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Design modern methods of nonlinear control systems of nonlinear objects in the majority assume transformation of initial object model to some special forms. In these cases, it is reasonable to use quasilinear models as they can be designed on condition only of differentiability of the nonlinearities of the initial objects models. These models allow to find control analytically, i.e. as a result of the solution of some equations system, if the object, naturally, meets the controllability condition. The quasilinear models are synthesized traditionally analytically, bytransformation of initial nonlinear models using operation of the taking of partial derivatives from the nonlinearities of the initial objects models and the subsequent integration of these derivatives on the auxiliary variable with application of the known formulas of differentiation and integration. However, in many cases, the objects nonlinearities have so complicated character, that the operations of the differentiation and, in particular, the integration are executed very difficult by shown way. This complexity can be overcome by application of the new numerical design method of the quasilinear models, which excludesneed of the analytical differentiation and integration, but demands considerable number of the arithmetic operations. But now it is not the big problem since the modern multiprocessor controllers can carry out all the necessary operations for a short time. The developed method allows to receive rather exact, approximate piecewise-constant quasilinear models for the objects with the complicated nonlinearities. It is convenient to apply such models at numerical control of the nonlinear objects. The efficiency of a numerical method is shown by comparison of phase portraits of piecewise constant quasilinear and nonlinear models of a simple object and also by comparison of the state variables values of these models. The offered method can be applied to nonlinear control systems design for the nonlinear, characterized by complicated characteristics objects ship, aviation, chemical, agricultural and other industries.

Additive Manufacturing (AM) allows for the manufacturing of complex geometry parts as a single object regardless of their geometric complexity. However, manufacturing a consolidate object is not always to be better than the assembly approach. There are several practical scenarios which often require an assembly approach, i.e., (1) to achieve specific mechanical functionality in the product and aesthetic aspects; (2) to fit a product component in a predefined buildable space, particularly the case where large-scale products are required to be fitted with a developing platform space; and (3) to improve the additive manufacturing productivity (by minimizing processing time, improving product quality, surface finish and reducing material/support cost). In this paper, a computational framework is proposed to decompose the initial object design into several assemblies with the aim to minimize the total AM processing time. The decomposed components can be arranged into a minimum printing height space, thus it reduces the number of printing layer significantly, yielding to a build-up time reduction even if some time is spent in required assembling operations. Computation framework is implemented for three medium size object geometries. The presented study points out that the part decomposition and assembling approach can considerably reduce the total AM processing time. The methodology supports AM to be extended for a broad range of medium size products, and leads to strengthening the customizability of the products.

When adopting the matching method of the least squares image based on object-patch to match tilted images, problems like the low degree of connection points for images with the discontinuity of depth or the discrepancy in elevation or low availability of aerotriangulation points would frequently appear. To address such problems, a tilted-image-matching algorithm based on an adaptive initial object-patch is proposed by this paper. By means of the existing initial values of the interior and exterior orientation elements of the tilted image and the information of object points generated in the matching process, the algorithm takes advantage of the method of multi-patch forward intersection and object variance partition so as to adaptively calculate the elevation of the object-patch and the initial value of the normal vector direction angle. Furthermore, this algorithm aims to solve the problem of difficulties in matching the tilted image with its corresponding points brought about by the low accuracy of the initial value of the tilted image when adopting the matching method of the least squares image based on object-patch to match the tilted image with high discrepancy in elevation. We adopt the algorithm as proposed in this paper and the least squares image matching method in which the initial state of the object-patch is horizontal to the object-patch respectively to conduct the verification process of comparing and matching two groups of tilted images. Finally, the effectiveness of the algorithm as proposed in this paper is verified by the testing results.

In the first part of the paper, we clarify the connections between several algebraic objects appearing in matroid theory: both partial fields and hyperfields are fuzzy rings, fuzzy rings are tracts, and these relations are compatible with the respective matroid theories. Moreover, fuzzy rings are ordered blueprints and lie in the intersection of tracts with ordered blueprints; we call the objects of this intersection pastures. In the second part, we construct moduli spaces for matroids over pastures. We show that, for any non-empty finite set $E$, the functor taking a pasture $F$ to the set of isomorphism classes of rank-$r$ $F$-matroids on $E$ is representable by an ordered blue scheme $Mat(r,E)$, the moduli space of rank-$r$ matroids on $E$. In the third part, we draw conclusions on matroid theory. A classical rank-$r$ matroid $M$ on $E$ corresponds to a $\mathbb{K}$-valued point of $Mat(r,E)$ where $\mathbb{K}$ is the Krasner hyperfield. Such a point defines a residue pasture $k_M$, which we call the universal pasture of $M$. We show that for every pasture $F$, morphisms $k_M\to F$ are canonically in bijection with $F$-matroid structures on $M$. An analogous weak universal pasture $k_M^w$ classifies weak $F$-matroid structures on $M$. The unit group of $k_M^w$ can be canonically identified with the Tutte group of $M$. We call the sub-pasture $k_M^f$ of $k_M^w$ generated by ``cross-ratios' the foundation of $M$,. It parametrizes rescaling classes of weak $F$-matroid structures on $M$, and its unit group is coincides with the inner Tutte group of $M$. We show that a matroid $M$ is regular if and only if its foundation is the regular partial field, and a non-regular matroid $M$ is binary if and only if its foundation is the field with two elements. This yields a new proof of the fact that a matroid is regular if and only if it is both binary and orientable., 85 pages; some additional material, e.g. a new section 5.6; the terminology has been adapted to the usage in follow-up papers

Digital solutions are more and more employed in the industry with the aim of improving manufacturing processes. In this paper, we consider the issue of accurately localizing objects for augmented reality applications. Augmented reality has become a major asset for manufacturing processes as it enables to interactively provide relevant information about manufactured objects. These applications require a high object localization accuracy to avoid displaying wrong information. However, standard object localization methods do not always meet the industry’s accuracy constraints. We address this problem with a novel RGB-D refinement method in order to provide the optimal object localization accuracy. Given a coarse initial object localization, we iteratively refine the input by combining a geometric constraint and depth consistency. We show that fusing these two constraints enables to significantly improve the object localization accuracy. Our refinement method is evaluated on the challenging Linemod and Occlusion datasets. We demonstrate high accuracy and robustness. Furthermore, we propose quantitative and qualitative results on several industrial objects to show the contribution of our method in the applicative field.

Intelligent service robot is a challenging area of research that is rapidly expanding in our daily life. To meet robot’s object detection requirements in a messy surrounding, this paper provides a visual object detection method based on color and shape features. Firstly, a color hierarchical model and a multi-size filter are built to obtain initial object regions from scene image. Then a straight line-corner-arc strategy is presented to detect shape features. After comparing color and shape features with known-objects’ features stored in database, the detection scope is narrowed. So speeded up robust features algorithm is used to quickly match object features. The proposed method is tested by mobile robot in a semi-structured indoor environment. Finally, combined with the above steps, the total detection accuracy achieves 88.5% that confirms the feasibility of the proposed method.

The characteristic is a simple yet important invariant of an algebra. In this paper, we study the characteristic of a Rota–Baxter algebra, called the Rota–Baxter characteristic. We introduc...

This paper presents the development of a control system for vision-guided pick-and-place tasks using a robot arm equipped with a 3D camera. The main steps include camera intrinsic and extrinsic calibration, hand-eye calibration, initial object pose registration, objects pose alignment algorithm, and pick-and-place execution. The proposed system allows the robot be able to to pick and place object with limited times of registering a new object and the developed software can be applied for new object scenario quickly. The integrated system was tested using the hardware combination of kuka iiwa, Robotiq grippers (two finger gripper and three finger gripper) and 3D cameras (Intel realsense D415 camera, Intel realsense D435 camera, Microsoft Kinect V2). The whole system can also be modified for the combination of other robotic arm, gripper and 3D camera.

In this paper, we explore generalizable, perception-to-action robotic manipulation for precise, contact-rich tasks. In particular, we contribute a framework for closed-loop robotic manipulation that automatically handles a category of objects, despite potentially unseen object instances and significant intra-category variations in shape, size and appearance. Previous approaches typically build a feedback loop on top of a real-time 6-DOF pose estimator. However, representing an object with a parameterized transformation from a fixed geometric template does not capture large intra-category shape variation. Hence we adopt the keypoint-based object representation proposed in kPAM for category-level pick-and-place, and extend it to closed-loop manipulation policies with contact-rich tasks. We first augment keypoints with local orientation information. Using the oriented keypoints, we propose a novel object-centric action representation in terms of regulating the linear/angular velocity or force/torque of these oriented keypoints. This formulation is surprisingly versatile -- we demonstrate that it can accomplish contact-rich manipulation tasks that require precision and dexterity for a category of objects with different shapes, sizes and appearances, such as peg-hole insertion for pegs and holes with significant shape variation and tight clearance. With the proposed object and action representation, our framework is also agnostic to the robot grasp pose and initial object configuration, making it flexible for integration and deployment., IEEE Robotics and Automation Letter. The video demo is on https://sites.google.com/view/kpam2/

This chapter provides a temporal topos theoretic formulation for the relationship of the conscious (cognitive) states of an entity for the past, present, and future in terms of nonfunctorially induced mnemonic morphisms. The past is recalled by memories, and the future consists of possible states with a probability space of possibilities. When our present consciousness and behavior change, through our memory our interpretation of the past changes, and simultaneously the range of probability distribution of future states will be affected. We describe the internal relationship among the conscious states in terms of the temporal topos (t-topos) theory. A conscious entity can be expressed as a pair (p, δp), where p is an object of the t-topos S^ over t-site S, and δp is a uniquely determined morphism from an initial object α of t-topos to p. For three objects U, V, and W in the t-site S (which correspond to the past, present, and future), we introduce noncanonical (i.e., nonfunctorial) mnemonic morphisms among the three states of p defined over U, V, and W, respectively. Then we study the interplay among conscious states \(\delta_{{{U}}}^{{{p}}}\), \(\delta_{{{V}}}^{{{p}}}\) and \(\delta_{{{W}}}^{{{p}}}\) of p corresponding to the past, present, and future.

Identification of visual patterns in cluster of similar objects in an aerial scene is a challenge for drone surveillance. Similar objects may form different patterns representing non-identical meanings in a scene. For example, a group of cars in a scene may form either traffic or a parking area, subjected to their position and arrangements. In this work, we proposed an approach to this issue by distinguishing between a parking area and any other arrangement of cars by generating a grouping pattern. Initial object detection in the aerial images is carried out by Mask-RCNN and then an algorithm is developed to form the arrangement pattern of the vehicles. A comparative analysis between parking spaces and non-parking spaces is provided in this work and distinct variations were reported between the generated patterns. The pattern generated showed formation of distinct geometric shapes in case of cars in a parking plot whereas cars in a traffic or non-parked condition displayed uneven shapes where many edges intersected at various points. However, the pattern generated will depend on the elevation of the camera from which the scene is captured and the ability of the object detection algorithm to detect cars. This approach can be used for understanding parking area organization, traffic managements, and direct cluster identification using deep learning methods for aerial surveillance applications in the near future.

Mastering skills of spatial orientation is a very important issue for the blind people. However, there are widely available or dedicated systems that support independent movement of them, i.e. the solutions based on GPS-navigation or the use of ultrasonic sonars or cameras, there is the lack of approaches that supports learning of spatial orientation in a smart way by helping blind people with recognition of real objects or assisting them with moving along unknown routes. To make a step forward to fulfill this gap, we propose an approach based on Object Map Ontology and binaural sounds. It allows us to describe unknown objects on the street and shows a new path for the blind user. The core of this proposal is a special ontology that stores knowledge about different objects that can be found in the city and set of binaural sounds that are integrated with these objects. The route that is a sequence of objects taken from the ontology is translated into a series of binaural sounds and auxiliary text descriptions. The preliminary studies have confirmed that blind users such as students but also adults are interested in developing such a solution. Investigations showed that the proposed system would be even useful for sighted trainers who teach spatial orientation. The initial Object Map Ontology that covers an exemplary root was created and expressed as a set of OWL classes, relations, and individuals. The preliminary sound classification was created and a couple of binaural sounds was recorded.

We construct a functor, from the category of schemes to the category of graded rings, that is an initial object for having a theory of Chern classes with an additive first Chern class. For any scheme $X$, the graded ring that our functor associates to $X$ is related to the associated graded ring of the $\gamma$-filtration on the Grothendieck ring of finite rank locally free sheaves on $X$ via a Grothendieck-Riemann-Roch type theorem., Comment: 14 Pages. To appear in Journal of Algebra

Homotopy methods are known from topology to describe deformations of certain mathematical objects O, e.g. geometrical bodies, sets, functions, etc., such that an initial object O1 is continuously transformed into a terminal one O2.

The generation of object proposals plays an important role in object detection. Most existing methods produce object proposals by using bottom-up cues, such as closed contour or superpixel. In this paper, we propose a novel method to improve the ranking of object proposals by combining bottom-up cues with top-down information of objectivity. Firstly, we utilize the bottom-up method to generate initial object proposals of the given test image. Then we retrieve its top-k similar images from training images set. Considering both appearance and spatial similarity between initial object proposals and the ground truth bounding boxes of these top-k similar images, we obtain the top-down guided scores of initial object proposals. Finally, the refined score of each initial object proposal is modeled as a fusion of the bottom-up score and the top-down score. Experiments show that our method achieves better performance compared with the state-of-art on the Pascal VOC2007 dataset.

The category of all idempotent generated semigroups with a prescribed structure E of their idempotents E (called the biordered set) has an initial object called the free idempotent generated semigroup over E, defined by a presentation over alphabet E, and denoted by IG(E). Recently, much effort has been put into investigating the structure of semigroups of the form IG(E), especially regarding their maximal subgroups. In this paper we take these investigations in a new direction by considering the word problem for IG(E). We prove two principal results, one positive and one negative. We show that, for a finite biordered set E, it is decidable whether a given word w ∈ E∗represents a regular element; if in addition one assumes that all maximal subgroups of IG(E) have decidable word problems, then the word problem in IG(E) restricted to regular words is decidable. On the other hand, we exhibit a biorder E arising from a finite idempotent semigroup S, such that the word problem for IG(E) is undecidable, even though all the maximal subgroups have decidable word problems. This is achieved by relating the word problem of IG(E) to the subgroup membership problem in finitely presented groups.

In this work, we study 'reduction monads', which are essentially the same as monads relative to the free functor from sets into multigraphs. Reduction monads account for two aspects of the lambda calculus: on the one hand, in the monadic viewpoint, the lambda calculus is an object equipped with a well-behaved substitution; on the other hand, in the graphical viewpoint, it is an oriented multigraph whose vertices are terms and whose edges witness the reductions between two terms. We study presentations of reduction monads. To this end, we propose a notion of 'reduction signature'. As usual, such a signature plays the role of a virtual presentation, and specifies arities for generating operations---possibly subject to equations---together with arities for generating reduction rules. For each such signature, we define a category of models; any model is, in particular, a reduction monad. If the initial object of this category of models exists, we call it the 'reduction monad presented (or specified) by the given reduction signature'. Our main result identifies a class of reduction signatures which specify a reduction monad in the above sense. We show in the examples that our approach covers several standard variants of the lambda calculus., POPL 2020

Vehicle positioning and ranging are the current research hotspots. To attain the competition goal of the MMSP Witcomm Challenge 2019 and promote the development of the autonomous driving technology, a novel framework is proposed in this paper, which combines the 2D object tracking and 3D reprojection methodologies. Firstly, a correlation filter using the deep convolutional features is designed to detect the bounding box of the moving objects which is achieved via finding the maximum response of the initial object in the convolutional feature maps. Next the homography matrix is calculated based on the image coordinate points and the corresponding world coordinate points to project the vehicle 2D boundary into the real world. The validity of the proposed framework is verified using the dataset provided by the MMSP Witcomm Challenge 2019 competition, where our method was awarded the second-place prize.

Every $F$-inverse monoid can be equipped with the unary operation which maps each element to the maximum element of its $\sigma$-class. In this enriched signature, the class of all $F$-inverse monoids forms a variety of algebraic structures. We describe universal objects in several classes of $F$-inverse monoids, in particular free $F$-inverse monoids. More precisely, for every $X$-generated group $G$ we describe the initial object in the category of all $X$-generated $F$-inverse monoids $F$ for which $F/\sigma=G$., Comment: 21 pages

A quasi-pointed category in the sense of D. Bourn is a finitely complete category \(\mathcal {C}\) having an initial object such that the unique morphism from the initial object to the terminal object is a monomorphism. When instead this morphism is an isomorphism, we obtain a (finitely complete) pointed category, and as it is well known, the structure of zero morphisms in a pointed category determines an enrichment of the category in the category of pointed sets. In this note we examine quasi-pointed categories through the structure formed by the zero morphisms (i.e. the morphisms which factor through the initial object), with the aim to compare this structure with an enrichment in the category of pointed sets.

For any biordered set of idempotents [Formula: see text] there is an initial object [Formula: see text], the free idempotent generated semigroup over[Formula: see text], in the category of semigroups generated by a set of idempotents biorder-isomorphic to [Formula: see text]. Recent research on [Formula: see text] has focused on the behavior of the maximal subgroups. Inspired by an example of Brittenham, Margolis and Meakin, several proofs have been offered that any group occurs as a maximal subgroup of some [Formula: see text], the latest being that of Dolinka and Ruškuc, who show that [Formula: see text] can be taken to be a band. From a result of Easdown, Sapir and Volkov, periodic elements of any [Formula: see text] lie in subgroups. However, little else is known of the “global” properties of [Formula: see text], other than that it need not be regular, even where [Formula: see text] is a semilattice. The aim of this paper is to deepen our understanding of the overall structure of [Formula: see text] in the case where [Formula: see text] is a biordered set with trivial products (for example, the biordered set of a poset) or where [Formula: see text] is the biordered set of a band [Formula: see text]. Since its introduction by Fountain in the late 1970s, the study of abundant and related semigroups has given rise to a deep and fruitful research area. The class of abundant semigroups extends that of regular semigroups in a natural way and itself is contained in the class of weakly abundant semigroups. Our main results show that (1) if [Formula: see text] is a biordered set with trivial products then [Formula: see text] is abundant and (if [Formula: see text] is finite) has solvable word problem, and (2) for any band [Formula: see text], the semigroup [Formula: see text] is weakly abundant and moreover satisfies a natural condition called the congruence condition. Further, [Formula: see text] is abundant for a normal band [Formula: see text] for which [Formula: see text] satisfies a given technical condition, and we give examples of such [Formula: see text]. On the other hand, we give an example of a normal band [Formula: see text] such that [Formula: see text] is not abundant.

A convergence class is introduced on every object of a given category by using certain generalized nets for expressing the convergence. The obtained concrete category is then investigated whose objects are the pairs consisting of objects of the original category and convergence classes on them and whose morphisms are the morphisms of the original category that preserve the convergence. We define, in a natural way, separation and compactness of objects of the concrete category under investigation and study their behavior.

For a given category KAC 2 , the present paper deals with the existence problem for the category DTC 2 (k), which is equivalent to KAC 2 , where DTC 2 (k) is the category whose objects are simple closed K-curves with even number l of elements in Z n , l ≠ 6, and morphisms are (digitally) K-continuous maps, and KAC 2 is a category whose objects are simple closed A-curves and morphisms are A-maps. To address this issue, the paper starts from the category denoted by KAC 1 whose objects are connected nD Khalimsky topological subspaces with Khalimsky adjacency and morphisms are A-maps in [S. E. Han and A. Sostak, Comput. Appl. Math., 32, 521–536 (2013)]. Based on this approach, in KAC 1 the paper proposes the notions of A-homotopy and A-homotopy equivalence and classifies the spaces in KAC 1 or KAC 2 in terms of the A-homotopy equivalence. Finally, the paper proves that, for Sa given category KAC 2 , there is DTC 2 (k), which is equivalent to KAC 2 .

In this article we give necessary and sufficient conditions for the existence of a pullback of a two sink, in a partial morphism category.

This paper investigates how three widely used calculus textbooks in the U.S. realize the derivative as a point-specific object and as a function using Sfard’s communicational approach. For this purpose, the study analyzed word-use and visual mediators for the limit process through which the derivative at a point was objectified, and word-use and visual mediators for the derivative process through which the derivative as a function was objectified. The analysis highlighted inconsistency in realizations of the limit process and object, and derivative process and object found in some instances, and implicit discussion on relations among different visual mediators. Specifically, the results of this study led to four observations about issues suggested by one or more of the textbooks: a) visual mediators of the initial and final objects, and the visual mediators of these processes were often inconsistent; b) transformations of visual mediators from initial object, through process, to final object were often implicit both in one visual mediator and across multiple visual mediators; c) visual mediators for the limit processes were sometimes disconnected from the initial and final objects, or the connections were not explicit; and d) realizations of both the derivative at a point and the derivative of a function were mediated with nearly identical symbols suggesting a possible difficulty with understanding the difference between them.

It is known that an Ehresmann monoid P ( T , Y ) may be constructed from a monoid T acting via order-preserving maps on both sides of a semilattice Y with identity, such that the actions satisfy an appropriate compatibility criterion. Our main result shows that if T is cancellative and equidivisible (as is the case for the free monoid X ⁎ ), the monoid P ( T , Y ) not only is Ehresmann but also satisfies the stronger property of being adequate. Fixing T, Y and the actions, we characterise P ( T , Y ) as being unique in the sense that it is the initial object in a suitable category of Ehresmann monoids. We also prove that the operator P defines an expansion of Ehresmann monoids.

In this paper we introduce the categories of fuzzy implications and R-implications and we introduce terminal and initial object on fuzzy implication category, then we discuss on relation between T-NORM category and R-implication category.

This paper proposes a novel online video object segmentation method by using region and edge consistency information. Motivated by the fact that the object edge information is similar between adjacent frames, we firstly generate object proposal based on region and edge consistency, which strengthens the confidence of regions nearby the obvious edges. Subsequently, we fuse optical flow into Markov Random Field (MRF) model to accurately segment moving object. Given an annotation frame for the initial object region, we can process video frames online within a short time. The experiments on benchmark video dataset demonstrate that the proposed method outperforms the existing state-of-the-art methods, especially in the scenarios with similar objects.

Given a model category C enriched over groupoids, we study and characterize the class of strongly fibered objects F ( K ) in terms of homotopy limits, with respect to a suitable subcategory K of C . We also show that the strong shape category for the pair ( C , K ) turns out to be isomorphic to the usual shape category for the pair ( C , F ( K ) ) . This applies, in particular, to topological shape and strong shape.

We show that every exact fully faithful functor from the category of perfect complexes on the spectrum of dual numbers to the bounded derived category of a noetherian separated scheme is of Fourier-Mukai type. The kernel turns out to be an object of the bounded derived category of coherent complexes on the product of the two schemes. We also study the space of stability conditions on the derived category of the spectrum of dual numbers., 23 pages, Final version to appear in J. Algebra

We study the properties of the relative derived category $D_{\mathscr{C}}^{b}$($\mathscr{A}$) of an abelian category $\mathscr{A}$ relative to a full and additive subcategory $\mathscr{C}$. In particular, when $\mathscr{A}=A{\text -}\mod$ for a finite-dimensional algebra $A$ over a field and $\mathscr{C}$ is a contravariantly finite subcategory of $A$-$\mod$ which is admissible and closed under direct summands, the $\mathscr{C}$-singularity category $D_{\mathscr{C}{\text sg}}$($\mathscr{A}$)=$D_{\mathscr{C}}^{b}$($\mathscr{A}$)/$K^{b}(\mathscr{C})$ is studied. We give a sufficient condition when this category is triangulated equivalent to the stable category of the Gorenstein category $\mathscr{G}(\mathscr{C})$ of $\mathscr{C}$., 17 pages, to appear in Journal of Pure and Applied Algebra

We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with a basic rigid object T, and show a bijection between the set of isomorphism classes of basic rigid objects in the finite presented category pr T of T and the set of isomorphism classes of basic τ-rigid pairs in the module category of the endomorphism algebra Endc(T) op . As a consequence, basic maximal objects in pr T are one-to-one correspondence to basic support τ-tilting modules over End c (T) op . This is a generalization of correspondences established by Adachi–Iyama–Reiten.

We introduce and study relative Rickart objects and dual relative Rickart objects in abelian categories. We show how our theory may be employed in order to study relative regular objects and (dual) relative Baer objects in abelian categories. We also give applications to module and comodule categories.

The (usual) Caldero–Chapoton map is a map from the set of objects of a category to a Laurent polynomial ring over the integers. In the case of a cluster category, it maps reachable indecomposable objects to the corresponding cluster variables in a cluster algebra. This formalizes the idea that the cluster category is a categorification of the cluster algebra. The definition of the Caldero–Chapoton map requires the category to be 2-Calabi-Yau, and the map depends on a cluster-tilting object in the category. We study a modified version of the Caldero–Chapoton map which requires only that the category have a Serre functor and depends only on a rigid object in the category. It is well known that the usual Caldero–Chapoton map gives rise to so-called friezes, for instance, Conway–Coxeter friezes. We show that the modified Caldero–Chapoton map gives rise to what we call generalized friezes and that, for cluster categories of Dynkin type A, it recovers the generalized friezes introduced by combinatorial means in recent work by the authors and Bessenrodt.

We developed a top-down and bottom-up segmentation ofobjects using shape contours through a two-stage procedure. First, the object was identified using an edge-based contour feature and then the object contour was obtained using a constraint optimization procedure based on the results from the earlier identified contours. The initial object detection provides object category specific information for the contour completion to be effected. We argue that top-down bottom-up interaction architecture has plausible neurological correlates. This method has an advantage in that it does not require learning boundaries with large datasets.

In this paper, we propose a video co-segmentation based superpixel co-saliency. Our approach is based on a hypothesis, the common or similar objects in multiple video clips are salient, and they shares the similar feature. At first, we try to find out the regions in every clip which are salient and share the similar feature by proposing a new superpixel co-saliency scheme. Then, the most salient superpixels are chosen as the initial object marker superpixels. Starting from these superpixels, merge the neighboring and similar regions, and segment out the final object parts. The experimental results demonstrate that the proposed model can efficiently segment the common objects from a group of video clips with generally lower error rate than some existing methods.

We address the problem of object segment proposal generation, which is a critical step in many instance-level semantic segmentation and scene understanding pipelines. In contrast to prior works that predict binary segment masks from images, we take an alternative refinement approach to improve the quality of a given segment candidate pool. In particular, we propose an efficient deep network that learns 2D spatial transforms to warp an initial object mask towards nearby object region. We formulate this segment refinement task as a regression problem and design a novel feature pooling strategy in our deep network to predict an affine transformation for each object mask. We evaluate our method extensively on two challenging public benchmarks and apply our refinement network to three different initial segment proposal settings. Our results show sizable improvements in average recall across all the settings, achieving the state-of-the-art performances.

Unsupervised object modeling is important in robotics, especially for handling a large set of objects. We present a method for unsupervised 3D object discovery, reconstruction, and localization that exploits multiple instances of an identical object contained in a single RGB-D image. The proposed method does not rely on segmentation, scene knowledge, or user input, and thus is easily scalable. Our method aims to find recurrent patterns in a single RGB-D image by utilizing appearance and geometry of the salient regions. We extract keypoints and match them in pairs based on their descriptors. We then generate triplets of the keypoints matching with each other using several geometric criteria to minimize false matches. The relative poses of the matched triplets are computed and clustered to discover sets of triplet pairs with similar relative poses. Triplets belonging to the same set are likely to belong to the same object and are used to construct an initial object model. Detection of remaining instances with the initial object model using RANSAC allows to further expand and refine the model. The automatically generated object models are both compact and descriptive. We show quantitative and qualitative results on RGB-D images with various objects including some from the Amazon Picking Challenge. We also demonstrate the use of our method in an object picking scenario with a robotic arm. ispartof: pages:431-439 ispartof: Proceedings International Conference on 3D Vision pages:431-439 ispartof: International Conference on 3D Vision location:Qingdao, China date:10 Oct - 12 Oct 2017 status: published

We find a partial solution to the longstanding problem of Kostant concerning description of the so-called locally finite endomorphisms of highest weight irreducible modules. The solution is obtained by means of its reduction to a far-reaching extension of the quantization problem. While the classical quantization problem consists in finding *product deformations of the commutative algebras of functions, we consider the case when the initial object is already a noncommutative algebra, the algebra of functions within q-calculus.

In this work we propose a topology-preserving framework for tracking deforming objects in a sequence of video frames. The shape of the object is modeled as obtained through the action of a group of diffeomorphisms on the initial object boundary. We formulate a state-space model for the diffeomorphic deformation of the object and implement a particle filter on this shape space to estimate the state of the shape in each video frame. We use a practical method for sampling diffeomorphic shapes in which we generate deformations via flows of finitely generated vector fields. Based on the observations and the proposed samples we obtain an approximate estimate for the posterior distribution of the shape.

In this paper, we present a method of pattern recognition based on obtaining the photoanisotropic copies of object images. Such copies are induced on the dynamic polarization-sensitive material when the amplitude image of the object formed by a spatial light modulator is transilluminated by linearly polarized light with a wavelength actinic for the used material. In this case, the distribution of the intensities over the amplitude image is converted into the distribution of photoanisotropy over the sample of a polarization-sensitive material. In the recognition process, this copy is illuminated by parallel circularly polarized nonactinic light. The distribution of elliptical polarization occurs directly behind the photoanisotropic copy, and it is reduced to a summary ellipse in the Fraunhofer diffraction region. It has been shown that the parameters of this ellipse are related to the characteristics of the object and uniquely identify the initial object. The polarization-holographic diffraction element that we developed enables determining the polarization state of a summary ellipse to obtain all the Stokes parameters in real time. The obtained results were compared with the Stokes parameters of the recognizable object in the database. The method invariance with regard to the position, scale, and rotation of the pattern were investigated. In addition, the resolution and sensitivity of this method were determined. The polarization-sensitive materials used to obtain copies are reversible, with practically an unlimited number of recording-deleting cycles. To obtain a photoanisotropic copy of another object on the same material, the previous copy should be deleted with a pulse of circularly polarized actinic light, and then the next copy can be recorded. A laboratory model of the recognition device and the appropriate software were created, and a theoretical model was developed. Databases were obtained for the images of various objects.

Generic object proposal generator plays an essential role in promoting the speed and accuracy of subsequent classification because of its ability of determining a general location of generic object in the image. Nevertheless many current object proposal generators somehow have the problems of time consuming or localization bias. In this paper, a new approach, Double Layer Multi-Threshold Extension (DLMTE) is proposed, which substantially is a bounding box refinement process to improve the performance of the object-locating method. Firstly, the object proposals produced by Binarized Normed Gradients (BING) method is taken as the initial object bounding boxes. And for validation of our method, the Edge Boxes is also regarded as an input. After box alignment procedure employed in the Multi-Thresholding Straddling Expansion (MTSE) method, according to superpixel boundary cue and global search, our DLMTE is utilized to refine the aligned object proposals to increase the location accuracy with simple computation. Experiments on PASCAL VOC 2007 dataset represent a better performance compared with M-Bing and M-EB improved by MTSE method.

Despite the rapid advance of additive manufacturing (AM) technologies in recent years, methods to fully encase objects with multilayer, thick features are still undeveloped. This issue can be overcome by printing layers conformally about an object's natural boundary, as opposed to current methods that utilize planar layering. With this mindset, two methods are derived to generate layers between the boundaries of initial and desired geometric objects in both two and three dimensions. The first method is based on variable offset curves (VOCs) and is applicable to pairs of initial and desired geometric objects that satisfy mild compatibility conditions. In this method, layers are generated by uniformly partitioning each of the normal line segments emanating from the initial object boundary and intersecting the desired object. The second method is based on manipulated solutions to Laplace's equation and is applicable to all geometric objects. Using each method, we present examples of layer generation for several objects of varying convexities. Results are compared, and the respective advantages and limitations of each method are discussed.

The popular multiresolution segmentation (MRS) algorithm is time and memory consuming when dealing with large images because it uses the pixel-grid for the initial object representation. In this study, we have tested a new workflow for image segmentation of remote sensing data, starting the MRS (using the ESP2 tool) from the superpixel level (using SLIC superpixels) and aiming at dramatically reducing the amount of time and computational resources needed to automatically partition relatively large datasets of very high resolution (VHR) remote sensing images. Tests were done on Quickbird and WorldView-2 data and the results show that the proposed workflow outperforms the traditional approach (MRS starting from pixels). The computational time was reduced in all cases, the biggest improvement being from 5h 35min to 13 min, for a WorldView-2 scene with 8 bands and an extent of 12.2 million pixels. This also comes with a slight improvement of the geometric accuracy of the extracted objects. This approach has the potential to enhance the automation of big remote sensing data analysis and processing, especially when time is an important constraint.

A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for distinct objects c,c'. If we keep in place the latter axiom but allow for more than one morphism between objects, we have a sort of generalized poset in which there are multiplicities attached to covering relations, and possibly nontrivial automorphism groups. We call such a category an "updown category". In this paper we give a precise definition of such categories and develop a theory for them. We also give a detailed account of ten examples, including updown categories of integer partitions, integer compositions, planar rooted trees, and rooted trees., arXiv admin note: substantial text overlap with arXiv:math/0402450

There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely eliminated. Category theory seems to be the correct mathematical theory for clarifying conceptual possibilities in this respect. In this theory, objects acquire their identity either by definition, when in defining category we postulate the existence of objects, or formally by the existence of identity morphisms. We show that it is perfectly possible to get rid of the identity of objects by definition, but the formal identity of objects remains as an essential element of the theory. This can be achieved by defining category exclusively in terms of morphisms and identity morphisms (objectless, or object free, category) and, analogously, by defining category theory entirely in terms of functors and identity functors (categoryless, or category free, category theory). With objects and categories eliminated, we focus on the "philosophy of arrows" and the roles various identities play in it (identities as such, identities up to isomorphism, identities up to natural isomorphism...). This perspective elucides a contrast between "set ontology" and "categorical ontology"., Comment: 13 pages, no figures

This paper proposes a new real-time object tracking algorithm using particle filters with color and texture features in moving CCD camera images. If the user selects an initial object, this region is declared as a target particle and an initial state is modeled. Then, N particles are generated based on random distribution and CS-LBP (Centre Symmetric Local Binary Patterns) for texture model and weighted color distribution is modeled from each particle. For observation likelihoods estimation, Bhattacharyya distance between particles and their feature models are calculated and this observation likelihoods are used for weights of individual particles. After weights estimation, a new particle which has the maximum weight is selected and new particles are re-sampled using the maximum particle. For performance comparison, we tested a few combinations of features and particle filters. The proposed algorithm showed best object tracking performance when we used color and texture model simultaneously for likelihood estimation.

Substantially nonlinear objects function at limitations of arbitrary kind. These limitations are not necessarily «convex» areas. For such objects the construction of area of the fully the fully-controlled state area is a serious problem. In the article it has been suggested to replace this task the task of the fully-controlled state area estimation from within. The secure estimation method of the fully-controlled state area has been developed for this purpose. Other dynamic system has been used as a «tester» (measure) of the fully-controlled state area. Construction and estimation of controllability and accessibility area of this dynamic system well methodically validate and deserved researchers confession. The descriptions concordance requirements of this new object with properties of initial object must be executed and provide property of «immersion» of new object in an initial object. Possibility is thus opened on the the fully-controlled state area of new object to define the the fully-controlled state area of the initial system

Shape control of a deformable object by a robotic system is a challenging problem because of the difficulty of imposing shape change by a finite number of actuation points to an essentially infinite-dimensional object. In this paper, a new approach to shape changing of deformable objects by a system of manipulators is presented. First, an integrated dynamic equation of motion for a system of multiple manipulators handling a deformable object is developed. A shape correspondence between the initial contact points of the multiple manipulators on a deformable object and a two-dimensional curve that represents the final desired shape is determined. A shape Jacobian that contains the local shape information of the desired shape of the object is formulated and is introduced into the control law. We develop a shape estimator with a second-order dynamics that is used to estimate the curve parameters corresponding to the end-effector position in each time step as the initial object is deformed to its desired final...

We give a characterization of those finitely complete categories with initial object and pushouts of split monomorphisms that admit categorical semidirect products. As an application we examine the case of groupoids with fixed set of objects. Further, we extend this to the internal case. (C) 2010 Elsevier B.V. All rights reserved.