Boundary Path Research Articles

Liver vessel MRI image segmentation based on dual-path diffusion model

Accurate segmentation of liver blood vessels in magnetic resonance imaging (MRI) images is a challenging task due to the complex tree-like structure and anisotropic diffusion properties of blood vessels. To solve this problem, we propose a new Dual-Path Diffusion Model (DPDM) framework. The framework consists of two collaborative diffusion paths: a local feature learning path based on convolution operations and a global context modeling path based on transform blocks. Local path encodes rich shape priors and preserve spatial details, while global path captures long-distance dependencies and enhance representation. In the decoding phase, the boundary features from the boundary path are fused with the features of the ordinary path decoding, which further enhances the shape sensitivity. In addition, we leverage a multi-task learning scheme to jointly optimize vascular segmentation and boundary prediction tasks in an end-to-end manner. Experiments on retrospective clinical dataset demonstrate that the proposed DPDM framework achieves excellent performance on the liver vessel segmentation task. Compared with state-of-the-art methods, our approach achieved a 6.0% and 7.3% performance improvement in Dice coefficient and IoU index, respectively. Our approach offers a promising solution for automated blood vessel segmentation in precision medicine.

Entanglement entropy and the boundary action of edge modes

We consider an antisymmetric gauge field in the Minkowski space of d-dimension and decompose it in terms of the antisymmetric tensor harmonics and fix the gauge. The Gauss law implies that the normal component of the field strength on the spherical entangling surface will label the superselection sectors. From the two-point function of the field strength on the sphere, we evaluate the logarithmic divergent term of the entanglement entropy of edge modes of p-form field. We observe that the logarithmic divergent term in entanglement entropy of edge modes coincides with the edge partition function of co-exact p-form on the sphere when expressed in terms of the Harish-Chandra characters. We also develop a boundary path integral of the antisymmetric p-form gauge field. From the boundary path integral, we show that the edge mode partition function corresponds to the co-exact (p − 1)-forms on the boundary. This boundary path integral agrees with the direct evaluation of the entanglement entropy of edge modes extracted from the two-point function of the normal component of the field strength on the entangling surface.

Boundary-Repairing Dual-Path Network for Retinal Layer Segmentation in OCT Image with Pigment Epithelial Detachment.

Automatic retinal layer segmentation in optical coherence tomography (OCT) images is crucial for the diagnosis of ocular diseases. Currently, automatic retinal layer segmentation works well with normal OCT images. However, pigment epithelial detachment (PED) dramatically alters the retinal structure, causing blurred boundaries and partial disappearance of the Bruch's Membrane (BM), thus posing challenges to the segmentation. To tackle these problems, we propose a novel dual-path U-shaped network for simultaneous layer segmentation and boundary regression. This network first designs a feature interaction fusion (FIF) module to strengthen the boundary shape constraints in the layer path. To address the challenge posed by partial BM disappearance and boundary-blurring, we propose a layer boundary repair (LBR) module. This module aims to use contrastive loss to enhance the confidence of blurred boundary regions and refine the segmentation of layer boundaries through the re-prediction head. In addition, we introduce a novel bilateral threshold distance map (BTDM) designed for the boundary path. The BTDM serves to emphasize information within boundary regions. This map, combined with the updated probability map, culminates in topology-guaranteed segmentation results achieved through a topology correction (TC) module. We investigated the proposed network on two severely deformed datasets (i.e., OCTA-500 and Aier-PED) and one slightly deformed dataset (i.e., DUKE). The proposed method achieves an average Dice score of 94.26% on the OCTA-500 dataset, which was 1.5% higher than BAU-Net and outperformed other methods. In the DUKE and Aier-PED datasets, the proposed method achieved average Dice scores of 91.65% and 95.75%, respectively.

Tracial weights on topological graph algebras

Abstract We describe two kinds of regular invariant measures on the boundary path space $\partial E$ of a second countable topological graph E, which allows us to describe all extremal tracial weights on $C^{*}(E)$ which are not gauge-invariant. Using this description, we prove that all tracial weights on the C $^{*}$ -algebra $C^{*}(E)$ of a second countable topological graph E are gauge-invariant when E is free. This in particular implies that all tracial weights on $C^{*}(E)$ are gauge-invariant when $C^{*}(E)$ is simple and separable.

A NOTE ON PROJECTIONS IN ÉTALE GROUPOID ALGEBRAS AND DIAGONAL-PRESERVING HOMOMORPHISMS

Abstract Carlsen [‘ $\ast $ -isomorphism of Leavitt path algebras over $\Bbb Z$ ’, Adv. Math.324 (2018), 326–335] showed that any $\ast $ -homomorphism between Leavitt path algebras over $\mathbb Z$ is automatically diagonal preserving and hence induces an isomorphism of boundary path groupoids. His result works over conjugation-closed subrings of $\mathbb C$ enjoying certain properties. In this paper, we characterise the rings considered by Carlsen as precisely those rings for which every $\ast $ -homomorphism of algebras of Hausdorff ample groupoids is automatically diagonal preserving. Moreover, the more general groupoid result has a simpler proof.

Dynamical actions and q-representation theory for double-scaled SYK

We show that DSSYK amplitudes are reproduced by considering the quantum mechanics of a constrained particle on the quantum group SUq(1, 1). We construct its left-and right-regular representations, and show that the representation matrices reproduce two-sided wavefunctions and correlation functions of DSSYK. We then construct a dynamical action and path integral for a particle on SUq(1, 1), whose quantization reproduces the aforementioned representation theory. By imposing boundary conditions or constraining the system we find the q-analog of the Schwarzian and Liouville boundary path integral descriptions. This lays the technical groundwork for identifying the gravitational bulk description of DSSYK. We find evidence the theory in question is a sine dilaton gravity, which interestingly is capable of describing both AdS and dS quantum gravity.

Occlusion relationship reasoning with a feature separation and interaction network

Occlusion relationship reasoning aims to locate where an object occludes others and estimate the depth order of these objects in three-dimensional (3D) space from a two-dimensional (2D) image. The former sub-task demands both the accurate location and the semantic indication of the objects, while the latter sub-task needs the depth order among the objects. Although several insightful studies have been proposed, a key characteristic of occlusion relationship reasoning, i.e., the specialty and complementarity between occlusion boundary detection and occlusion orientation estimation, is rarely discussed. To verify this claim, in this paper, we integrate these properties into a unified end-to-end trainable network, namely the feature separation and interaction network (FSINet). It contains a shared encoder-decoder structure to learn the complementary property between the two sub-tasks, and two separated paths to learn specialized properties of the two sub-tasks. Concretely, the occlusion boundary path contains an image-level cue extractor to capture rich location information of the boundary, a detail-perceived semantic feature extractor, and a contextual correlation extractor to acquire refined semantic features of objects. In addition, a dual-flow cross detector has been customized to alleviate false-positive and false-negative boundaries. For the occlusion orientation estimation path, a scene context learner has been designed to capture the depth order cue around the boundary. In addition, two stripe convolutions are built to judge the depth order between objects. The shared decoder supplies the feature interaction, which plays a key role in exploiting the complementarity of the two paths. Extensive experimental results on the PIOD and BSDS ownership datasets reveal the superior performance of FSINet over state-of-the-art alternatives. Additionally, abundant ablation studies are offered to demonstrate the effectiveness of our design.

Shortest Path to Boundary for Self-Intersecting Meshes

We introduce a method for efficiently computing the exact shortest path to the boundary of a mesh from a given internal point in the presence of self-intersections. We provide a formal definition of shortest boundary paths for self-intersecting objects and present a robust algorithm for computing the actual shortest boundary path. The resulting method offers an effective solution for collision and self-collision handling while simulating deformable volumetric objects, using fast simulation techniques that provide no guarantees on collision resolution. Our evaluation includes complex self-collision scenarios with a large number of active contacts, showing that our method can successfully handle them by introducing a relatively minor computational overhead.

Note on the action with the Schwarzian at the stretched horizon

In this paper, we discuss the quantization of an interesting model of Carlip which appeared recently. It shows a way to associate boundary degrees of freedom to the stretched horizon of a stationary non-extremal black hole, as has been done in JT gravity for near-extremal black holes. The path integral now contains an integral over the boundary degrees of freedom, which are time reparametrizations of the stretched horizon keeping its length fixed. These boundary degrees of freedom can be viewed as elements of $Diff(S^1)/S^1$, which is the coadjoint orbit of an ordinary coadjoint vector under the action of the Virasoro group. From the symplectic form on this manifold, we obtain the measure in the boundary path integral. Doing a one-loop computation about the classical solution, we find that the one-loop answer is not finite, signalling that either the classical solution is unstable or there is an indefiniteness problem with this action, similar to the conformal mode problem in quantum gravity. Upon analytically continuing the field, the boundary partition function we get is independent of the inverse temperature and does not contribute to the thermodynamics at least at one-loop. This is in contrast to the study of near-extremal black holes in JT gravity, where the entire contribution to thermodynamics is from boundary degrees of freedom.

The effect of the motion attributes of spokes-characters on app launch pages on brand memory

PurposeThe use of brand slogans that represent brand concepts on app launch pages can improve user brand impressions. The purpose of this paper is to investigate the impact of using animated or static spokes-characters with brand slogans on app launch pages.Design/methodology/approachUsing the theory of attention selection, the authors conducted two experiments to study the boundary and mediation path of the influence of the motion attributes of spokes-characters (static vs animated) on brand memory based on app launch time (3 s vs 5 s), user engagement with spokes-characters and the level of attention to brand slogans.FindingsStudy 1 explores the effect of the interaction between launch time and the motion attributes of spokes-characters on brand memory. The results show that when the launch time of the app is 3 s, the advertisement memory effect of using a static spokes-character is better than that of using an animated spokes-character; when the launch time of the app is 5 s, the advertisement memory effect of using an animated spokes-character is better than that of using a static spokes-character. Study 2 shows that user engagement with spokes-characters and the level of attention given to brand slogans play a continuous mediating role in the effect of the interaction between launch time and the motion attributes of spokes-characters on brand memory.Originality/valueThis paper contributes to the marketing literature by expanding the knowledge of spokes-characters and animated visual images, providing new insights for future research.

Fourier series and Search Space Reduction based Control profiles for Reentry Trajectory Optimization

In this paper, the reentry trajectory of a space shuttle is obtained using search space reduction (SSR) optimization technique along with the finite Fourier series-based parametrization of control variables. The reentry trajectory design for the space shuttle is most important and challenging because of non-linear entry dynamics, the vehicle being unpowered, the presence of boundary conditions and path constraints that are to be satisfied accurately. To solve this problem, it is essential to find optimal control profiles such as bank angle and angle of attack using which optimal reentry trajectory is generated. In this paper, finite Fourier series-based parametrization of the angle of attack and bank angle is proposed. To show that this novel parametrization approach results in a reentry trajectory, three reentry mission objectives are considered such as maximizing the crossrange, minimizing the total heat experienced by the vehicle and minimizing the total heat with mínimum oscillations in reentry trajectory. Further, the optimal Fourier coefficients are obtained using the search space reduction optimization technique to achieve mentioned reentry mission objectives. The simulation results show that this parametrization method has resulted in optimal reentry trajectories which satisfy the terminal constraints accurately.

Boundary path groupoids of generalized Boolean dynamical systems and their C⁎-algebras

In this paper, we provide two types of boundary path groupoids from a generalized Boolean dynamical system (B,L,θ,Iα). For the first groupoid, we associate an inverse semigroup to a generalized Boolean dynamical system and use the tight spectrum T as the unit space of a groupoid Γ(B,L,θ,Iα) that is isomorphic to the tight groupoid Gtight. The other one is defined as the Renault-Deaconu groupoid Γ(∂E,σE) arising from a topological correspondence E associated with a generalized Boolean dynamical system. We then prove that the tight spectrum T is homeomorphic to the boundary path space ∂E obtained from the topological correspondence. Using this result, we prove that the groupoid Γ(B,L,θ,Iα) equipped with the topology induced from the topology on Gtight is isomorphic to Γ(∂E,σE) as a topological groupoid. Finally, we show that their C⁎-algebras are isomorphic to the C⁎-algebra of the generalized Boolean dynamical system.

Efficient estimation of boundary integrals for path-space differentiable rendering

Boundary integrals are unique to physics-based differentiable rendering and crucial for differentiating with respect to object geometry. Under the differential path integral framework---which has enabled the development of sophisticated differentiable rendering algorithms---the boundary components are themselves path integrals. Previously, although the mathematical formulation of boundary path integrals have been established, efficient estimation of these integrals remains challenging. In this paper, we introduce a new technique to efficiently estimate boundary path integrals. A key component of our technique is a primary-sample-space guiding step for importance sampling of boundary segments. Additionally, we show multiple importance sampling can be used to combine multiple guided samplings. Lastly, we introduce an optional edge sorting step to further improve the runtime performance. We evaluate the effectiveness of our method using several differentiable-rendering and inverse-rendering examples and provide comparisons with existing methods for reconstruction as well as gradient quality.

RoboPV: An integrated software package for autonomous aerial monitoring of large scale PV plants

In this paper, a novel software package, called RoboPV, is introduced for autonomous aerial monitoring of PV plants. RoboPV automatically performs aerial monitoring of PV plants, from optimal trajectory planning to image processing and pattern recognition for real-time fault detection and analysis. RoboPV consists of four integrated components: boundary area detection, path planning, dynamic processing, and fault detection. To design an optimal flight path, aerial images of PV plants, which have been collected from experimental flights, are given as inputs to a developed encoder-decoder deep learning architecture to extract boundary points of PV plants automatically. Then, a novel path planning algorithm is conducted by RoboPV to design an optimal flight path with full coverage of whole regions of the PV plant. Aerial images are analysed in real-time during the flight by a high precise neural network trained for automatic fault detection. In this study, several decision-making and maneuver algorithms were developed for various real-world flight conditions to improve the performance of RoboPV during an autonomous aerial inspection. RoboPV is a modular processing library that can be installed on any micro-computer processor with a low computational power. Moreover, supporting the MAVLink communication protocol enables RoboPV to connect with an intelligent Pixhawk flight autopilot and navigate a wide range of multi-rotors. To demonstrate the performance of RoboPV, a six degrees of freedom dynamic model of a multi-rotor is developed in a SIMULINK environment with a defined aerial monitoring mission on three different real megawatt-scale PV plants. The results prove that RoboPV can execute the autonomous aerial inspection with an overall accuracy of 93% for large-scale PV plants.

Orbit equivalence of higher-rank graphs

We study the notion of continuous orbit equivalence of finitely-aligned higher-rank graphs. We show that there is a continuous orbit equivalence between two finitely-aligned higher-rank graphs that preserves the periodicity of boundary paths if and only if the boundary path groupoids are isomorphic. We also study eventual one-sided conjugacy of finitely-aligned higher-rank graphs and two-sided conjugacy of row-finite higher-rank graphs.

Accurate floorplan reconstruction using geometric priors

We present an accurate and automatic bottom-up floorplan reconstruction method by leveraging geometric priors extracted from raw point clouds of indoor scenes. Compared to two state-of-the-art methods which adopt point density as priors only, our designed geometric priors integrate point density with indoor area recognition and normal information. These geometric priors are used to calculate the confidence score for each unit region as part of the external boundaries. A cost function is developed according to the confidence scores and the normals along a certain edge, as well as the edge length. By minimizing the cost function, we can automatically estimate candidate edges, and connect them edge by edge to generate rough external boundaries. After diminishing the redundant edges, we can finally solve for a fine closed-loop external boundary path via an efficient heuristic method. We validate our method on intensive real indoor scenes. Experimental results show that our method outperforms two state-of-the-art methods in terms of reconstructing accurate external floorplan boundaries.

Tool path planning on triangular mesh surfaces based on the shortest boundary path graph

ABSTRACT In this paper, a new method is developed for tool path planning on triangular mesh surfaces with consideration of the scallop height restriction and the path smoothness. This method first maps the triangular mesh surface into a unit disk region by using a harmonic map algorithm, and then the shortest boundary path graph (SBPG) is constructed on the unit disk region to describe the shortest geodesic distance from each mesh vertex to the surface boundary. The tool path is then obtained by inversely mapping the contours of SBPG from the harmonic mapped region to the physical space of mesh surface. During this process, a subdivision method is used to boost the computing efficiency and a smoothing treatment is conducted on the SBPG to improve the path smoothness. The tool path planning is performed starting from the surface boundary in an iteration process. Taking the level difference of SBPG contours as the initial path interval and being supplemented by a correction process, the maximal step distance between any two paths, which meets the requirement of scallop height restriction, can be determined efficiently. Typical simulation cases and experiments are carried out to illustrate the effectiveness of the proposed method.

RECOVERING THE BOUNDARY PATH SPACE OF A TOPOLOGICAL GRAPH USING POINTLESS TOPOLOGY

AbstractFirst, we generalize the definition of a locally compact topology given by Paterson and Welch for a sequence of locally compact spaces to the case where the underlying spaces are $T_{1}$ and sober. We then consider a certain semilattice of basic open sets for this topology on the space of all paths on a graph and impose relations motivated by the definitions of graph C*-algebra in order to recover the boundary path space of a graph. This is done using techniques of pointless topology. Finally, we generalize the results to the case of topological graphs.

In-Situ optical Microscopy Corrosion Experiments for Correlating Microstructure to Corrosion Susceptibility in Aluminum Alloy

Aluminum-Magnesium alloys (5xxx series) are widely used in marine applications, structural components in transportation, and military due to their high corrosion resistance, low density, and good mechanical properties. However, at moderate and high temperatures (>50oC) these alloys are vulnerable to sensitization, or precipitation of β phase (Al3Mg2) preferentially on grain boundaries, resulting in susceptibility to intergranular corrosion and environmentally induced stress corrosion cracking. The primary research theme of this talk is to understand how microstructure variations dictate local corrosion susceptibility of aluminum 5456 in corrosive environments. To explore microstructure effects, we corroded sensitized aluminum 5456 in a dilute nitric acid solution. Prior to corrosion, electron backscatter diffraction (EBSD) was used to characterize the microstructure and deformation state of the alloy in terms of the grain structure, geometrically necessary dislocation density, constituent particles, and grain boundary character. In situ optical microscopy corrosion experiments were then used to directly observe corrosion initiation and propagation behavior, with fiducial markers used to correlate the observed corrosion behavior with the characterized microstructure. Image recognition algorithms facilitated the quantification of corrosion sites and corrosion propagation rates as a function of time and grain boundary path. Obtaining this information is crucial as the microstructural features that govern corrosion initiation may be different from the features that dictate propagation pathways. My talk will focus on the microstructure characteristics that dictate corrosion susceptibility to initiation as well as propagation and the relevance of these data for developing corrosion- and sensitization-resistant microstructures.

Evaluation of Grain Boundary Network and Improvement of Intergranular Cracking Resistance in 316L Stainless Steel after Grain Boundary Engineering.

For understanding the improvement of intergranular stress corrosion cracking (IGSCC) propagation in grain boundary engineering (GBE)-processed metals exposed to a simulated pressurized water reactor (PWR) environment, characteristics of the grain boundary network of 316L stainless steel before and after GBE were investigated and compared, including proportions both in length and in number of ∑3n boundaries, sizes, and topology of grain clusters (or twin-related domains), and connectivity of random boundaries. The term through-view random boundary path (TRBP) was proposed to evaluate the random boundary connectivity. A TRBP is a chain of end-to-end connected crack-susceptible boundaries that passes through the entire mapped microstructure. The work provides the following key findings: (I) the length fraction of ∑3n boundaries was increased to approximately 75% after GBE, but the number fraction was only approximately 50%; (II) a connected non-twin boundary network still existed in the GBE sample due to the formation of grain clusters; (III) the GBE sample exhibited a higher resistance to IGSCC; and (IV) as the twin boundary fraction increased, the number of TRBPs decreased and the normalized length of the minimum TRBP increased monotonically, leading to a higher resistance to IGSCC.