Managing contextual preferences To handle the overwhelming amount of information currently available, personalization systems allow users to specify through preferences which pieces of data interest them. Most often, users have different preferences depending on context. In this paper, we introduce a model for expressing such contextual preferences. Context is modeled using a set of hierarchical attributes, thus allowing context specification at various levels of detail. We formulate the context resolution problem as the problem of selecting appropriate preferences based on context for personalizing a query. We also propose algorithms for context resolution based on data structures that index preferences by exploiting the hierarchical nature of the context attributes. Finally, we evaluate our approach from two perspectives: usability and performance. Usability evaluates the overheads imposed on users for specifying context-dependent preferences, as well as their satisfaction from the quality of the results. Our performance results focus on the context resolution using the proposed indexes. Personalized information delivery aims at addressing the explosion of the amount of data currently available to an increasingly wider spectrum of users. Instead of overwhelming the users with all available data, personalization systems provide users with only the data that is of interest to them. Preferences have been used as a means to address this challenge. To this end, a variety of preference models have been proposed; most of which follow either a qualitative or a quantitative approach. With the qualitative approach (such as the work in [1, 2] ), preferences between two pieces of data are specified directly, typically using binary preference relations. For instance, using a qualitative model, users may explicitly state that they prefer visiting archaeological sites than science museums. With the quantitative approach (e.g., [3] [4] [5] ), users employ scoring functions that associate a numerical score with specific pieces of data to indicate their interest in them. For instance, a preference in archaeological sites may be expressed by assigning high scores to such places.. However, most often users have different preferences under different circumstances. For instance, the current weather conditions may influence the place one wants to visit. For example, when it rains, a museum may be preferred over an open-air archaeological site. Context is a general term used in several domains, such as in machine learning and knowledge acquisition [37, 39] . Our focus here is on how context can be used in conjunction with relational databases to personalize the results of queries. In this respect, we consider as context any information that can be used to characterize the situations of an entity, where an entity is a person, place, or object that is relevant to the interaction between a user and an application [6, 7] . Common types of context include the computing context (e.g., network connectivity, nearby resources), the user context (e.g., profile, location), the physical context (e.g., noise levels, temperature) and time [8, 9] .. In this paper, we propose enhancing preferences with context-related information. Preferences express user interest on specific pieces of information stored in a relational database. There has been a variety of context models [40] . We follow a data-centric approach by representing context as a set of context parameters that take values from multi-level domains. These parameters capture information that is not part of the database, such as the user location or the current weather. A specific context state or situation corresponds to an assignment of values to context parameters. By allowing context parameters to take values from hierarchical domains, different levels of abstraction for the captured context data are introduced. For instance, the context parameter user location may take values from a city, country or continent domain. Preferences are enhanced with context descriptors that specify the context states under which they hold with varying levels of detail.. Each database query is also associated with one or more context states through context descriptors. The context state of a query may, for example, be the current state at the time of its submission. Furthermore, a query may be explicitly enhanced with context descriptors to allow exploratory queries about hypothetical context states. A central problem that we address in this paper is preference selection, that is, given a set of preferences and a query, determining which of the preferences are the most relevant to the query. We focus on context aspects and consider as relevant those preferences whose context states are related to those of the query. We call context resolution the problem of selecting preferences based on context. We consider that the context state of a preference is related to a query context state, if it is the same or more general than the query context state. This is captured through a cover relation defined over context states that relates context states expressed with different levels of detail. For instance, with cover, we relate a context state in which location is expressed at the level of country with a context state in which location is expressed at the level of continent. We also propose a number of distance metrics that capture similarity among context states. This allows selecting a smaller number of the qualifying preferences thus controlling the degree of personalization.. We introduce algorithms for context resolution that build upon two data structures, namely the preference graph and the profile tree, that index preferences based on their associated context states. The preference graph explores the partial order of context states induced by the cover relation to organize them in some form of a lattice. A top-down traversal of the graph supports an incremental specialization of a given context state, whereas a bottom-up traversal an incremental relaxation. The profile tree offers a space-efficient representation of context states by taking advantage of the co-occurrence of context values in preferences. It supports exact matches of context states very efficiently through a single root-to-leaf traversal.. Our focus is on managing context for preferences, i.e., expressing, storing and indexing contextual preferences. In general, preferences may be collected using various ways. Preferences may be provided explicitly by the users or constructed automatically, for instance, based on the past behavior of the same or similar users. Such methods for the automatic construction of preferences have been the focus of much current researches (e.g., [10] ) and are beyond the scope of this paper. A practical way to create profiles that we have used in our experiments is to assemble a number of default profiles and then ask the users to update them appropriately.. Note that, in this paper, we take a system or designer point of view, in that, our aim is managing context efficiently. Another important aspect is to take the user point of view, for example, by expanding his interaction with the system, acquiring user feedback and supporting incremental adaptation.. We have evaluated our approach along two perspectives: usability and performance. Our usability experiments consider the overhead imposed on the users for specifying context-dependent preferences versus the quality of the personalization thus achieved. We used two databases of different sizes. The sizes of the database have two important implications for usability. First, they affect the number of preferences. Then, and most importantly, they require different methods for evaluating the quality of results. Our performance experiments focus on our context resolution algorithms that employ the proposed data structures to index preferences for improving response time and storage overheads.. In a nutshell, in this paper, we propose a model for annotating preferences with contextual information; our hierarchical model of context allows expressing contextual preferences at various levels of detail;. formulate the problem of context resolution as the problem of selecting appropriate preferences for personalizing a query based on context; present data structures and algorithms for implementing context resolution and evaluate our approach in terms of both usability and performance.. The rest of this paper is structured as follows. In Section 2, we present our context and preference model, while in Section 3, we formulate the context resolution problem. In Section 4, we introduce data structures used to index contextual preferences and algorithms for context resolution. Sections 5 and 6 present our usability and performance evaluation results, respectively. Section 7 describes related work and finally, Section 8 concludes the paper with a summary of our contributions. The focus of this paper is on annotating database preferences with contextual information. Context is modeled using a set of context parameters that take values from hierarchical domains, thus, allowing different levels of abstraction for the captured context data. A context state corresponds to an assignment of values to each of the context parameters from its corresponding domain. Database preferences are augmented with context descriptors that specify the context states under which a preference holds. Similarly, each query is related with a set of context states. We consider the problem of identifying those preferences whose context states (as specified by their context descriptors) are the most similar to that of a given query. We call this problem context resolution. To realize context resolution, we propose two data structures, namely the preference graph and the profile tree, which allow for a compact representation of the contextdependent preferences.. To evaluate the usefulness of our model, we have performed two usability studies. Our studies have showed that annotating preferences with context improves the quality of the retrieved results considerably. The burden of having to specify contextual preferences is reasonable and can be reduced by providing users with default preferences that they can edit. We have also performed a set of experiments to evaluate the performance of context resolution using both real and synthetic datasets. The proposed data structures were shown to improve both the storage and the processing overheads. In general, the profile tree is more space-efficient than the preference graph. It also clearly outperforms the preference graph in the case of exact matches. The main advantage of the preference graph is the possibility for an incremental refinement of a context state. In particular, at each step of the resolution algorithm, we get a state that is closer to that of the query. This is not possible with the profile tree.. There are many directions for future work. One is to extend our model so as to support non-strict hierarchies. Although the cover relation is still valid in this case, this will require a revision of our definitions of distances between context states and possibly small modifications of the proposed data structures. Another direction for future work is preference application. In our current work, we assume that preferences are applied after the execution of a query to rank its result. Re-writing the query to incorporate contextual preferences is a promising alternative. In this paper, we use context to confine database querying by selecting as results the best matching tuples based on user preferences that depend on context. We first review research on preferences, then on context and finally, on contextual preferences.. The research literature on preferences is extensive. In particular, in the context of database queries, there are Cell accesses for finding preferences related to queries using the enhanced profile tree (denoted with tree), the heuristic approach for the preference graph (denoted with graph), and when no index is used (denoted with ni). Fig. 15 . Cell accesses for finding preferences related to queries for synthetic profiles using the query tree and the query graph for synthetic profiles for (a) exact match and (b) non exact match. With p we denote the profile tree and with g the preference graph.. two different approaches for expressing preferences: a quantitative and a qualitative one. In the quantitative approach (e.g., [3, 4, 18] ), preferences are expressed indirectly by using scoring functions that associate a numeric score with every tuple of the query answer. In this work, we have adapted the general quantitative framework of Agrawal and Wimmers [3] , since it is easier for users to employ than the qualitative one. In the quantitative framework of Koutrika and Ioannidis [5, 14] , user preferences are stored as degrees of interest in atomic query elements (such as individual selection or join conditions) instead of interests in specific attribute values. Our approach can be generalized for this framework as well, by making the degree of interest for each atomic query element depends on context. In the qualitative approach (for example, [1, 2, 19] ), the preferences between tuples in the answer to a query are specified directly, typically using binary preference relations. This framework can also be readily extended to include context. There has been much work on developing a variety of context infrastructures and context-aware middleware and applications (such as the Context Toolkit [20] and the Dartmouth Solar System [21] ). However, although there is much research on location-aware query processing in the area of spatio-temporal databases, integrating other forms of context in query processing is less explored. In the context-aware query processing framework of Feng et al. [22] , there is no notion of preferences, instead context parameters are treated as normal attributes of relations. Recently, context has been used in information filtering to define context-aware filters which are filters that have attributes whose values change frequently [23] .. Storing context data using data cubes, called context cubes, is proposed in [24] for developing context-aware applications that use archive sensor data. In this work, data cubes are used to store historical context data and to extract interesting knowledge from large collections of context data. The Context Relational Model (CR) introduced in [25] is an extended relational model that allows attributes to exist under some contexts or to have different values under different contexts. CR treats context as a first-class citizen at the level of data models, whereas in our approach, we use the traditional relational model to capture context as well as context-dependent preferences. Context as a set of dimensions (e.g., context parameters) is also considered in [26] where the problem of representing context-dependent semistructured data is studied, while in [27] , an overview of a Multidimensional Query Language is given, that may be used to express context-driven queries. A context model is also deployed in [28] for enhancing web service discovery with contextual parameters. In [29] , the current contextual state of a system is represented as a multidimensional subspace within or near other situation subspaces.. Extending the typical recommendation systems beyond the two dimensions of users and items to include further contextual information is studied in [30] . Contextual information is modeled using a number of parameters with hierarchical structure [31, 30] . Using context is shown to improve the prediction of customer behavior.. There has been some recent work on contextual preferences. In [32] , authors consider ranking database results based on contextual qualitative preferences. Context parameters are part of the database schema, while in our approach, context parameters are considered to be outside the database. Furthermore, our context parameters have a hierarchical nature that we explore in context resolution. A knowledge-based context-aware query preference model is proposed in [33] , where context parameters are treated as normal attributes of relations. Contextual preferences, called situated preferences, are also discussed in [34] . In this approach, a context state is represented as a situation. Situations are uniquely linked through an N:M relationship with preferences expressed using the qualitative approach. Again, the context model is not hierarchical.. Finally, note that a preliminary abridged version of this paper appears in [35] . The preference graph, computing scores, multi-state resolution, various other enhancements and most of the experiments are new here.. In other previous work [36] , we have addressed the same problem of expressing contextual preferences. However, the model used there for defining preferences includes only a single context parameter. Interest scores of preferences involving more than one context parameter are computed by a simple weighted sum of the preferences expressed by single context parameters. Here, we extend context descriptors, so that contextual preferences involve more than one context parameter and also, associate context with queries. Context resolution is also new here. In [38] , we focus on the efficient execution of contextual queries. In particular, we are interested in creating groups of similar preferences for which we precompute rankings of database tuples.

O O B 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 B O O O O O O O O O O O B B 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 O B 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 B 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 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 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 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 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 B 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 B O O O B 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 B O O O B O O O O O O O O O O O O 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Use of the University of Minnesota Biocatalysis/Biodegradation Database for study of microbial degradation Microorganisms are ubiquitous on earth and have diverse metabolic transformative capabilities important for environmental biodegradation of chemicals that helps maintain ecosystem and human health. Microbial biodegradative metabolism is the main focus of the University of Minnesota Biocatalysis/Biodegradation Database (UM-BBD). UM-BBD data has also been used to develop a computational metabolic pathway prediction system that can be applied to chemicals for which biodegradation data is currently lacking. The UM-Pathway Prediction System (UM-PPS) relies on metabolic rules that are based on organic functional groups and predicts plausible biodegradative metabolism. The predictions are useful to environmental chemists that look for metabolic intermediates, for regulators looking for potential toxic products, for microbiologists seeking to understand microbial biodegradation, and others with a wide-range of interests. Microbial degradation here refers to the microbial conversion of organic compounds, often those of that negatively impact human health, to less toxic or more useful forms, in the environment or the laboratory. Knowledge of the genes, enzymes, and pathways involved in this process help us understand environmental processes, obtain useful products, engineer remediation of polluted environments, and predict the fate of chemicals in the environment. This minireview focuses on the past ten years of research in this field; for earlier work, see [1] .. Hundreds of thousands of natural products are known; millions of compounds have been synthesized by organic chemists. There is no end in sight to chemical synthesis. The number of stable organic compounds that are less than 500 molecular weight are estimated to range from 10 20 to 10 200 [2] . Of the chemicals currently sythesized, almost 100,000 are used commercially. Most naturally-occurring molecules, and many of the synthetic ones, are transformed by at least some microbe, somewhere on the earth. How does nature handle such a vast range of compounds?. Life has likely existed on Earth for at least 3.6 billion years, during which time living things have acquired the ability to catabolize almost every available carbon source. It has been estimated that there are 5 × 10 30 prokaryotes on Earth [3] and every free-living prokaryote typically contain 1,000 -10,000 genes [4] , making for an enzyme diversity of approximately 10 34 . While many of those 10 32 enzymes are isofunctional, there is still enormous untapped metabolic diversity in the microbial world. For example, there are a class of antibiotics produced by Streptomyces species that contain an azoxy functional group. Until recently [5] , there was no information about the enzymes that biosynthesize the azoxy group, and information is still lacking on the catabolism of azoxy groups. There are many examples in the literature of chemical groups identified in natural products for which metabolic information is lacking [1] . Since the structures have been rigorously identified, and the compounds derive from biological sources, novel biosynthetic enzymes must exist. Moreover, since these natural product compounds are not observed to accumulate in the biosphere, it is likely that enzymes participate in their biodegradation.. The range of microbial biodegradative metabolism is broad and, based on the discussion above, expandable almost infinitely. To more systematically organize and display this information reported in the scientific literature, the University of Minnesota Biocatalysis/Biodegradation Database (UM-BBD) [6, 7] began in February, 1995. For 16 years, the UM-BBD has served as a repository for the growing body of knowledge on microbial biodegradative metabolism. KEGG has also expanded to include a substantial amount of biodegradation. However, the vast majority of the millions of known chemicals have not been evaulated for their biodegradation. Computational prediction can help address that problem and the UM-PPS and PathPred are designed to do that. The predictions are useful to government regulatories, industries producing chemicals, and scientists conducting biodegradation research.

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SIFT-Based Non-blind Watermarking Robust to Non-linear Geometrical Distortions This paper presents a non-blind watermarking technique that is robust to non-linear geometric distortion attacks. This is one of the most challenging problems for copyright protection of digital content because it is difficult to estimate the distortion parameters for the embedded blocks. In our proposed scheme, the location of the blocks are recorded by the translation parameters from multiple Scale Invariant Feature Transform (SIFT) feature points. This method is based on two assumptions: SIFT features are robust to non-linear geometric distortion and even such nonlinear distortion can be regarded as "linear" distortion in local regions. We conducted experiments using 149,800 images (7 standard images and 100 images downloaded from Flickr, 10 different messages, 10 different embedding block patterns, and 14 attacks). The results show that the watermark detection performance is drastically improved, while the baseline method can achieve only chance level accuracy. key words: watermarking, scale invariant feature transform (SIFT), nonlinear geometric distortion attacks Due to the advancement in capturing techniques for images and video [1] - [5] , a variety of pirating methods for digital content have become possible. Therefore, digital watermarking technologies for protecting the content holders' rights are becoming important [6] - [9] .. There are many choices in digital watermarking, such as blind or non-blind, robust or fragile, reversible or inseparable, and public or private [6] - [9] . The main scope of this paper is robust non-blind watermarking aimed at copy detection, copy source detection, etc. Namely, we assume that the copyright holders know what message they embedded, and how/where the messages are embedded. It is not strictly necessary to have the original content but the copyright holders need to have all the information required to recover the embedded message. Such information is secret to the users. And we want to make the embedded message as robust to the attacks as possible.. A lot of watermarking algorithms that are robust to "linear" geometric distortions (i.e., affine transforms) have been reported [10] - [15] . In [10] , watermark information was embedded in discrete Fourier transform coefficients. A Fourier transform based method with log-polar mapping was presented in [11] . In [12] , feature extraction using Harris corners and data embedding with Delaunay tessellation was employed. In [13] , a projective transform was proposed. In [14] , a SIFT-based watermarking scheme with polar mapping was developed. Our previous work can also handle affine transform [16] . For further discussion of linear geometric distortion attacks, please refer to [12] . However, these algorithms do not consider non-linear geometric distortions. Taherinia and Jamzad [17] demonstrated that image retargeting (non-linear image resizing) such as seam carving [1] can easily destroy the watermark. In fact, not only the image retargeting but also other nonlinear geometric distortions can easily make it impossible to read out the embedded message without degrading the quality of the attacked image. Comparing the attacked content with the original content does not solve the problem because it is difficult to estimate how the content is distorted. In addition, using the original content is not practical from the viewpoints of storage cost, computational efficiency, processing accuracy, etc.. To the best of our knowledge, our previous paper [18] was the first trial that tackled this non-linear image distortion problem. [18] was based on the geometrically invariant object-based watermarking [16] . In [16] , the protected content within the attacked content was automatically detected using the SIFT algorithm [19] . The message was embedded in the discrete cosine transform (DCT) coefficients of randomly selected 16×16 blocks. The linearly distorted content was restored to its original size and shape by a combination of the SIFT and random sample consensus (RANSAC) algorithms [20] . The robustness to conventional attacks, such as lossy compression, image filtering, affine transform, and replacement has already been presented in [16] . However, as shown in Sect. 3, [16] is also sensitive to non-linear image distortion attacks.. Despite the content being non-linearly geometrically distorted and difficult to recover the original size and shape, it can be assumed that any kind of distortion is regarded as "linear" distortion in a small local area. The idea is similar to modeling non-linear electronic circuits as small signal equivalent circuits and analyzing it as linear circuits [21] . Based on this assumption, in the embedding phase of this paper, the positions of the message-embedded blocks are represented as the relative position from multiple SIFT feature points near the blocks. Namely, multiple SIFT feature points around the block are used as reference points to identify the location of the block. In the detection phase, we restore the local area of the content to its original size and shape using [20] . Then, the locations of the embedded Copyright c 2013 The Institute of Electronics, Information and Communication Engineers blocks are calculated by averaging the addresses pointed to from the SIFT features.. Although some reference SIFT feature points are sometimes not found or their locations are distorted by the attacks, the embedded watermark information can be successfully extracted by using multiple reference points. Clearly, our proposed algorithm is also robust to affine transformation or other conventional attacks. Experimental results demonstrate that the proposed algorithm is highly robust to non-linear geometrical distortion attacks such as waving, imploding, swirling, and seam carving [1] .. As mentioned above, the core algorithm is already presented in [18] . The contribution of this paper is extensive experiments with 100 images in addition to the 7 images used in [18] . The results show the validity and generality of our algorithm. In addition, detailed investigation for each attack and each image is also given.. The remainder of this paper is organized as follows. In Sect. 2, the proposed algorithm is described. Then, experimental results are demonstrated in Sect. 3, followed by conclusions in Sect. 4. In this paper, we have presented an object-based non-blind watermarking technology that is robust to non-linear geometrical distortion attacks. By memorizing the location of the embedded blocks using SIFT feature points as reference, the watermark detection was made very robust. The validity of the proposed algorithm was demonstrated by a variety of non-linear geometrical distortion attacks such as waving, imploding, swirling, and seam carving. The percentage of detected bits was very high while that of the state-of-the-art approach yielded only a chance level detection rate. Experiments were conducted using seven standard grayscale images (in Fig. 4 ) whose size was 512 × 512 and 100 Flickr images. The Flickr images were the top 100 images in the "interesting" ranking † whose licenses were creative commons. They were resized to be within the 640 × 480 bounding box and converted to gray-scale images. The embedded message was a 64-bit random binary sequence. In the experiments, 10 different 64-bit binary patterns were used and 10 different block patterns for embedding the watermark data were generated. Then, 14 different attacks were applied. Therefore, the total number of the tested images was 149,800 (107 × 10 × 10 × 14). The mean peak signal-to-noise ratio of the watermarked images was 46.5 dB, which is unnoticeable by human perception.. The performance of the proposed algorithm was evaluated in terms of the number of bits of correctly read out before the error correction. And in this paper, we only focus on the robustness to non-linear geometrical attacks. For the performance to conventional attacks such as affine transform, JPEG compression, filtering, rotation, resizing, noise, and so on, please refer to [16] .. The non-linear geometrical distortion attacks employed in this paper are shown in Fig. 5 , namely, waving, imploding, swirling, and seam carving. Figures 5 (b) -(m) were generated using ImageMagick † † . The parameters are also described in the figure (for the explanation of the parameters, please refer to the ImageMagick website). The seam carving is based on [1] . The white grids are shown only for facilitating readers to understand the kind and the strength of the attacks. Such white lines do not exist in the original images. Even without detecting the proper blocks, it is possible to "extract" a certain message. However, the probability of such extracted message coinciding with the messages in the database is quite low. The cumulative probability of coinciding with a certain number of bits by a random guess is illustrated in Fig. 6 . For instance, the probability of correctly detecting more than 50 bits (78%) out of 64 bits by chance is about 10 −6 . The probability gets much lower if the length of the messages is longer than 64 bits.. The effect of the number of reference points for each block is shown in Fig. 7 . In Fig. 7 , the mean detection rates for Lena and Baboon images are shown. Each detection rate was calculated by averaging the detection accuracy for 10 different messages, 10 different block patterns, and 14 different non-linear geometric distortion attacks (i.e., 1,400 images). It is shown that the detection accuracy is almost the same for 20 reference points and less. The accuracy then degrades slightly as the number of reference points increases. This is because the additional reference points are farther from the embedded block and the local linearity cannot be assumed any more. If the number of reference points (10) 46 (31) 50 (50) 62 (41) 58 (33) 61 (30) 62 (51) 60 (49) 57 (41) Swirl (15) 43 (33) 48 (35) 61 (41) 52 (32) 59 (29) 61 (44) 55 (47) 54 (37) Swirl (20) 42 (35) Wave (5 × 256) 78% (44%) 70% (52%) 95% (52%) 89% (47%) 92% (44%) 95% (47%) 92% (52%) 87% (48%) Wave (10 × 256) 56% (50%) 63% (48%) 86% (52%) 77% (52%) 83% (47%) 84% (48%) 77% (50%) 75% (50%) Wave (20 × 256) 50% (55%) 52% (48%) 66% (50%) 66% (48%) 66% (50%) 67% (50%) 66% (53%) 66% (53%) Wave (5 × 512) 80% (64%) 67% (38%) 98% (48%) 94% (67%) 97% (61%) 97% (47%) 97% (48%) 90% (53%) Wave (10 × 512) 73% (53%) 61% (48%) 94% (48%) 88% (55%) 92% (52%) 92% (44%) 91% (45%) 84% (49%) Wave (20 × 512) 66% (47%) 56% (48%) 84% (50%) 80% (44%) 84% (48%) 78% (47%) 78% (47%) 75% (47%) Implode (0.05) 91% (50%) 80% (72%) 98% (80%) 97% (50%) 98% (77%) 98% (88%) 97% (83%) 94% (71%) Implode (0.1) 64% (38%) 77% (47%) 97% (80%) 91% (44%) 95% (55%) 97% (83%) 95% (78%) 88% (61%) Implode (0.2) 53% (50%) 77% (86%) 94% (75%) 78% (50%) 88% (47%) 94% (78%) 84% (75%) 87% (66%) Swirl (10) 72% (48%) 78% (78%) 97% (64%) 91% (52%) 95% (47%) 97% (80%) 94% (77%) 89% (64%) Swirl (15) 67% (52%) 75% (55%) 95% (64%) 81% (50%) 92% (45%) 95% (69%) 86% (73%) 84% (64%) Swirl (20) 66% (55%) 59% (52%) 92% (63%) 77% (48%) 86% (48%) 92% (69%) 84% (73%) 79% (58%) Seam carving (−20× − 61) 92% (97%) 63% (56%) 86% (47%) 77% (55%) 73% (50%) 80% (50%) 84% (50%) 79% (58%) Seam carving (−61× − 20) 88% (94%) 44% (63%) 83% (50%) 75% (53%) 75% (50%) 84% (48%) 75% (48%) 75% (58%) Average 71% (57%) 66% (56%) 90% (59%) 83% (51%) 89% (51%) 89% (60%) 86% (61%) 82% (56%) is small, the risk of failing to detect any of them becomes higher. On the other hand, if the number of reference points is large, it would result in larger database size. Therefore, the number of reference points is set to 10 in the following experiments.

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


An Automatic and Robust Algorithm of Reestablishment of Digital Dental Occlusion Abstract-In the field of craniomaxillofacial (CMF) surgery, surgical planning can be performed on composite 3-D models that are generated by merging a computerized tomography scan with digital dental models. Digital dental models can be generated by scanning the surfaces of plaster dental models or dental impressions with a high-resolution laser scanner. During the planning process, one of the essential steps is to reestablish the dental occlusion. Unfortunately, this task is time-consuming and often inaccurate. This paper presents a new approach to automatically and efficiently reestablish dental occlusion. It includes two steps. The first step is to initially position the models based on dental curves and a point matching technique. The second step is to reposition the models to the final desired occlusion based on iterative surface-based minimum distance mapping with collision constraints. With linearization of rotation matrix, the alignment is modeled by solving quadratic programming. The simulation was completed on 12 sets of digital dental models. Two sets of dental models were partially edentulous, and another two sets have first premolar extractions for orthodontic treatment. Two validation methods were applied to the articulated models. The results show that using our method, the dental models can be successfully articulated with a small degree of deviations from the occlusion achieved with the gold-standard method. We develop a two-step approach to automatically and digitally articulate the maxillary and mandibular teeth. The first step is the initial alignment that aligns the mandibular dental model relatively closer to the maxillary model in an approximate MI.. Two set of feature points of dental curves are extracted. One is the feature points for the curve of central groove and pits of the maxillary dental model, and the other is the feature points for the curve of the cusps and incisal edges of the mandibular dental model. By matching these two set of feature points using point matching algorithm, an initial occlusion can be achieved by intentionally ignoring any possible collision between digital dental models. The second step is the final alignment. We align and fine-tune the initially-aligned models to their final occlusion that is collision-free using our ISMDM algorithm. Two controlling mechanisms are designed. The first is the collision constraints to detect and prevent the penetration between the maxillary and the mandibular dental models. The second is the minimization of average distance of surface between the models in order to articulate the models. These two mechanisms are incorporated into an optimization problem and can be solved by quadratic programming. Our approach is validated by using 12 sets of the dental models. Using our approach, the maxillary and mandibular models can be successfully articulated. There is only a small degree of deviation between the digitally articulated occlusion established with our approach and the scanned occlusion established using the current gold standard. This small degree of deviation does not have clinical significance. We have developed an automatic and robust approach to digitally articulate dental models. This approach consists of two major steps. The first step is the initial alignment, in which the point match algorithm is used to match the feature points of dental curves in order to bring the models relatively close to each other. The second step is the final alignment, in which we develop the ISMDM algorithm to minimize the average distance of surfaces of the models in order to articulate the maxillary and mandibular models to the MI without overlapping each other. This approach has been validated using 12 pairs of the dental models. The results of validation shows the models are successfully articulated with a small degree of deviation. The accurate results can be attributed to the intuitive assumption that maximizing contact areas of upper and lower teeth is equivalent to minimizing the average distance defined in (8) .. The results of the validation show the robustness of our approach. First, the initial alignment algorithm can bring the models to proper positions even before performing the ISMDM. Shown in Tables III and IV, the models aligned by the initial alignment algorithm are close enough to successfully complete final articulation by the ISMDM. Second, each mandibular model is docked to a final occlusion since the average distance of surface converges at (illustrated in Fig. 10 ) using our ISMDM algorithm. Shown in Tables III and IV , the deviations are small enough to satisfy clinical requirements. They demonstrate the feasibility of our approach towards fully automatic digital dental articulation. In addition, our validation includes the models with special conditions: partial edentulous dentition and first premolar extraction due to orthodontic treatment. We initially expect these models may result in a larger deviation. However, even with the models with special conditions, the models in experimental group still achieve a same small degree of deviation. This further proves the robustness of our approach. Of the note a small portion of results of the -axis (under "ISMDM" in Table III) shows the standard deviations of Point and are slightly larger (close to 0.5 mm) than the others. This contributes to a larger range of angular deviation on the axial plane (under "ISMDM" in Table IV ). During the dental articulation, the mandibular models have more rotational freedom on the axial plane in comparison to the sagittal and coronal planes. A possible solution to reduce the rotational freedom on the axial plane is to add more constraints, i.e., coincidence between maxillary and mandibular dental midlines.. Our initial alignment algorithm plays an important role in reducing the number of executions of nearest point searching of ISMDM. The high-quality dataset of digital dental models may drastically increase the computational time in ISMDM since the calculation of nearest point searching is tremendous. Our initial alignment algorithm is designed to bring the high-resolution digital dental models used in our clinic to an approximate MI position and orientation, without considering whether there is a collision between the upper and the lower teeth. The advantage of using initial alignment is to tremendously increase the computational speed of convergence in final alignment using ISMDM algorithm and significantly reduce the computational time in planning the CMF surgeries. As illustrated in Fig. 10 , all the models can be quickly articulated in only 30 executions of iteration in ISMDM without intensively searching for the position at MI. In our simulation, the computational time of both initial alignment algorithm and the ISMDM for each set of the models is only several minutes.. Our final alignment is to bring the dental models from the position achieved by initial alignment to their final occlusion at the MI and free of collision using our ISMDM algorithm. In this algorithm, the convergence in average distance of surface between the models can be used to decide whether the models have been articulated. The correspondence of vertices in upper and lower teeth and linear constraints are dynamically updated in each iteration, resulting in different parameters of quadratic programming in (19) . In this algorithm, the optimal transformation is solved by quadratic programming in each iteration. When the maxillary and mandibular models are getting closer to be articulated, the optimal transformation approximates a null since these linear constraints prevent the models from overlap and stop the models. Once this is achieved, the null transformation will not further update the correspondence and constraints in following iterations. Thus, the average distance will converge.. The final alignment should be completed without overlapping between the upper and the lower models. Another advantage of our ISMDM algorithm is that it has successfully overcome the notorious problem of uncontrollable overlap by applying linear constraints and allowable penetration depth . Each of the constraints is determined by one vertex in the upper teeth and its corresponding vertex in the lower teeth. Therefore, the number of constraints depends on the parameter and resolution of datasets. However, the models may not be able to entirely articulate if too many constraints are incorporated in quadratic programming. As we observed, an appropriate value of the parameter is approximate to the resolution of dataset. Theoretically, the penetration depth is zero, leading to no overlap of upper and lower teeth. However, since the surfaces of the digital models are slightly expanded outward [ Fig. 2(b) ] due to the process of triangulation, the articulated digital models must have little overlap at the contact areas. Therefore, the choice of the allowable penetration depth relies on the extent of overlap in the dataset. In this experiment, we set the penetration depth was 0.1 mm.. Finally, our approach is different from others. The ultimate goal of our approach is to digitally articulate dental models for patient treatment. Hiew et al. [25] used the right and posterior surfaces of the model bases to perform the dental model alignment. They first trimmed the right and posterior surfaces of the upper and lower plaster model bases so they would be perfectly in the same plane with the teeth in the correct occlusion. After the models were separately digitized, the centroids and normal vectors of these surfaces were calculated by using a -means plane detection algorithm. This initial step was to align the digital models in anteroposterior ( -axis) and transverse ( -axis) directions. The final alignment was then completed by adjusting one of the models in superoinferior ( -axis) direction. Finally, the vertical alignment was optimized by collision detection, and the transformation was applied to the lower model. However, this approach is not designed based on the occlusal criteria. Thus it is impossible to incorporate their method into the actual surgical planning procedure clinically. Zhang et al. [26] designed a two-stage occlusal analysis algorithm. In the first stage, each vertex of the teeth models is checked whether it is considered as a penetration. In the second stage, the distance of each vertex to the opposing model was calculated, and the color ranges of distance were shown on the 3-D teeth models. The color ranges are useful for manual alignment in the computer, but it still needs iterative process of collision detection and manual transformation of the models. Finally, DeLong et al. [27] utilized a "3-point alignment" method. Three pairs of contacting points on both the upper and lower teeth models were initially identified on the plaster models and then digitized onto the digital models. The points on the lower teeth were aligned using a fitting algorithm to the points on the upper teeth model, and the transformation was applied to the lower model. The established occlusion was then visually checked, and the 3-point alignment method was repeated by selecting different pairs of points until the visual outcome was satisfactory and overlap of the models is free. We had independently developed and tested this method before DeLong et al. published their results. Although this method could bring the upper and lower teeth close to MI, it is almost impossible to be certain that what is seen in the computer truly represents the best possible alignment. Since even a small deviation in the occlusion causes a significant clinical problem, this 3-point alignment may be used as an initial alignment but one should not rely on this method of dental alignment to treat real patients. Comparing to the above methods, our method is more practical and can be immediately used in the patient surgical planning process.

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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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


Dendritic action potentials connect distributed dendrodendritic microcircuits Abstract Lateral inhibition of cells surrounding an excited area is a key property of sensory systems, sharpening the preferential tuning of individual cells in the presence of closely related input signals. In the olfactory pathway, a dendrodendritic synaptic microcircuit between mitral and granule cells in the olfactory bulb has been proposed to mediate this type of interaction through granule cell inhibition of surrounding mitral cells. However, it is becoming evident that odor inputs result in broad activation of the olfactory bulb with interactions that go beyond neighboring cells. Using a realistic modeling approach we show how backpropagating action potentials in the long lateral dendrites of mitral cells, together with granule cell actions on mitral cells within narrow columns forming glomerular units, can provide a mechanism to activate strong local inhibition between arbitrarily distant mitral cells. The simulations predict a new role for the dendrodendritic synapses in the multicolumnar organization of the granule cells. This new paradigm gives insight into the functional significance of the patterns of connectivity revealed by recent viral tracing studies. Together they suggest a functional wiring of the olfactory bulb that could greatly expand the computational roles of the mitralgranule cell network. Lateral inhibition plays a central role in processing sensory information in most sensory systems. Its most obvious role is in the visual system, where it serves to enhance contrast between points of different illumination, as first shown for ganglion cells in the retina (Kuffler 1953 ) and subsequently at higher levels of visual processing. In the olfactory bulb, a combination of experimental and computational approaches identified a model of interactions between mitral and granule cells which predicted a dendrodendritic synaptic circuit mediating self and lateral inhibition of the mitral cells. This has been useful in guiding and accounting for a variety of experimental results (Rall et al. 1966; Rall and Shepherd 1968; Shepherd and Brayton 1979; Xu et al. 2003; Schoppa et al. 1998; Urban and Sakmann 2002; Egger and Urban 2006) . Yokoi et al. (1995) showed preferential tuning of mitral cells to different members of a homologous chemical series. Sharpening of the tuning by inhibition of neighboring members of the series implied a spatial center-surround organization. It was proposed that lateral inhibition, through the dendrodendritic synapses of mitral cells receiving inputs from different olfactory sensory neuron subsets (Ressler et al. 1994; Vassar et al. 1994; Mombaerts 1996) , mediates this odor refinement and contrast enhancement. Previous modeling studies have implemented this contrast phenomenon (e.g. Davison et al. 2003; Cleland and Linster 2005; Linster and Hasselmo 1997) .. The original dendrodendritic model accounts for such interactions between nearby mitral cells. However, evidence from odor maps in the glomerular layer (Xu et al. 2003; Leon and Johnson 2003; Mori et al. 2006) shows that neighboring members of a homologous chemical series activate not only clusters but also widely distributed glomeruli. This activation of widely distributed glomeruli has come to be referred to as "non-topographical", i.e. non-neighboring glomerular, odor representation (Cleland and Sethupathy 2006) . Long range connections of up to a millimeter or more are required for lateral inhibition to occur between mitral cells belonging to these distributed glomeruli.. How is the dendrodendritic microcircuit incorporated into this more widely distributed network? We analyze this question with realistic cell properties and network connectivity in order to test the hypothesis that propagating action potentials in mitral cell lateral dendrites play a critical role. We focus on a single respiratory cycle, which has been shown to be sufficient for odor recognition (Uchida and Mainen 2003 ; see also Abraham et al. 2004 ). The results provide new insights into the nature of lateral inhibition through active lateral mitral cell dendrites and the columnar organization of granule cells. They predict a new function for granule cells in providing for selective control of activity in individual mitral cell lateral dendrites with minimal effect on soma and other lateral dendrites. The results depend on the dendritic architecture and cannot be obtained with reduced or artificial networks. The model predicts new specific computational roles of granule cells in processing the odor maps for output to the cortex. The results give several new insights into the mechanism of lateral inhibition in the olfactory bulb and its possible significance for odor processing. Some of these points have been noted in the Results, and we summarize the salient ones here. All the simulations were carried out with the NEURON simulation program (Hines and Carnevale 1997, v5.8) using its variable time step feature. The model and simulation files are available for public download under the ModelDB section of the Senselab database (http:// senselab.med.yale.edu).

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


The Steiner Tree Problem with Delays: A compact formulation and reduction procedures This paper investigates the Steiner Tree Problem with Delays (STPD), a variation of the classical Steiner Tree problem that arises in multicast routing. We propose an exact solution approach that is based on a polynomial-size formulation for this challenging NP-hard problem. The LP relaxation of this formulation is enhanced through the derivation of new lifted Miller-Tucker-Zemlin subtour elimination constraints. Furthermore, we present several preprocessing techniques for both reducing the problem size and tightening the LP relaxation. Finally, we report the results of extensive computational experiments on instances with up to 1000 nodes. These results attest to the efficacy of the combination of the enhanced formulation and reduction techniques. The Steiner Tree Problem (STP) is defined on a connected undirected graph G = (V , E), where V is the set of nodes and E is the set of edges, with cost c e on each edge e ∈ E. The STP requires finding a minimum-cost tree of G that spans a subset of nodes R ⊂ V , whose elements are called terminal (or, required) nodes, making possibly use of additional nodes (so-called Steiner nodes) from S := V \ R. The STP is a very fundamental combinatorial optimization problem with a long history (see e.g., [6, 13] ). During the last two decades, this N P -hard problem has been intensely investigated and several effective exact solution strategies have been proposed so far (see e.g., [1, 16, 24] ). These research efforts are mainly motivated by the pertinence of the STP to a wide range of complex network design applications. Recently, and prompted by the dramatic growth of the telecommunication sector, several new variants of the STP have been proposed and studied. For instance, some of these new variations include Steiner problems with profits, where besides the costs associated with edges, there are also revenues associated with nodes (see e.g. [4] ). In addition, alternative variations aim at enriching the classical STP model by including a Quality of Service (QoS) requirement. The importance of this latter concept stems from its relevance to several real-time applications, where it is required to deliver the same information from a source toward all the members of a multicast group within a specified delay limit [17, 23] . Naturally, the QoS requirement and, specifically, the maximumdelay constraint impose a restriction on an acceptable multicast tree. To this aim, in this paper, we consider the following generalization of the STP. We are given a connected, undirected graph G = (V , E), where V = {1, . . . , n} is the node set, with node 1 being a source node, and E is the edge set, along with a nonnegative edge weight c e and delay θ e associated Many heuristics for solving the STPD arising in the telecommunication context have been proposed so far. Kompella et al. present in [17] greedy heuristics where they find a spanning tree of the closure graph of the constrained shortest path between the source and the terminal nodes. Sriram et al. in [28] propose two-phase algorithms for sparse and static communication groups where in Phase 1, all the possible shortest paths from the source to each terminal, respecting the maximum delay requirement, are computed and then, in Phase 2, these paths are used for constructing the multicast tree. Zhu et al. [31] propose a heuristic based on a feasible search optimization method that starts with the minimum delay tree and, then, decrease the cost of the delay-bounded tree. Standard approaches have been used to solve the Steiner tree problem with delay constraints. These approaches include, for instance, tabu search [7] and simulated annealing [18] .. Furthermore, it is noteworthy to observe that when all arcs have unit delays and the set R coincides with V , then the STPD problem reduces to the so-called hop-constrained minimum spanning tree problem (HMSTP). This latter model is a well-studied network optimization problem and important contributions pertaining to its solution have been presented so far. In particular, in [8] Gouveia presented several formulations that are based on liftings of MTZ subtour elimination constraints. Stronger multicommodity flow formulations are presented in [9] together with some computational results on graphs having up to 40 nodes.. Moreover in [25] , the authors introduced a distributed heuristic that produced better solutions with respect to previously known algorithms. Recently, Gouveia et al. presented in [11] a directed cut model on a layered graph in order to solve the HMSTP and they adapted the proposed approach to the diameter-constrained minimum spanning tree problem. In [11] a branch-and-cut algorithm has been used for solving the presented problems and this method is shown to be significantly better than previously known methods for both problems.. Finally, interesting results on the rooted distance constrained minimum spanning tree problem have been presented in [10] . This problem consists in finding a spanning tree such that the path from root node to any other node has a constrained total delay and generalizes the HMSTP, since the edges are assigned any delay value. In this paper Gouveia et al. presented several equivalent modeling approaches and results for complete graph instances with up to 40 nodes. In the test instances the mean of the delays was at most 5 and total delay was at most 25. The proposed approach might be adapted for the STPD with small delay values.. Our main contributions in this paper are the following:. (i) We develop an exact approach for the STPD.. (ii) We propose a valid compact formulation for the STPD that is based on new lifted Miller-Tucker-Zemlin subtour elimination constraints. (iii) We describe effective reduction techniques. (iv) We provide the results of extensive computational experiments that attest the strong evidence that the combination of the aforementioned contributions allow to solve to optimality STPD instances, having up to 1000 nodes for some sparse graphs.. The remainder of this paper is organized as follows. In Section 2, we present an enhanced polynomial-length mixedinteger programming formulation for the STPD. In Section 3, we describe several tailored reduction techniques. In Section 4, we report the results of extensive computational experiments. Finally, some concluding remarks are provided in the last section. In this paper, we have proposed an exact approach for the STPD. Our approach is based on a new tightened compact formulation for the Steiner Tree Problem with Delays. The proposed formulation is based on a new lifted MillerTucker-Zemlin subtour elimination constraint. Furthermore, we have described several tailored preprocessing techniques for both reducing the problem size and tightening the LP relaxation.. The relevance of our research stems from the well-known fact that the classical MTZ subtour elimination constraints consistently yield the weakest LP relaxation of all proposed formulations. Consequently, even though the MTZ constraintsbased formulations are both elegant and compact, they are often disregarded because of their hopeless ineffectiveness. Hence, an interesting issue that was investigated in this paper is to develop new enhanced variants of the MTZ constraints that prove useful for solving instances of practical size. Our primary contribution is to demonstrate the efficacy of the combination of the new enhanced MTZ constraints and reduction techniques. Indeed, we have reported the results of comprehensive computational experiments that provide strong evidence that the proposed compact formulation-based approach can consistently solve medium to large-scale STPD instances to optimality. These results were obtained on a large set of STPD instances that includes both sparse and dense graphs as well as weakly and tightly constrained instances. To the best of our knowledge, this is the first significant contribution with regard to the optimal solution of nontrivial instances of an NP-hard problem using MTZ constraints-type constraints. (ii) (h * , i) ̸ ∈ ϕ ij and (k * , j) ̸ ∈ ϕ ji . In this case (21) becomest i −t j ≤ M ij − θ ij which is obviously correct. (iii) (h * , i) ̸ ∈ ϕ ij and (k * , j) ∈ ϕ ji . In this case (21) reads. which is obviously correct sincet i ≤ µ i andt j ≥ λ k * + θ k * j = β k * j + λ j . (iv) (h * , i) ∈ ϕ ij and (k * , j) ̸ ∈ ϕ ji . This case is similar to (iii) and concludes the proof.

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


Eigenface-domain super-resolution for face recognition Abstract-Face images that are captured by surveillance cameras usually have a very low resolution, which significantly limits the performance of face recognition systems. In the past, super-resolution techniques have been proposed to increase the resolution by combining information from multiple images. These techniques use super-resolution as a preprocessing step to obtain a high-resolution image that is later passed to a face recognition system. Considering that most state-of-the-art face recognition systems use an initial dimensionality reduction method, we propose to transfer the super-resolution reconstruction from pixel domain to a lower dimensional face space. Such an approach has the advantage of a significant decrease in the computational complexity of the super-resolution reconstruction. The reconstruction algorithm no longer tries to obtain a visually improved high-quality image, but instead constructs the information required by the recognition system directly in the low dimensional domain without any unnecessary overhead. In addition, we show that face-space super-resolution is more robust to registration errors and noise than pixel-domain super-resolution because of the addition of model-based constraints. T HE performance of existing face recognition systems decreases significantly if the resolution of the face image falls below a certain level. This is especially critical in surveillance imagery where often only a low-resolution video sequence of the face is available. If these low-resolution images are passed to a face recognition system, the performance is usually unacceptable. Therefore, super-resolution techniques have been proposed for face recognition that attempt to obtain a high-resolution face image by combining the information from multiple low-resolution images [1] - [4] . In general, super-resolution algorithms try to regularize the ill-posedness of the problem using prior knowledge about the solution, such as smoothness or positivity [5] - [8] . Recently, researchers have proposed algorithms that attempt to use model-based constraints in regularization. While [1] demonstrates how super-resolution (without model-based priors) can improve the face recognition rate, [2] - [4] provide super-resolution algorithms that use face-specific constraints for regularization. All these systems propose super-resolution as a separate preprocessing block in front of a face recognition system. In other words, their main goal is to construct a high-resolution, visually improved face image that can later be passed to a face recognition system for improved performance. This is perfectly valid as long as computational complexity is not an issue. However, in a real-time surveillance scenario where the super-resolution algorithm is expected to work on continuous video streams, computational complexity is usually a very critical issue. In this paper, we propose an efficient super-resolution method for face recognition that transfers the super-resolution problem from the pixel domain to a low dimensional face space. This is based on the observation that nearly all state-of-the-art face recognition systems use some kind of front-end dimensionality reduction, and that a lot of redundant information generated by the preprocessing super-resolution algorithm is not used by the face recognition block. Hence, we perform the super-resolution reconstruction in the low-dimensional framework so that only the necessary information is reconstructed. In addition, we show that face-space super-resolution is more robust to registration errors and noise than the pixel-domain super-resolution because of the addition of model-based constraints.. There are two important sources of noise in this problem. One is the observation noise that results from the imaging system. The other is the representation error, which is a result of the dimensionality reduction. We derive the statistics of these noise processes for the low-dimensional face space by using examples from the human face image class. Substitution of this modelbased information into the algorithm provides a higher robustness to noise. We test our system on both real and synthetic video sequences.. Currently, by far the most popular dimensionality reduction technique in face recognition is to use subspace projections based on the Karhunen-Loeve Transform (KLT). This type of dimensionality reduction has been central to the development of face recognition algorithms for the last ten years. We propose to use a similar KLT-based dimensionality reduction technique to decrease the computational cost of the super-resolution algorithm by transforming it from a problem in the pixel domain to a problem in the lower-dimensional subspace, which is called the face space.. In Section II, we briefly review the KLT-based dimensionality reduction method for face recognition. Then, in Section III, we formulate the super-resolution problem in the low-dimensional framework. Section IV details the reconstruction algorithm, and Section V provides experimental results addressing several issues, such as sensitivity to noise and motion estimation errors. Conclusions are given in Section VI. The performance of face recognition systems decreases significantly if the resolution of the face image falls below a certain level. For video sequences, super-resolution techniques can be used to obtain a high-resolution face image by combining the information from multiple low-resolution images. Although super-resolution can be applied as a separate preprocessing block, in this paper, we propose to apply super-resolution after dimensionality reduction in a face recognition system. In this way, only the necessary information for recognition is reconstructed. We have also shown how to incorporate the model-based information into the face-space reconstruction algorithm. This helps to obtain more robust results when compared to the traditional super-resolution algorithms. In the experiments, we demonstrated robustness to noise and motion estimation error. We have investigated the effect of face-space dimension on the reconstruction, and provided recognition results for real video sequences. This paper only examines the case for face images; however, the idea can be extended to other pattern recognition problems easily. One such application is the recognition of car license plates from video. His research interests include image processing and computer vision.

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Orientation uncertainty goes bananas: An algorithm to visualise the uncertainty sample space on stereonets for oriented objects measured in boreholes Measurements of structure orientations are afflicted with uncertainties which arise from many sources. Commonly, such uncertainties involve instrument imprecision, external disturbances and human factors. The aggregated uncertainty depends on the uncertainty of each of the sources. The orientation of an object measured in a borehole (e.g. a fracture) is calculated using four parameters: the bearing and inclination of the borehole and two relative angles of the measured object to the borehole. Each parameter may be a result of one or several measurements. The aim of this paper is to develop a method to both calculate and visualize the aggregated uncertainty resulting from the uncertainty in each of the four geometrical constituents. Numerical methods were used to develop a VBA-application in Microsoft Excel to calculate the aggregated uncertainty. The code calculates two different representations of the aggregated uncertainty: a 1-parameter uncertainty, the 'minimum dihedral angle', denoted by Ω; and, a non-parametric visual representation of the uncertainty, denoted by χ. The simple 1-parameter uncertainty algorithm calculates the minimum dihedral angle accurately, but overestimates the probability space that plots as an ellipsoid on a lower hemisphere stereonet. The non-parametric representation plots the uncertainty probability space accurately, usually as a sector of an annulus for steeply inclined boreholes, but is difficult to express numerically. The 1-parameter uncertainty can be used for evaluating statistics of large datasets whilst the non-parametric representation is useful when scrutinizing single or a few objects. Today, construction of underground facilities, such as tunnels for cars and trains, electricity cables or fresh/waste water are widespread. Examples of future, more challenging, constructions are the planned deeply seated, geological repositories for spent fuel from nuclear-power plants. For such constructions, not only the constructability is important, but also the possibility to predict the long-term behaviour from a safety aspect. A key to a successful construction and safety assessment is a well performed investigation of the rock, where the properties are accurately characterized. Together with size, intensity and spatial correlation, information about orientation of geological features such as fractures, foliations and rock contacts are important for stability, flow and transport modelling. The information is preferably acquired from the intended depth of the facility, but in advance of any excavated tunnel the only possibility to obtain direct information is through boreholes.. Gathering data to orient objects seen in a borehole does not only entail consideration of the measure of the orientation and the uncertainty of the object relative to the borehole, but also the measured orientation and uncertainty of the borehole itself.. The orientation uncertainty of a fracture is twofold. On the one hand it tends to blur an orientation model towards less concentrated or erroneously oriented set divisions. On the other hand, it might explain outliers that do not fit a conceptual model. In other words, the uncertainty is not necessarily a curse, but can be a solution in some situations. Consequently, it is very important to neither overestimate nor underestimate the sample space of the uncertainty. When analyzing the data, the estimated uncertainty can be used to rank the measured data and thus develop more accurate models of the rock. Bleakly et al. (1985a Bleakly et al. ( , 1958b and Nelson et al. (1987) attempted to estimate the magnitude of orientation uncertainty for fractures using a mechanical goniometer on oriented cores. The uncertainty was a rough estimation by simply adding scalar values to a one parameter uncertainty. However, to our knowledge no one has previously presented how to calculate or visualize the true sample space of the orientation uncertainty of objects measured in boreholes. The objective of this article is, thus, to develop a method to calculate and visualize the sample space using uncertainties in the parameters measured in boreholes. Despite the importance of correct representation of fracture orientation when developing Discrete Fracture Network (DFN) models the authors have not found any attempt in the literature to calculate the true uncertainty sample space of objects measured in boreholes. The uncertainty may not only be used to classify data, but could also be a possible cause of outliers not fitting into a conceptual model. For instance, if the conceptual model predicts that fractures parallel to the direction of maximum horizontal stress (s 1 ) ought to have small flow resistance, but the measured orientation of a fracture with high specific capacity (i.e. an indication of low flow resistance) differs markedly from the orientation of maximum horizontal stress, the uncertainty space, χ, could be used to demonstrate compliance with the model, provided it is large enough. Hence, knowing the degree of uncertainty might provide a possibility to explain outliers.. Further, the uncertainty has an impact on the fracture set orientation concentration parameters, e.g. Fisher κ, which will be less concentrated with large uncertainty. Incorrect estimations of fracture set orientation concentration parameters will directly affect connectivity of the DFN model and hence all downstream models, e.g. flow and transport models. It is, therefore, important to continue research on the uncertainty of objects measured in boreholes. The developed Microsoft Excel VBA algorithm calculates two different representations of the aggregated orientation uncertainty of an oriented object measured in a borehole: a 1-parameter uncertainty, the 'minimum dihedral angle', denoted by Ω; and, a non-parametric visual representation of the uncertainty, denoted by χ.. The minimum dihedral angle, Ω, is the smallest angle that, when revolved around the expected fracture pole, encloses the true sample space of the uncertainty, see Fig. 3 . The circle, which plots like an ellipsoid on a lower hemisphere equal area stereonet, will, hence, overestimate the probability space for the orientation of the object. Though Ω cannot be used for reinterpretation of orientation, it is instead useful to evaluate the size of the uncertainty of all objects in a whole borehole or a section of a borehole.. The non-parametric representation, χ, plots the uncertainty space accurately, usually as something like a sector of an annulus, see Fig. 3 . The surface is not easy to express in a few parameters, and numerical methods are needed to calculate it. Hence the nonparametric representation is powerful when scrutinizing or reinterpreting single or a few objects measured in boreholes, but tedious to use for thousands of fractures or objects.

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