Frechet Distance Research Articles

Minimizing Task-Space Fréchet Error via Efficient Incremental Graph Search

We present an anytime algorithm that generates a collision-free configuration-space path that closely follows a desired path in task space, according to the discrete Frechet distance. By leveraging tools from computational geometry, we approximate the search space using a cross-product graph. We use a variant of Dijkstra's graph-search algorithm to efficiently search for and iteratively improve the solution. We compare multiple proposed densification strategies and empirically show that our algorithm outperforms a set of state-of-the-art planners on a range of manipulation problems. Finally, we offer a proof sketch of the asymptotic optimality of our algorithm.

Day-Ahead System Marginal Price Forecasting Using Artificial Neural Network and Similar-Days Information

Day-ahead system marginal price (SMP) forecasting constitutes essential information in the competitive energy market. Hence, this paper presents the development of a day-ahead SMP forecasting model via implementing an artificial neural network (ANN) algorithm. The accuracy of the ANN-based model is improved by including long-term historical data in addition to short-term historical data and by applying the k-fold cross-validation optimization algorithm. The selection of the short-term type input variable applies the Pearson correlation coefficient. Whereas the long-term type input variable is selected by applying the discrete Frechet distance in conjunction with the information related to the season and type of the day to find the Similar-Days Index. In order to verify the model, the forecasted load and actual SMP for 15 years of historical data are used. The results indicate that the proposed model can forecast SMP with higher accuracy than the conventional forecasting model.

Walking the Dog Fast in Practice: Algorithm Engineering of the Fréchet Distance

The Frechet distance provides a natural and intuitive measure for the popular task of computing the similarity of two (polygonal) curves. While a simple algorithm computes it in near-quadratic time, a strongly subquadratic algorithm cannot exist unless the Strong Exponential Time Hypothesis fails. Still, fast practical implementations of the Frechet distance, in particular for realistic input curves, are highly desirable. This has even lead to a designated competition, the ACM SIGSPATIAL GIS Cup 2017: Here, the challenge was to implement a near-neighbor data structure under the Frechet distance. The bottleneck of the top three implementations turned out to be precisely the decision procedure for the Frechet distance. In this work, we present a fast, certifying implementation for deciding the Frechet distance, in order to (1) complement its pessimistic worst-case hardness by an empirical analysis on realistic input data and to (2) improve the state of the art for the GIS Cup challenge. We experimentally evaluate our implementation on a large benchmark consisting of several data sets (including handwritten characters and GPS trajectories). Compared to the winning implementation of the GIS Cup, we obtain running time improvements of up to more than two orders of magnitude for the decision procedure and of up to a factor of 30 for queries to the near-neighbor data structure.

Numerical model for distributors of railway vehicles equipped with composite blocks

The paper describes the main features of a new numerical model of distributor for railway vehicles equipped with type K composite blocks, available in the TrainDy software. The composite brake blocks (CBB) type K guarantee better braking performance and quieter operation than traditional cast iron blocks (P10). Railway wagons with this type of shoes have different braking systems compared to wagons with traditional shoes, since their performance changes, for example, depending on the load carried by the wagon and the type of braking regime. The paper shows a series of tests comparing the numerical results provided by the new module with the experimental data. In this work, the parameters of the numerical model of the distributor are automatically calculated, by using the Mathworks "Global Optimization toolbox" for comparison between numerical and experimental data, provided by Faiveley Transport (Wabtec group) during the revision process of Leaflet UIC 421. The Frechet distance, which allows evaluating the degree of similarity of two curves, is the basis for the comparison. This approach allows identifying, on a rational and numerical basis, the parameters of the distributor, without having to use the support of an expert user.

Multi-Feature Fusion: A Driver-Car Matching Model Based on Curve Comparison

With the development of the mobile Internet, novel things are constantly emerging, and among them, online car-hailing is one of the representatives. However, the rapid development of online car-hailing also brings about normative problems and safety loophole, the most prominent of which is the inconsistency between operating cars and registered drivers. Some existing algorithms based on curve similarity measurements, such as Hausdorff distance and discrete Frechet distance, can be used to solve this problem. However, they only consider one of the characteristics of the two curves, such as the distance or the area between two curves, which does not achieve good results on this problem. On this ground, we propose a model based on curve comparison, named multi-feature fusion (MFF), which extracts the features of length, distance, and area from the GPS positioning track of car and the application mobile phone of the driver, to testify whether the car is being operated by the registered driver and thus solving the problem of mismatch between the driver and the car during the operation. Among them, the MFF model designs different algorithms for different features and fuses different features by an ensemble learning method. The experimental results prove that the model can effectively detect the mismatch between drivers and cars.

Similarity measures for identifying material parameters from hysteresis loops using inverse analysis

Sum-of-square based error formulations may be difficult to implement on an inverse analysis consisting of multiple tension-compression hysteresis loops. Five alternative measures of similarity between curves are investigated as useful tools to help identify parameters from hysteresis loops with inverse analyses. A new algorithm is presented to calculate the area between curves. Four additional methods are presented from literature, which include the Partial Curve Mapping value, discrete Frechet distance, Dynamic Time Warping, and Curve Length approach. These similarity measures are compared by solving a non-linear regression problem resembling a single load-unload cycle. The measures are then used to solve more complicated inverse analysis, where material parameters are identified for a kinematic hardening transversely anisotropic material model. The inverse analysis finds material parameters such that a non-linear FE model reproduces the behavior from five experimental hysteresis loops. Each method was shown to find useful parameters for these problems, and should be considered a viable alternative when sum-of-square based methods may be difficult to implement. It is important to consider multiple similarity measures in cases when it is impossible to obtain a perfect match.

Influence measures in beta regression models through distance between distributions

In this paper, case-deletion diagnostics in beta regression models are proposed. The diagnostics are based on the distance between the distributions of the maximum likelihood estimates of the model parameters resulting from the entire sample and after removing a sample case. Two metrics between probability distributions are considered: the Frechet distance (Frechet in Comptes Rendus hebdomadaires des seances de l’Academie des Sciences de Paris 244:689–692, 1957), and the Rao distance (Rao in Indian J Stat Ser A 9:246–291, 1949). Moreover, a jackknife-after-bootstrap transformation of the diagnostics is also proposed to make clear the decision about cases to be considered as influential. Artificial and real examples are included to illustrate the usefulness of the diagnostics and to compare them to others in the literature.

АДАПТИВНИЙ МЕТОД СЕГМЕНТАЦІЇ ЗОБРАЖЕНЬ НА ОСНОВІ МЕТРИК

Проаналізовано сучасні алгоритми сегментації зображень, що дало змогу виділити їх переваги та недоліки для застосування в медичних цілях. Для діагностування передракових та ракових станів молочної залози використовують цитологічні та гістологічні зображення. Процес опрацювання таких зображень є важким і рутинним процесом, що потребує наявності спеціалізованих знань у медиків в галузі комп'ютерного зору. Недоліком біомедичних зображень є низька якість, неоднорідність освітлення у процесі формування зображень, низька контрастність. Неможливо застосувати одні і ті ж алгоритми і їх параметри до різних зображень, тому актуальним постає завдання розроблення адаптивних систем сегментації зображень. З'ясовано, що алгоритм сегментації методом водорозподілу у комбінації з методом порогової сегментації показав найкращі результати. Охарактеризовано закономірності між вхідними даними біомедичних зображень та алгоритмами сегментації. Сформовано правила нечіткої логіки для підбору параметрів алгоритмів біомедичних зображень. Розроблення автоматичної системи підбору параметрів сегментації цитологічних і гістологічних зображень є актуальним завданням, що підвищить якість опрацювання зображень.

Map matching algorithm: curve simplification for Frechet distance computing and precise navigation on road network using RTKLIB

Map matching is the process which work for location measurement and also find out appropriate route for smooth traveling on the road network, but map matching accuracy fully depends on GPS trajectory data and electronic map of the road network. Unfortunately, GPS data is not accurate because, it’s through weak GPS signaling and low quality GPS devices. So, it is difficult to calculate accurate location of movements.This work provides, a map mapping algorithm for simplifying appropriate path, including curves on road network and also, we proposed Frechet distance computing algorithm with road Preliminaries for network simplification.

Cocaine-Induced Changes in Low-Dimensional Attractors of Local Field Potentials in Optogenetic Mice.

Optogenetically evoked local field potential (LFP) recorded from the medial prefrontal cortex (mPFC) of mice during basal conditions and following a systemic cocaine administration were analyzed. Blue light stimuli were delivered to mPFC through a fiber optic every 2 s and each trial was repeated 100 times. As in the previous study, we used a surrogate data method to check that nonlinearity was present in the experimental LFPs and only used the last 1.5 s of steady activity to measure the LFPs phase resetting induced by the brief 10 ms light stimulus. We found that the steady dynamics of the mPFC in response to light stimuli could be reconstructed in a three-dimensional phase space with topologically similar “8”-shaped attractors across different animals. Therefore, cocaine did not change the complexity of the recorded nonlinear data compared to the control case. The phase space of the reconstructed attractor is determined by the LFP time series and its temporally shifted versions by a multiple of some lag time. We also compared the change in the attractor shape between cocaine-injected and control using (1) dendrogram clustering and (2) Frechet distance. We found about 20% overlap between control and cocaine trials when classified using dendrogram method, which suggest that it may be possible to describe mathematically both data sets with the same model and slightly different model parameters. We also found that the lag times are about three times shorter for cocaine trials compared to control. As a result, although the phase space trajectories for control and cocaine may look similar, their dynamics is significantly different.

A novel clustering algorithm of extracting road network from low-frequency floating car data

Keeping the digital road maps up-to-date is of critical importance, because the quality of many road-dependent services relies on it, but traditional measurement methods are still time-consuming and expensive. With the GPS technology and wireless communication technology maturing, the positioning data from floating car become a new data source for updating road maps. The paper presents a novel incremental clustering algorithm for automatically extracting the topology of the road network employing the floating car data. A trajectory is selected as a road Link and then the remaining trajectories are added in turn until all tracks are processed. Further, the algorithm determines whether to merge the trajectory or divide it into a new Link by judging the relations of the space position between the newly added trajectory and the existing Link. A partial curve matching method based on Frechet distance is employed to measure the partial similarity between a Trajectory and a Link and the time complexity of the proposed algorithm is reduced. Experiments show that the algorithm can quickly extract the geometric shape and topology of the road network with lightweight floating car data.

M3: visual exploration of spatial relationships between flight trajectories

Outlier detection and clustering are important to analyze trajectory. While many algorithms have been developed to tackle these issues, they lack the combination with visualization to enable the involvement of human intelligence during the analyzing process. We propose a visual framework called M3, which combines data mining algorithms with visualization technique through three coordinated views: Map, MST, and FSDMatrix. Map view displays the spatial information of trajectories. MST is a minimum spanning tree, which presents the relationships between trajectories. In MST, each node represents a trajectory; edges between nodes denote the Frechet distance between trajectories. FSDMatrix shows a matrix of pairwise Free Space Diagram to assist in detecting outliers and clustering trajectories. The three views are interacted with each other. Through case studies, we discuss the applicability of our framework and demonstrate the convenience brought by it.

3D Face Similarity Measure by Fréchet Distances of Geodesics

3D face similarity is a critical issue in computer vision, computer graphics and face recognition and so on. Since Frechet distance is an effective metric for measuring curve similarity, a novel 3D face similarity measure method based on Frechet distances of geodesics is proposed in this paper. In our method, the surface similarity between two 3D faces is measured by the similarity between two sets of 3D curves on them. Due to the intrinsic property of geodesics, we select geodesics as the comparison curves. Firstly, the geodesics on each 3D facial model emanating from the nose tip point are extracted in the same initial direction with equal angular increment. Secondly, the Frechet distances between the two sets of geodesics on the two compared facial models are computed. At last, the similarity between the two facial models is computed based on the Frechet distances of the geodesics obtained in the second step. We verify our method both theoretically and practically. In theory, we prove that the similarity of our method satisfies three properties: reflexivity, symmetry, and triangle inequality. And in practice, experiments are conducted on the open 3D face database GavaDB, Texas 3D Face Recognition database, and our 3D face database. After the comparison with iso-geodesic and Hausdorff distance method, the results illustrate that our method has good discrimination ability and can not only identify the facial models of the same person, but also distinguish the facial models of any two different persons.

Development of a metric and the methods for quantitative estimation of the segmentation of biomedical images

We analyzed modern digital microscopy. In order to categorize digital microscopy, the following criteria are introduced: level of automation, software level, the level of application of network technologies. To quantitatively estimate the quality of image segmentation, we devised the technique based on a metric approach using the Frechet and Hausdorff metrics. Modern algorithms for calculating the Hausdorff and Frechet distances were analyzed. We have introduced the Frechet distance between trees. It was proven that the Frechet distance between trees is a metric. We devised a method for estimating a distance between trees of the non-convex regions, based on finding skeletons of regions and determining the distance between them. The algorithm for finding the Hausdorff distance between the non-convex regions is described. We constructed the algorithm for finding a distance between the non-convex regions based on the Frechet metric between trees. The developed algorithms are included into a hybrid intelligent system for automated microscopy, which is designed to process histological and cytological images. The algorithms were tested using the results of segmentation of histologic and cytologic images from a database as an example

Malicious Domain Detection Based on Traffic Similarity

Domain name system is an important resource in the Internet. Malicious domain detection techniques are used to find the malicious domains which are designed for malicious behaviors. The paper analyzes the existing malicious domain detection techniques and then proposes a new malicious domain detection technique based on traffic similarity. In this paper, we analyze the public botnet traffic dataset and get the DNS traffic pattern. We apply this pattern to spam as well. In this paper, we use normalized Frechet distance to evaluate two traffic curves’ similarity. Our experiments over simulation botnet and spam network show that the proposed technique can achieve high true positive rates (94.3% in average) as we change the botnet connection frequency, DGA types and spam sent rules. The proposed technique provides a new idea for malicious domain detection.

Grid-Based Method for GPS Route Analysis for Retrieval

Grids are commonly used as histograms to process spatial data in order to detect frequent patterns, predict destinations, or to infer popular places. However, they have not been previously used for GPS trajectory similarity searches or retrieval in general. Instead, slower and more complicated algorithms based on individual point-pair comparison have been used. We demonstrate how a grid representation can be used to compute four different route measures: novelty, noteworthiness, similarity, and inclusion. The measures may be used in several applications such as identifying taxi fraud, automatically updating GPS navigation software, optimizing traffic, and identifying commuting patterns. We compare our proposed route similarity measure, C-SIM, to eight popular alternatives including Edit Distance on Real sequence (EDR) and Frechet distance. The proposed measure is simple to implement and we give a fast, linear time algorithm for the task. It works well under noise, changes in sampling rate, and point shifting. We demonstrate that by using the grid, a route similarity ranking can be computed in real-time on the Mopsi2014 1 route dataset, which consists of over 6,000 routes. This ranking is an extension of the most similar route search and contains an ordered list of all similar routes from the database. The real-time search is due to indexing the cell database and comes at the cost of spending 80% more memory space for the index. The methods are implemented inside the Mopsi 2 route module.

Fréchet Distance Between a Line and Avatar Point Set

Frechet distance is an important geometric measure that captures the distance between two curves or more generally point sets. In this paper, we consider a natural variant of Frechet distance problem with multiple choice, provide an approximation algorithm and address its parameterized and kernelization complexity. A multiple choice problem consists of a set of color classes $$\mathcal {Q}=\{Q_1,Q_2,\ldots ,Q_n\}$$ , where each class $$Q_i$$ consists of a pair of points $$Q_i = \{q_i, \bar{q_i}\}$$ . We call a subset $$A\subset \{q_i , \bar{q_i}:1\le i\le n\}$$ conflict-free if A contains at most one point from each color class. The standard objective in multiple choice problem is to select a conflict-free subset that optimizes a given function. Given a line-segment $$\ell $$ and a set $$\mathcal {Q}$$ of a pair of points in $$\mathbb {R}^2$$ , our objective is to find a conflict-free subset that minimizes the Frechet distance between $$\ell $$ and the point set, where the minimum is taken over all possible conflict-free subsets. We first show that this problem is NP-hard, and provide a 3-approximation algorithm. Then we develop a simple randomized FPT algorithm for the problem when parametrized by the solution size, which is later derandomized using universal family of sets. We believe that our derandomization technique can be of independent interest, and can be used to solve other parameterized multiple choice problems. The randomized algorithm runs in $$\mathcal {O}(2^k n \log ^2 n)$$ time, and the derandomized deterministic algorithm runs in $$2^k k^{\mathcal {O}(\log k)} n \log ^2 n$$ time, where k, the parameter, is the number of elements in the conflict-free subset solution. Finally we present a simple branching algorithm for the problem running in $$\mathcal {O}(2^k n\log n)$$ time. We also show that the problem does not have a polynomial sized kernel under standard complexity theoretic assumptions.

Interactive Fault Extraction in 3-D Seismic Data Using the Hough Transform and Tracking Vectors

The exploration of reservoir regions has a close relationship with the localization of faults. Although faults can be labeled in seismic volumes by experienced interpreters, such manual interpretation is inefficient when dealing with a dramatically growing amount of collected seismic data. To speed up the interpretation efficiency of faults, in this paper, we propose a method that semiautomatically detects fault surfaces by using the Hough transform as well as tracking vectors. In the proposed method, we classify seismic sections into reference and predicted ones by borrowing the concept of I- and B-frames in video-coding techniques. For these two types of seismic sections, we introduce different strategies to delineate faults. In reference sections, we first highlight likely fault regions from corresponding coherence maps and apply the Hough transform to extract the features of faults. After removing false features, we optimally connect remaining features under the constraints of coherence maps. Since the accuracy of fault detection in reference sections depends highly on several parameters, to avoid replicating the tweaking of parameters in all seismic sections, we propose tracking detected faults in reference sections through remaining predicted sections, in which faults are labeled based on estimated tracking vectors and geological constraints. To evaluate the performance of the proposed method, we introduce a fault similarity (FauSIM) index that describes the similarity between detected faults and manually picked faults. The FauSIM index based on the Frechet distance focuses on both the local and global comparisons of faults. Experimental results show that the proposed method has the capability to accurately detect faults in seismic sections, and the tracking process improves interpretation efficiency by eliminating tweaked parameters. In addition, comparisons between faults delineated by various methods and faults manually picked show that the FauSIM index is highly correlated with interpreters’ subjective perception.

Frechet distance between weighted rooted trees

Frechet distance between weighted rooted trees

Long‐term intuitionistic fuzzy time series forecasting model based on vector quantisation and curve similarity measure

In existing fuzzy time series forecasting models, the accuracy of forecasting excessively relies on priori knowledge and output cannot effectively forecast multi values. The forecasting accuracy reduces drastically when time series data deviate from experience boundary in most models. The generalisation performance is insufficient. To overcome defects of traditional methods, this study proposed a long-term intuitionistic fuzzy time series (IFTS) forecasting model based on vector quantisation and curve similarity measure. In preprocessing of the proposed model, FTS theory is extended to long-term IFTS forecasting scope, the raw historical data are quantised vectors and optimum clustering centroids are searched by intuitionistic fuzzy c-means clustering algorithm. Curve similarity measure algorithm is proposed in procedure of forecasting, which avoids influence of mutation points and overcomes limitation of priori information. Euclidean distance is replaced by Frechet distance, it is appropriate for such directed time series in vector matching. The proposed model and relevant models are implemented on three different datasets, a synthetic dataset, the monthly total retail sale of social consumer goods and daily mean temperature dataset. The forecasting results, index mean square error and average forecasting error rate indicate that our model performance better in different time series patterns than others.