the test collection (i.e. collections that have various levels of misclassification). If the ordering of the systems is preserved, or highly correlated, we can conclude that the effect of misclassified documents on our created collection is minimal.

O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I I O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Drawing for Illustration and Annotation in 3D We present a system for sketching in 3D, which Drawing has long been an intuitive way to communicate complexity in a comprehensible and effective manner, due to visual abstraction. Compared to a photograph of a real object, extraneous details can be omitted, and thus attention can be focused on relevant features. The impression a drawing produces on a viewer is very different from the one a solid model produces: strokes mark the presence of a surface or a contour, but they can be "heavier" or "lighter", giving an indication of uncertainty where needed. The viewer's imagination is immediately engaged.. This kind of communication is useful in educational applications such as teaching, but also in the early stages of design, because drawing a sketch is much faster than creating a 3D model, and definitely more convenient to express ideas. However, the obvious drawback of 2D sketches is their limitation to a single viewpoint. The user cannot move around the object drawn, nor view it from different angles. the artist is significantly reduced. As an example, consider Fig. 1 , which shows two views of a single rough landscaping sketch, generated by our system. It is imperative that such a system be interactive, since a slow, non-interactive system would interfere with the natural artistic creation process.. The aim of this paper is to provide a system that enhances classical sketching with 3D capabilities. Here, as in traditional 2D drawing systems, the user draws strokes that may represent either surface silhouettes or 1D features. These strokes may either belong to a single object or to many different ones, embedded in a complex scene. Both open and closed strokes may be used. As in 2D drawing, the user can draw several neighbouring strokes to accentuate a given contour. The main difference is that the viewpoint can be changed while drawing, thus creating a 3D sketch. The central idea of our approach is to represent strokes in 3D space, thus promoting the idea of a stroke to a full-fledged 3D entity. Even in 3D, we think that strokes are an excellent way to indicate the presence of a surface silhouette: several neighbouring strokes reinforce the presence of a surface in the viewer's mind, while attenuated strokes may indicate imprecise contours or even hidden parts.. Finding surface properties of objects from their silhouette is a classic hard problem in computer vision. The algorithms presented here do not address this issue, since our goal is to develop a drawing system rather than to perform geometric reconstruction. As a consequence, we develop approximate solutions that are appropriate in the context of drawing and sketching.. To enable the user to view stroke-based sketches from multiple viewpoints, we interpret 2D silhouette strokes as curves, and use a curvature estimation scheme to infer a local surface around the original stroke. This mechanism permits efficient stroke-based rendering of the silhouette from multiple viewpoints. In addition to stroke deformations, this includes variation of intensity according to the viewing angle, since the precision of the inferred local surface decreases when we move away from the initial viewpoint. It also includes relative stroke occlusion, and additive blending of neighbouring strokes in the image.. Apart from silhouette strokes, our system also provides line strokes that represent 1D elements. These have the ability to remain at a fixed position in 3D while still being occluded by surfaces inferred using silhouette strokes. They can be used to add 1D detail to the sketches, such as the arrow symbols in the example of annotation (see Fig. 11 ).. Because strokes have to be positioned in space, we present an interface for 3D stroke input. The user always draws on a 2D plane which is embedded in space. This plane is most often the screen plane, selected by changing the viewpoint. The depth location of this plane can be controlled either explicitly via the user interface or implicitly by drawing onto an existing object. The user may also draw strokes that are not in the screen plane, but that join two separate objects.. The combination of rapid local surface reconstruction and graphics hardware rendering with OpenGL results in truly interactive updates when using our system. Finally, we show that our method can be applied to artistic illustration as well as annotation of existing 3D scenes, such as for rough landscaping or educational purposes. An existing 3D object can also be used as a guide to allow the design of more involved objects, e.g., using a model mannequin to create 3D sketches for clothing design. We have presented a system which enhances the traditional 2D drawing process with 3D capabilities, notably by permitting multiple viewpoints for a single drawing. Instead of attempting a complete 3D reconstruction from 2D strokes, we infer a local surface around the stroke. This is achieved by assuming that strokes are drawn in a plane, and by using differential geometry properties of the curve. The resulting local surfaces are then drawn efficiently using hardware accelerated rendering of a clipped part of the local surface, corresponding approximately to a silhouette. Color blending is used to gracefully diminish the intensity of the strokes as we move away from the initial viewpoint, and to allow reinforcement of intensity due to multiple strokes. We have also introduced a multipass method for stroke intervisibility, which results in a visually pleasing gradual occlusion.. Our approach is built into a system which provides an interface which retains many of the characteristics of traditional 2D drawing. We aid the user in placing the drawing plane in empty space, and positionning it relative to other objects (strokes or geometry) in the sketch. We have chosen a Bézier surface representation for storing silhouette stroke information. This approach is convenient but it can result in a large number of hardware rendered polygons. Other representations could be used instead.. For instance, a volumetric data structure would have allowed us to combine information about the local surface: the more strokes are drawn at a given location in space, the more we are certain that it corresponds to a true surface point. To render strokes from a new viewpoint, we would have used a variant of the marching cubes algorithm to produce a surface estimation, associated with a mesh silhouette detection algorithm to generate new silhouette strokes. The obvious drawbacks of this approach are memory consumption and data loss due to volumetric sampling of user input. A particlebased approach, i.e., strokes composed of particles that try to satisfy a set of constraints such as "stay on silhouette", etc., would produce interesting stroke transformations. However, numerical stability would undoubtedly be an issue as well as computational overhead, which would impede interactivity.. Our user interface is clearly far from perfect. Plane positioning is not completely intuitive, and alternatives should be considered. For example, a computer vision approach in which the user defines two viewpoints for each stroke and implicitly reconstructs positions in space (within an error tolerance) could potentially prove feasible. But it is questionable whether such an approach would truly be more intuitive.. We are investigating various such alternatives with the goal of finding an appropriate combination to improve our current solution, both in terms of stroke rendering quality and user interface. Our work is a natural continuation of drawing or sketching tools which have been developed in computer graphics over the last few years. In particular, researchers have realized the importance of providing usable tools for the initial phase of design, beyond traditional 3D modeling. These have taken the form of 3D sketch or drawing systems, typically with direct line drawing or stroke interfaces.. Some of these systems are directly based on 3D input 7 4 19 . They require special equipment (VR glasses, tracking sensors, arm-support, etc.) and often cannot be used on traditional workstations. We will not discuss them further; we will instead concentrate on solutions which do not require specific additional equipment and which are more practical than drawing directly in 3D.. Some systems use direct 2D drawing to reconstruct 3D scenes. Cohen et al. 6 , present a system in which each 3D curve is entered by successively drawing its screen plane projection and its shadow on the floor plane. This approach can be useful for camera path description for example, but seems potentially unintuitive for drawing shapes. Tolba et al. 24 , use projective 2D strokes in an architectural context. By projecting 2D points onto a sphere, 3D reprojection is achieved under different viewing conditions. Other systems restrict drawing to predefined planes, either as a generalization of traditional axis aligned views 15 , or specifically onto cross-sections 10 .. Another family of systems 12 25 8 17 , try to infer 3D models from 2D drawings and a set of constraints. Ivan Sutherland's "Sketchpad" system in 1963 23 can be considered as the inspiration for this work. During the 1990's a number of researchers advanced in this direction.. Among them, Pugh 17 presented the "Viking" system, where preferred directions and cutting planes guide the user in the placement of 3D vertices. Direct user intervention is possible both for explicit constraint specification and hidden line designation. Akeo et al. 1 used cross section lines to infer 3D shape, while Branco et al. 2 required the user to draw models without hidden lines, and used a classification scheme and direct user input to reconstruct in 3D. Eggli et al. 8 9 interpret pen strokes by matching them to a small set of predefined primitives, and by applying a sophisticated constraint based system. The result is rapid construction of high-quality, CAD-like models. Lipson and Shpitalni 13 use optimization on a 2D edge-vertex graph which is tolerant to inaccurate positioning and missing entities; in addition, a number of different object types are supported.. In some of these systems, the advantage of viewing the designed model or scene in a non-photorealistic manner has been exploited to get a result that does not inhibit the designer imagination, as stressed by Strothotte et al. 22 . The SKETCH system 25 concentrates heavily on the use of efficient gestural input and non-photorealistic rendering to allow the creation of approximate, but complete, 3D models. More recently, the "Teddy" system 12 takes closed 2D freeform strokes as input, and reconstructs a polygonal object, which is converted back to strokes for rendering. Both systems emphasize a natural binding of gestures for the creation of specific shapes, affording a powerful and intuitive interface for rapid creation of specific types of 3D models.. The "Harold" system 5 is probably the most closely related previous work. The goal of this system is to provide a world populated by 3D "drawings". Three specific modes are provided: billboard (projection in a plane which turns towards the user), terrain and ground mode. The system allows the creation of "bridge strokes" between billboards. However, it does not handle strokes that correspond to the silhouette of a 3D object, and should thus deform when the point of view changes. As we shall see, this is an essential feature of our approach, since the capability to draw silhouettes is heavily required in both annotation and initial design applications.

B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Assessing correlations between lingual movements and formants First and second formant histories have been used in studies of both normal and disordered speech to indirectly measure the activity of the vocal tract. The purpose of the present study was to determine the extent to which formant measures are reflective of lingual movements during diphthong production. Twenty native speakers of American English from the western United States produced four diphthongs in a sentence context while tongue movement was measured with a magnetic tracking system. Correlations were computed between the vertical tongue movements and the first formant, as well as between the anteroposterior movements and the second formant during the transition phase of the diphthong. In many instances the acoustic measures were clearly reflective of the kinematic data. However, there were also exceptions, where the acoustic and kinematic records were not congruent. These instances were evaluated quantitatively and qualitatively in an effort to understand the cause of the discrepancy. Factors such as coarticulation, motor equivalence (including the influence of structures other than the tongue), and nonlinearities in the linkage between movement and acoustics could account for these findings. Recognizing potential influences on the acoustic-kinematic relationship may be valuable in the interpretation of articulatory acoustic data on the individual speaker level. Speech production can be examined in a variety of ways, depending on the goals of the researcher. Perceptual evaluation offers the two key advantages of requiring no instrumentation and being closely linked to the experiences of everyday speakers and listeners. However, because of limitations in the precision and reliability of human perceptual performance, instrumental means of measuring speech have become a mainstay of research in our field [1] .. Acoustic analysis allows the noninvasive measurement of many aspects of voice and speech production. When recordings are made with high quality equipment in a quiet environment, it is relatively straightforward to generate sensitive indexes of phonation and articulation. Measures of phonatory function have application not only in research; they are also easily derived from clinical recordings in order to quantify dysphonia severity or treatmentrelated change. As such, they complement the clinician"s perceptual evaluation by providing objective evidence of the effects of intervention [2] .. The identification of articulatory movements from time-varying acoustic parameters is far more time-consuming than computing perturbation measures from sustained vowel phonation.. As a consequence, parameters such as formant transitions, voice onset time, and segment durations are typically not measured in everyday clinical practice. Rather, they are used in basic and clinical research in order to indirectly reveal aspects of the speech movements that underlie sound production. Patterns of change in the first and second formants (F1, F2) have been used in numerous studies to reflect the activity of the vocal tract [e.g, 3, 4] .. The transfer function of the vocal tract filter depends on the interaction of multiple resonating cavities, which prevents the straightforward identification of the anatomic origin of a particular formant. Nevertheless, the generally accepted view is that F1 is strongly influenced by the height of the tongue and jaw and F2 is to a large extent linked to tongue advancement in the mouth. Changes in overall vocal tract length, which result from adjustments to laryngeal height and lip rounding, influence the frequencies of all formants.. The fact that changes in the formant frequencies reflect adjustments to the vocal tract configuration has led to the widespread use of formant histories as indicators of articulatory activity. Weismer and colleagues [5] reported that speakers with amyotrophic lateral sclerosis had shallower formant transition slopes than healthy speakers, and that those with the poorest intelligibility in many instances had trajectories that were nearly flat. Weismer and Berry [6] examined formant trajectories at different speaking rates and found that there was not a linear compression or expansion of the transitions as individuals spoke more quickly or slowly.. F1 and F2 have also been used in the computation of vowel triangles or quadrangles, which reflect the extent of vocal tract movements in the production of corner vowels. Tjaden and Wilding [7] investigated the effects of loud or slow speech on the vowel space area of speakers with dysarthria and found that slower speech led to an expansion of the area, presumably because the articulators had more time to reach their spatial targets. The same study found that formant slopes in diphthongs did not change uniformly with rate or loudness adjustments.. In addition to reflecting certain features of articulatory behavior, formants have also been used as an index of vocal tract steadiness in spasmodic dysphonia or hyperkinetic dysarthria [8] [9] [10] [11] . In this context they have been valuable in characterizing the impact of a disorder on the vocal tract filter as distinct from the laryngeal sound source.. Acoustic analysis of speech is appealing because it is non-invasive and thus has no impact on the way words are spoken. However, there is a degree of ambiguity in the interpretation of the acoustic signal, since a given acoustic change can result from the contributions of several structures. This is one of the reasons why some researchers have turned their attention to the movements themselves that underlie the acoustic signal.. Kinematic analysis examines articulatory patterns by tracking the movement of articulators, such as the jaw, lips, and tongue. A number of devices have been developed over the last few decades, and these have enabled researchers to measure the movements of the articulators in both normal and disordered speech. Barlow, Cole, and Abbs [12] suggested a direct examination of disordered speech movements rather than only considering the acoustic result of these movements, because impaired control of muscle contraction and movement is the more direct consequence of neuromotor abnormality. Thus, kinematic analysis brings us a step closer to the disorder itself, removing the intermediate step of acoustic analysis.. Researchers have relied on a variety of techniques to reveal details of articulatory motion.. Strain gauges and optical tracking systems [12, 13] are relatively straightforward to use, but can only reveal the movements of visible structures. The collection of lingual kinematic data requires more invasive technologies. Using cinefluorography exposes participants to the danger of radiation. The complexity and cost of computerized X-ray microbeam, magnetic resonance imaging (MRI) tagging, and ultrasound systems have limited their use to a few specialized laboratories [14] . Electromagnetic articulography [15] [16] [17] has increased in popularity in recent years, although the systems are expensive and require careful setup for experimental use.. A jaw-tracking system that uses a single, permanent magnet has been used to quantify tongue movements during speech [14, 18] . While this system is limited to tracking a single flesh point on the tongue, its ease of set-up and modest cost allow its application where more sophisticated systems are either unavailable or impractical.. Because acoustic analysis focuses on the audible results of vocal tract activity, while kinematic approaches reveal details of the underlying movements, it would be valuable to examine the relationship between the data from these two signal sources. As noted earlier, F1 is understood to reflect the vertical movement of the tongue, and F2 its anteroposterior movement [19] . There are several factors that could potentially influence the relationship between these two types of signal. One of these would be motor equivalence [20] , whereby slightly different vocal tract configurations across individual speakers can result in the production of a perceptually equivalent phoneme. In other words, there can be more than one way to produce a similar result as movement in one part of the vocal tract co-occurs with adjustments elsewhere that combine to produce the target sound. A further influence on the acoustic-kinematic linkage would be coarticulation, because lingual movements for target sounds can be influenced by the production of neighboring sounds in the context of words or sentences [21] [22] [23] . Finally, according to the quantal theory of speech [24, 25] , the relationship between acoustic and kinematic parameters is not always linear, in that a given degree of articulator displacement in one position may have a much larger influence on acoustics than a similar displacement at a different point along its trajectory. The goal of the present study was to compare the patterns in the first two formants with the magnetically tracked movements of the tongue that they are assumed to represent.. Pearson correlation coefficients between the formant and kinematic records were computed during the diphthong transition to evaluate the extent to which the acoustic measures were reflective of the movements. Of particular interest were cases where the acoustic and kinematic data were not predictably correlated. It is generally accepted that changes in the formant frequencies of vowels and diphthongs indirectly reflect tongue movements; F1 reflects vertical displacement and F2 primarily reflects anteroposterior movement. Accordingly, the present study was performed to test the strength and consistency of this association. The results of the current study showed that in a number of instances, the formants reliably tracked the tongue movements, but in others the association was far less clear. In other words, there was variability across individuals and sounds in the strength of the correlations between the acoustic and kinematic variables. These findings suggest that assumptions about the relationship between the formants and tongue movements may be overly simplistic, and in connected speech their relationship can be more complex. Therefore, researchers should exercise caution when interpreting acoustic measures of lingual activity for an individual speaker, given the potential contributions of coarticulation, motor equivalence, and the contributions of other vocal tract structures to the production of these sounds. Note: St Dev = standard deviation Table Table 2 Note: St Dev = standard deviation; A-P = anteroposterior with only modest differences in the acoustic record. The lower panels show the same diphthong for speaker 4, who had lingual movements that were more variable than the formant histories for the three tokens. The purpose of this study was to investigate the correlation between acoustic and kinematic variables in perceptually normal speech during the production of four diphthongs in a sentence context. In many instances the association between the two data sets followed the pattern that would be predicted, based on typically accepted notions of the movements that contribute to changes in F1 and F2. However, there were also a number of exceptions that warrant further consideration, especially for F1. In the sections below, the primary focus will be on those instances where the formant histories did not appear to follow the movement of the tongue in a predictable way. Because no significant differences were found between the speakers with MS and the control group for these speakers in an earlier study [26] , the results represent the combined data from both groups. As noted above, all participants had perceptually normal speech, as judged by the experimenters. T-tests comparing the acoustic-kinematic correlations for men and women showed no differences, thus all further testing was done for the 20 speakers combined. For /aʊ/, 15 of the 20 speakers exhibited a negative correlation, although only five had a Pearson r value that was more negative than -.500. The mean correlation of -.268 indicated a modest negative association between the acoustic and kinematic variables when all speakers were considered as a group.. During the production of /aɪ/ all 20 speakers had a negative correlation during the transition. The strength of the negative correlation varied across speakers, although the mean value of -.727 indicated that the predicted relationship between the kinematic and acoustic variables was present for this sound. Fifteen of the speakers had a Pearson r value that was more negative than -.500. The mean vertical magnet displacement was similar for /aʊ/ and /aɪ/ (just over 1.5 mm for each).. For /eɪ/, 16 of the 20 speakers had a negative correlation, with a group mean of -.345. For 10 of the individuals the Pearson r value was more negative than -.500. The mean transition duration for this sound was the briefest of the four diphthongs (55.1 ms) and the vertical displacement of the magnet was the smallest (0.41 mm). Likewise, the mean extent of F1 change during the transition was the smallest (78.6 Hz). Table 2 For /aʊ/, 17 of the 20 speakers exhibited a positive correlation, which contributed to a mean Pearson r value of .470. For 10 individuals, the r was greater than .500. The mean anteroposterior displacement for /aʊ/ (1.87 mm) was greater than for /aɪ/ (1.61 mm), which was unexpected, given that the movement from a lower to a higher back vowel position had been anticipated to be primarily vertical.

O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O B O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A metrics system for quantifying operational coupling in embedded computer control systems One central issue in system structuring and quality prediction is the interdependencies of system modules. This paper proposes a novel technique for determining the operational coupling in embedded computer control systems. It allows us to quantify dependencies between modules, formed by different kinds of relationships in a solution, and therefore promotes a more systematic approach to the reasoning about modularity. Compared to other existing coupling metrics, which are often implementation-technology specific such as confining to the inheritance and method invocation relationships in OO software, this metrics system considers both communication and synchronization and can be applied throughout system design. The metrics system has two parts. The first part supports a measurement of coupling by considering individual relationship types separately. The quantification is performed by considering the topology of connections, as well as the multiplicity, replication, frequency, and accuracy of component properties that appear in a relationship. The second part provides a methodology for combining coupling by individual relationship types into an overall coupling, where domain specific heuristics and technology constraints are used to determine the weighting. Embedded computer control systems (ECS) are computer-based systems for advanced control, diagnostics, and monitoring in machinery [1] . Typical application areas include vehicles, avionics, and robotics. Because of the dynamics under control, such systems differ from other general-purpose computer systems in the aspects of real-time and safety criticality.. In ECS, computer software and hardware together constitute the physical embodiments of system functions for the purpose of system realization. Issues that are of particular concern in the software system design include: identification and classification of requirements and constraints, definition of components and relationships, assessment of feasibility and product qualities, and trade-offs between solution alternatives. Normally, the design is performed at different refinement levels, repeating a means-end pattern in the sense that an allocation of requirements to solutions will in turn derive some new requirements for the underling solutions (e.g., a hierarchy of mapping from end-to-end timing of control loops to code level timing) [2] . From a system engineering point of view, it is the design in the large, targeting pre-code artifacts at levels higher than detailed implementation, that has the key impacts on product qualities, complexity control, costs and time-to-market, see e.g., [3] [4] [5] . For example, [5] states that the front-end design in general determines 80% of system cost with only 20% of total product development costs spent. For ECS, there is currently a paradigm shift from a "traditional" software design that focuses on coding and testing to a model-based software design that emphasizes quality assessment and optimization using system descriptions at levels higher than code details, see e.g., [28] .. One important property of complex ECS, besides the mandatory functionality, real-time timeliness, and dependability, is modularity, indicating the extent to which a system is decomposed and classified into parts. This system property forms a key factor in complexity control, concurrent engineering and product flexibilities (including reusability and modifiability), see e.g., [6] [7] . As a rule-of-thumb, software systems with good modularity should exhibit low coupling and high cohesion, where the coupling indicates the strength of interconnections (i.e., the "wiring") between modules and the cohesion shows the strength of holding a module together (i.e., the "glue") [8] [9] .. For complex ECS, there is a need to support objective and repeatable measurement of coupling throughout the design at different levels of design refinement. Given the importance of design in the large, the designers must be able to verify high-level (e.g., architectural) solutions and perform tradeoffs between solution alternatives by taking modularity into consideration. However, little support exists in this area. Existing approaches to quantitative coupling measurement mainly target detailed software design and consider only program specific dependencies (e.g., calls). Due to their restrictions to implementations details, such approaches have very limited usability in the system level design. This paper proposes a technique for measuring the operational coupling in ECS, hence providing information for quantitative assessment of modularity in the system design. The metrics system transforms various communication and synchronization relationships, derived from a system meta-model of ECS, into quantitative coupling measures by considering parameters such as frequency and accuracy that affect the strength of dependencies. This paper includes 7 major sections. In the next section, we discuss the aim of this work and the solution strategy. Section 3 introduces the system model and concepts underlying the metrics system. Section 4 presents the metrics system that supports the measurement by considering individual relationships separately. Section 5 describes a methodology for combining these individual relationships. Finally, Section 6 describes related work and Section 7 concludes and discusses further work. A metrics system has been developed to support an objective and repeatable measurement of operational dependencies between system functions, hence a more systematic approach to structuring and quality prediction of ECS. Instead of implementationtechnology, the measurement targets the overall system structure and behavior, existing throughout the refinement hierarchy of a system. Based on a fine grained classification of such relationships, the quantification takes ECS specific issues into concern such as replication and timing.. There are several obvious avenues for further work. In the short term there is a need to gather more empirical evidence mainly for studying the influence and tuning of the following parameters part of the coupling metric: C δ , C RM , and the cross-type weighting. We believe that these depend on both human decision factors and system factors, such as system characteristics, the insight of the developers, the available modeling and tool support. I.e. we do not expect that coupling as a soft quality attribute will obey any natural laws. However, for the purpose of early estimations there is less of a need for highly precise metrics; the value lies in being able to reveal the sensitive points and to make multi-attribute trade-offs possible.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Evaluation of texture registration by epipolar geometry In the process of digitizing the geometry and appearance of 3D objects, texture registration is a necessary step that solves the 2D-3D mapping between the 2D texture images and the 3D geometric model. For evaluation of texture registration with ground truth, accurate datasets can be obtained with a complex setup consisting of calibrated geometry and texture capture devices. We do not have any knowledge of such evaluation performed; current evaluations reflect, at their best, the precision achieved by the algorithms, but fail to identify a possible bias. We propose a new evaluation measure based on the epipolar geometry of texture image pairs, with the advantage that the ground truth can be extracted solely from the texture images, independent of the 3D acquisition. We developed a noise model suitable to our purpose and analysed three distance measures based on epipolar geometry, well known in the computer vision community, to find new theoretical and experimental results. Finally, using the proposed framework, we evaluated a texture registration algorithm based on mutual information and found that its accuracy was under half-pixel. As 3D scanning techniques are become affordable, 3D reconstruction projects become widespread and numerous. Besides the geometric 3D shape, digitization may also include the surface appearance. Although many 3D acquisition devices are capable of capturing 3D geometry jointly with the surface appearance, the latter is more commonly generated from additional images of the model. The cameras used for 3D scanning are not suitable for high-quality color images, and often the light conditions required for geometry acquisition are different than for texture acquisition. Instead, the surface appearance is captured in distinct color images which are registered and fused onto a single texture map, suitable for real-time rendering on modern graphic cards. Texture registration is the process of aligning each image with the 3D model. Various algorithms have been successful for texture registration, but the field lacks a unified evaluation framework.. The goal of texture registration is to solve the 2D-3D mapping problem between each texture image and the 3D model. The mapping is most commonly modelled by a pinhole camera; the distortion-free pinhole camera is defined by the 3 × 4, rank 3 camera matrix P , and the fundamental equation x ∼ P X, where ∼ denotes equality in homogeneous coordinates, and X, respectively x, are the homogeneous coordinates of an arbitrary 3D point and its 2D projection.. The most common solution for texture registration uses 2D-3D feature point correspondences, often selected interactively; however, highly automatic algorithms based on a variety of criteria have been successfully proposed. The criteria include: point correspondences combined with outlines and color information [12] , silhouettes [10] , photoconsistency [3] , mutual information [5] , and even shadows [15] . The problem is formulated as an optimization for the camera parameters associated with each image and the algorithms typically are iterative in nature.. Evaluation of texture registration with ground truth requires highly accurate estimates for the camera matrices associated with each image. Since the camera matrices are useful only if they are known in the reference system of the 3D model, the ground truth can be estimated when the texture acquisition cameras are calibrated with respect to the 3D scanning devices, requiring elaborate setup and imposing limitations on test datasets. Any estimation of the camera matrices using only the digitized 3D model and the texture images requires solving a 2D-3D registration problem, therefore is not suitable to our purpose.. Gold standard datasets for evaluation of 2D-3D medical image registration, with applicability restricted to this field, were produced using a highly complex, state-of-the-art medical imaging system [16] . The Stanford robot, with an arm that can be positioned with accuracy of 0.01 degrees, was used to build a test set for evaluation of multiview stereo 3D reconstruction algorithms [13] . The high complexity and increased cost involved in producing accurate gold standard datasets motivated us to search for alternatives to ground truth estimation.. In this paper we propose a new measure for evaluation of texture registration, based on epipolar geometry, which overcomes the above-mentioned limitations. The advantage of our technique consists in the fact that the ground truth can be accurately obtained only from texture images, decoupling 3D scanning from texture acquisition, by full or weak calibration algorithms using known 3D patterns. The tradeoff is that, rather than the full camera matrices, the method recovers a limited ground truth consisting in the epipolar geometry between images. The proposed error measure is not single-image based, such as the reprojection error (a common error measure for texture registration which will be defined later), but based on pairs of registered texture images. We will not discuss the extraction of the ground truth in the form of epipolar geometry, for which the literature is comprehensive, but define an appropriate error measure for texture registration using the limited ground truth.. We studied several epipolar distances and their quantitative relation to the reprojection distance. The distances are widely known in computer vision community, but we used them in a novel way. We analysed the epipolar distances under a statistical model different than the ones commonly found in literature, suitable to model the registration errors of texture registration algorithms. We found new theoretical and experimental aspects of epipolar distances and confirmed others.. The proposed evaluation method is not limited to a particular algorithm; we evaluated a recent registration method using mutual information because the application, developed by the authors, was easily available. The algorithm proved to be highly accurate, with errors less than half-pixel.. In the remainder of the Introduction we will review the current methods and measures used for evaluation of 2D-3D registration, present our evaluation method, and, finally, we will give an overview of the rest for the paper. In the following Sect. 2 we define the three epipolar distances and develop an algorithm to estimate the manifold projection distance for normalized cameras. In Sect. 3 we motivate the statistical model and present a theoretical result for the manifold projection distance, then develop an extensive experimental evaluation for the epipolar distances, in Sect. 4. In Sect. 5 we evaluate a texture registration algorithm based on mutual information using the proposed framework. Finally, we draw the conclusions in Sect. 6. We proposed a new evaluation of texture registration algorithms using, as ground truth, the epipolar geometry estimated for pairs of images. The advantage is that the ground truth can be conveniently obtained independently of geometry acquisition, requiring the object and a calibration pattern kept fixed while taking the texture images. We discussed three distance measures based on epipolar geometry: the symmetric epipolar distance, the Sampson epipolar distance, and the manifold projection distance, and analysed them in relation to the reprojection distance, standard error measure when the full ground truth is known.. We compared the distances in a synthetic experiment with ground truth, using a novel noise model. We showed that the bias of the manifold projection distance with respect to the reprojection distance can be estimated theoretically and found the experimental values close to the expected one. We found that, after removing the bias, the manifold projection distance models the reprojection distance with the highest accuracy.. We applied the framework to evaluate a texture registration algorithm based on mutual information, against Zhang calibration, implemented in Bouguet toolbox. We found that the registration algorithm was highly accurate, below halfpixel for our case studies. The registration precision was about the same; thus, we conclude that the registration was precise and unbiased. We will relate our problem to the well-known problem of fundamental matrix estimation from noisy point correspondences in two images [8] . Several epipolar distances have been proposed as objective functions for estimation of the fundamental matrix from point correspondences. We mention the algebraic distance, the symmetric epipolar distance, the Sampson distance (gradient-weighted epipolar distance), and the reprojection distance. The algebraic distance is defined as the sum of squared residuals x T i F x i from (2). The symmetric epipolar distance and the Sampson distance were defined above in (3), respectively (4). The reprojection distance is defined by the same expression as the manifold projection distance (5), but the optimization space differs; the noisy coordinates of the projections, (x i , x i ), are known, and the optimization is performed for the essential matrix and the structure X i , i = 1, . . . , n.. In our case, an estimated 2-camera description and the 3D structure are given, and the problem is to compare this configuration with a highly accurate essential matrix. The distances used as objective functions for estimation of the essential matrix can be used to define a suitable distance measure for our problem. The differences between the two problems consist, firstly, in the different known and unknown parameters, and secondly, in the statistical noise model. For estimation of fundamental matrix, the imprecision is in the extraction of 2D coordinates, and the 3D structure is unknown, while in our case the noise is associated with inaccurately estimated camera matrices, and the 3D structure is known.. The algebraic distance, the symmetric epipolar distance, and the Sampson epipolar distance are applied in exactly the same manner in both problem instances. The reprojection error requires the 3D structure. As for our instance of the problem the structure is known, the search space consists in the parameters which, together with an essential matrix, identify the twelve free parameters of a pair of normalized cameras. For essential matrix estimation using the reprojection error, the search space consists in the five free parameters of the essential matrix and the 3n parameters defining n point coordinates in 3D space (the structure).. We illustrate the conceptual difference between the two problems in Fig. 1 . For our evaluation problem, the point correspondences lie on the joint image manifold with essential matrix F 1 , and we estimate the distance to the manifold defined by the gold standard F 2 , with the additional constraint that the solution should be consistent with the given 3D structure X i , i = 1, . . . , n. This is the motivation behind the name manifold projection distance. For the fundamental matrix estimation problem, the point correspondences do not lie on a manifold, and the essential matrix F defining the 'closest' manifold is searched for.. An alternative solution to our problem would be to use a matrix distance between two fundamental matrices. It has been shown in literature that a matrix distance, such as the Frobenius norm of the difference of two (normalized) fundamental matrices, is not appropriate to measure the difference between fundamental matrices [6, 17] . Zhang gives an algorithm 2 to compute a geometric distance between two fundamental matrices [17] . We believe that, having the 3D structure and a completely defined camera pair known, this distance is absorbed by the symmetric epipolar distance.. Several studies [14, 17, 18] considered various epipolar distances for estimation of the fundamental matrix. The algebraic distance performed the worst [8, 17] , as expected, since it does not reflect a geometric measure. The Sampson distance is considered to be better than the symmetric epipolar distance, as it is the first-order approximation of the geometric distance, the fact that was confirmed in experiments [17] .. In [18] the symmetric epipolar distance, the Sampson distance, and the reprojection distance were compared with respect to their use as optimization criteria, when the coordinates of the point correspondences are affected by i.i.d. Gaussian noise. The symmetric epipolar distance and the Sampson distance were equivalent only when the epipoles are at infinity and the images have the same scale of the scene. On the other hand, the reprojection distance and the Sampson distance were equivalent when the epipoles are at infinity and slightly different when the epipoles are in the images.. Other noise models have been considered for fundamental matrix estimation, such as heteroscedastic noise [9] or presence of outliers [14, 17] . For our problem, the geometry is known, and the 2D projections are generated by projecting the 3D structure, and therefore we do not face any outlier problem. We associate the noise model with the estimation of camera matrix, which generates correlated noise in the 2D projections over images. Likewise, it is beyond the scope of this paper to discuss the estimation of the golden standard fundamental matrix.

O O B I O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics Abstract An important dispersion-related characteristic of wave propagation through periodic materials is the existence of frequency bands. A medium effectively attenuates all incident waves within stopbands and allows propagation within passbands. The widths and locations of these bands in the frequency domain depend on the layout of contrasting materials and the ratio of their properties. Using a multiobjective genetic algorithm, the topologies of one-dimensional periodic unit cells are designed for target frequency band structures characterizing longitudinal wave motion. The decision variables are the number of layers in the unit cell and the thickness of each layer. Binary and mixed formulations are developed for the treatment of the optimization problems. Designs are generated for the following novel objectives: (1) maximum attenuation of time harmonic waves, (2) maximum isolation of general broadband pulses, and (3) filtering signals at predetermined frequency windows. The saturation of performance with the number of unit-cell layers is shown for the first two cases. In the filtering application, the trade-off between the simultaneous realization of passband and stopband targets is analyzed. It is shown that it is more difficult to design for passbands than it is to design for stopbands. The design approach presented has potential use in the development of vibration and shock isolation structures, sound isolation pads/partitions, and multiple band frequency filters, among other applications. Wave propagation in heterogeneous media is dispersive, i.e., a wave decomposes into multiple waves with different frequencies. In media with periodic heterogeneity, there are ranges of frequencies, known as stopbands or band gaps, over which all incident waves are effectively attenuated. This attenuation phenomenon is attributed to a mechanism of destructive interferences within the scattered wave field. In complementary frequency bands, passbands, constructive interferences dominate and waves effectively propagate through the medium. This frequency-banded dynamic response has triggered much interest in periodic materials, especially since these materials have practical applications across multiple disciplines (e.g., photonic crystals are used to control the propagation of electromagnetic waves, and phononic materials, or sonic crystals, are used to control the motion of acoustic and elastic waves). The reader is referred to an extensive review article on this broad field (Kushwaha 1996) . Of increasing interest is the design of periodic materials for desired wave dispersion characteristics, which, in turn, provides a means for passive control of the wave fields in the materials in accordance to the requirements of the given application. A review article on the inverse problem has recently been published (Burger et al. 2004) .. From a practical perspective, it has been shown that as long as a sufficient number of cells are available (usually around three to four are required), bounded structures formed from periodic materials can exhibit similar wave attenuation characteristics to those of the periodic materials (e.g., Day et al. 1994; Cao and Qi 1995; Jensen 2003; Hussein et al. 2003 Hussein et al. , 2004b Hussein et al. , 2005 Hussein 2004) .. By controlling the materials layout and the ratio of their properties within a unit cell, a periodic composite could be designed to have a desired frequency band structure (the size and location of stopbands). In this work, bimaterial layered (one-dimensional) composites are considered where the unit cell consists of sublayers of alternating material types with different thicknesses. The frequency band structure can therefore be controlled by varying the configuration of the layers. Three case studies are considered:. Case I Creation of a stopband for maximized wave atten-uation at a specified frequency Case II Maximization of the percentage of stopbands within a specified large frequency range for minimum wave transmissibility Case III Creation of multiple stopbands/passbands at specified frequency ranges. The designed materials could be used for isolating vibrations induced by single (case I) or multiple (case III) harmonic excitation. Material designs for case II could find application for shock isolation (defining a shock load as one that consists of a transient broadband pulse) and sound isolation in which the frequency spectrum is typically broad.. In all the considered cases, the decision variables are (1) the number of layers in the unit cell and (2) the thickness of each of the layers. The maximum number of unit-cell layers and the range of admissible layer thicknesses are important quantities from both the dynamic performance and practical points of view. Increasing these quantities provides more precise control of the frequency band structure, but it entails higher manufacturing costs. For practical considerations, there are limits (constraints) on (1) the minimum layer thickness and (2) the total cell length (the cell length is conveniently assigned with the value of unity).. Cases I and II are posed as multiobjective optimization problems where the number of cell layers and their thicknesses are optimized for maximum wave attenuation capacity with minimum number of layers. For case II, an additional study is carried out where the frequency content of the excitation load that is to be isolated is incorporated as a weighting function. This forces the locations of the generated band gaps to be biased towards the high-magnitude frequencies of the excitation load. Two formulations of the decision variables are developed, each with its own advantages (as will emerge). The first is a mixed-integer programming, where the number of layers is represented by an integer variable, and the layer thicknesses are represented as continuous variables. The second formulation is a zero-one integer programming, where the unit cell is divided into a fixed number of imaginary divisions, and the material type of each division is represented by the binary variables. In this manner, the binary variables control both the number and the thicknesses of the actual layers. Solutions to both formulations are attempted using an evolutionary optimization technique. A multiobjective genetic algorithm, namely, the Nondominated Sorting Genetic Algorithm (NSGA-II; Deb et al. 2000 , Deb 2001 , is employed. NSGA-II is a heuristic algorithm capable of efficiently generating quasi-Pareto optimal (noninferior) solutions.. For case III, only the binary formulation is followed, and the two previous competing objectives are replaced with the ones that are related solely to dynamic performance (namely, achievement of attenuation at specified frequency ranges and propagation at complementary frequency ranges). The multiobjective genetic algorithm described above is also used for case III.. A similar design problem to that of case I has been pursued in the contexts of electromagnetic Dobson 1999, 2000) and elastodynamic (Sigmund and Jensen 2003) wave propagation. In all these studies, two-dimensional periodic unit cells were optimized to produce a band gap (between two selected branches) with a maximum width and centered at a given frequency or at a minimum frequency. Local search optimization techniques were used. However, optimization problems on frequency band structures tend to be highly multimodal, and therefore, it is possible for a local search to converge to local optima. In this paper, the technique of genetic algorithms is chosen because it has the advantage that it simultaneously evolves multiple designs and eventually converges to near-global optimality.. In a previous work (Hussein et al. 2002) dealing with longitudinal wave propagation in layered periodic materials, cases I and II were pursued (as single-objective optimization problems). For a given maximum limit on the number of layers, the optimal design for each case was found by exhaustively searching over all possible cell configurations under the restriction that layers only could have thicknesses that are multiples of a minimum size. While the exhaustive search guarantees finding a global optimum, it is prohibitively expensive because the number of possible combinations of layer thicknesses increases exponentially with the number of layers. The adoption of genetic algorithms in this study efficiently extends the design space and therefore allows for better designs to be realized (preliminary results are presented in Hussein et al. 2004a) .. The new features of the present study are summarized as follows: (1) multiobjective optimization where a dynamic performance measure trades off with a manufacturing costrelated objective (cases I and II) or with another dynamic performance objective (case III); (2) employment of an objective function for the dynamic performance in case I that focuses solely on the attenuation strength as opposed to the width and location of the band gap; (3) design of band-gap materials for shock isolation (case II); (4) weighted band structure optimization where the frequency content of the excitation is incorporated in the formulation (second part of case II); (5) design for multiple stopbands and passbands, i.e., high-order filters (case III); and (6) development, and comparison, of a mixed formulation and a binary formulation for optimizing layered band-gap materials.. The rest of the paper is organized as follows. Section 2.1 describes the mathematical formulation of a transfer matrix method for computing frequency spectra (i.e., frequency vs wave number dispersion curves) for linear elastic periodic materials, and in Section 2.2, the dispersive response of a corresponding finite periodic structure (undamped and damped) is considered. In Section 3, the two formulations of the cell design problem are presented along with a description of the employed multiobjective genetic algorithm and the implementation techniques. Section 4 presents the description and results of the three case studies. A summary is provided and conclusions are drawn in Section 5.. 2 Dispersive wave motion in periodic layered materials and structures In this study, a multiobjective genetic algorithm was used for the design of periodic layered materials for desired frequency band structure (size and location of stopbands/passbands within the medium's frequency spectrum). The following three case studies were considered-(1) case I: maximizing wave attenuation capacity at a single specified frequency; (2) case II: maximizing the percentage of stopbands within a specified large frequency range, with and without a superimposed weight function to account for the frequency content of the pulse to be isolated; and (3) case III: synthesizing multiple stopbands/passbands at specified frequency ranges. The first and third cases apply to the problem of vibration isolation (or filtering) under single and multiple harmonic excitation, respectively, whereas the second case applies to the problems of shock and sound (or any general transient pulse) isolation.. Two formulations were developed, for each of cases I and II, namely, mixed-integer programming (mixed formulation) and zero-one integer programming (binary formulation). The formulations were implemented on example problems. The Pareto plots for both sets of results indicated that an increase in the number of cell layers improves the wave attenuation performance. Furthermore, better unit-cell designs were found compared to those previously reported (Hussein et al. 2002) . The results also show that the relevant measure of wave attenuation saturated at approximately 12 layers for periodic materials designed to stop a time harmonic wave and approximately 8 layers for isolation of transient pulses spanning a wide frequency range. The saturation is attributed to the existence of limits on the ratio of wavelength to the minimum characteristic length scale in the unit cell, above which the medium is nondispersive. The designed unit cells in case I had an attenuation strength as high as ξ imag ≈ 8.3, and in case II, a weighted transmissibility as low asT p ≈ 8%. In case III (implemented only using the binary formulation), it was shown that unit cells can be tailored to exhibit multiple stopbands/passbands at specified frequency ranges, but with less precision for targeted passbands.. The presented design approach suggests remarkable promise for generating periodic materials that could be used for forming bounded structures with advanced vibration, shock/sound isolation, or filtering characteristics. The results also motivate extending this approach to multidimensional structures, which is the topic of future research. 1 19 2 30 1 41 9 9 1 20 1 31 6 42 4 10 1 21 1 32 1 43 1 11 1 22 2 33 1 44 6 Design B 1 2 14 1 27 1 40 1 2 1 15 2 28 1 41 1 3 5 16 3 29 1 42 2 4 2 17 2 30 1 43 1 5 1 18 1 31 1 44 2 6 6 19 3 32 1 45 8 7 2 20 2 33 5 46 2 8 2 21 1 34 2 47 1 9 2 22 3 35 1 48 4 10 2 23 1 36 3 49 1 11 2 24 1 37 1 50 2 12 1 25 1 38 1 51 1 13 1 26 1 39 1 52 3

O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O