Segment Boundaries Research Articles

Along-strike extent of earthquakes on multi-segment reverse faults; insights from the Nevis-Cardrona Fault, Aotearoa New Zealand

Evaluating fault segmentation is important for our understanding of seismic hazard assessment and fault growth. However, it is still unclear what controls if reverse fault earthquakes will rupture across segment boundaries. Here, we combine fault mapping and trench data from the low slip rate (0.04-0.15 mm/yr) multi-segment Nevis-Cardrona Fault (NCF) in the South Island of Aotearoa New Zealand to assess if it has ruptured in single or multi-segment earthquakes during the late Quaternary. Two new trenches on its Nevis segment provide stratigraphic evidence for two surface rupturing earthquakes, which through Optically Stimulated Luminscence dating and OxCal modelling, are constrained to have occurred at 28.9 +12.9 -9.1 ka and 12.8 ± 4.9 ka. The most recent timing is only weakly correlated to surface rupture timings from two trenches along the NCF's NW Cardrona segment. Furthermore, the 2 ± 1 m Nevis segment single event displacements we estimate would be unusually low for a ~85 km long NCF multi-segment rupture. We therefore surmise that late Quaternary NCF surface rupturing earthquakes did not rupture through ~30-50° bends that link these segments. Our trench data and fault mapping also indicate lower slip rates on the Nevis segment than previous studies (0.04-0.1 mm/yr vs 0.4 mm/yr).

TopoSinGAN: Learning a Topology-Aware Generative Model from a Single Image

Generative adversarial networks (GANs) have significantly advanced synthetic image generation, yet ensuring topological coherence remains a challenge. This paper introduces TopoSinGAN, a topology-aware extension of the SinGAN framework, designed to enhance the topological accuracy of generated images. TopoSinGAN incorporates a novel, differentiable topology loss function that minimizes terminal node counts along predicted segmentation boundaries, thereby addressing topological anomalies not captured by traditional losses. We evaluate TopoSinGAN using agricultural and dendrological case studies, demonstrating its capability to maintain boundary continuity and reduce undesired loop openness. A novel evaluation metric, Node Topology Clustering (NTC), is proposed to assess topological attributes independently of geometric variations. TopoSinGAN significantly improves topological accuracy, reducing NTC index values from 15.15 to 3.94 for agriculture and 14.55 to 2.44 for dendrology, compared to the baseline SinGAN. Modified FID evaluations also show improved realism, with lower FID scores: 0.1914 for agricultural fields compared to 0.2485 for SinGAN, and 0.0013 versus 0.0014 for dendrology. The topology loss enables end-to-end training with direct topological feedback. This new framework advances the generation of topologically accurate synthetic images, with applications in fields requiring precise structural representations, such as geographic information systems (GIS) and medical imaging.

Multi-Modal LiDAR Point Cloud Semantic Segmentation with Salience Refinement and Boundary Perception

Point cloud segmentation is essential for scene understanding, which provides advanced information for many applications, such as autonomous driving, robots, and virtual reality. To improve the accuracy and robustness of point cloud segmentation, many researchers have attempted to fuze camera images to complement the color and texture information. The common fusion strategy is the combination of convolutional operations with concatenation, element-wise addition or element-wise multiplication. However, conventional convolutional operators tend to confine the fusion of modal features within their receptive fields, which can be incomplete and limited. In addition, the inability of encoder–decoder segmentation networks to explicitly perceive segmentation boundary information results in semantic ambiguity and classification errors at object edges. These errors are further amplified in point cloud segmentation tasks, significantly affecting the accuracy of point cloud segmentation. To address the above issues, we propose a novel self-attention multi-modal fusion semantic segmentation network for point cloud semantic segmentation. Firstly, to effectively fuze different modal features, we propose a self-cross fusion module (SCF), which models long-range modality dependencies and transfers complementary image information to the point cloud to fully leverage the modality-specific advantages. Secondly, we design the salience refinement module (SR), which calculates the importance of channels in the feature maps and global descriptors to enhance the representation capability of salient modal features. Finally, we propose the local-aware anisotropy loss measure the element-level importance in the data and explicitly provide boundary information for the model, which alleviates the inherent semantic ambiguity problem in segmentation networks. Extensive experiments on two benchmark datasets demonstrate that our proposed method surpasses current state-of-the-art methods.

Toward assessment of rupture risk predictors in abdominal aortic aneurysms including intraluminal thrombus based on 3D+t ultrasound images.

Image-based patient-specific rupture risk analysis for abdominal aortic aneurysms (AAAs) has shown considerable promise. However, clinical translation has been hampered by the use of invasive and costly imaging modalities. Despite being a promising alternative, ultrasound (US) makes a full analysis, including intraluminal thrombus (ILT), not trivial. This study explored the feasibility of assessing AAA rupture risk parameters, e.g., peak wall stress (PWS) and peak wall rupture index (PWRI), using US-based models of the AAA wall, finally including ILT. Three-dimensional US data were segmented from a group of AAA patients whose CT data were available within 30 days. The segmented vessel wall and ILT boundaries were converted into a mesh including and excluding ILT to evaluate the effect of adding ILT on the model output. US-based rupture risk parameters (PWS and PWRI) were compared to CT-based results. The US-based PWS and PWRI, including ILT, showed good agreement with CT-based results, and the model excluding ILT showed no significant bias in wall stress or rupture index. When including ILT, a lower US-based wall stress and rupture index of 7.2% and 3.8% were found, respectively. The intraclass correlation coefficient (ICC) of PWS was 0.60. The highest ICC was found for the PWRI (ICC = 0.86), indicating good absolute agreement. This study showed that PWRI can be estimated with US when including the ILT, yielding comparable results to CT, and good absolute agreement. Future work should focus on improving the contrast of ILT in US, since this will be essential to performing large-scale studies in AAA cohorts.

RSPS-SAM: A Remote Sensing Image Panoptic Segmentation Method Based on SAM

Satellite remote sensing images contain complex and diverse ground object information and the images exhibit spatial multi-scale characteristics, making the panoptic segmentation of satellite remote sensing images a highly challenging task. Due to the lack of large-scale annotated datasets for panoramic segmentation, existing methods still suffer from weak model generalization capabilities. To mitigate this issue, this paper leverages the advantages of the Segment Anything Model (SAM), which can segment any object in remote sensing images without requiring any annotations and proposes a high-resolution remote sensing image panoptic segmentation method called Remote Sensing Panoptic Segmentation SAM (RSPS-SAM). Firstly, to address the problem of global information loss caused by cropping large remote sensing images for training, a Batch Attention Pyramid was designed to extract multi-scale features from remote sensing images and capture long-range contextual information between cropped patches, thereby enhancing the semantic understanding of remote sensing images. Secondly, we constructed a Mask Decoder to address the limitation of SAM requiring manual input prompts and its inability to output category information. This decoder utilized mask-based attention for mask segmentation, enabling automatic prompt generation and category prediction of segmented objects. Finally, the effectiveness of the proposed method was validated on the high-resolution remote sensing image airport scene dataset RSAPS-ASD. The results demonstrate that the proposed method achieves segmentation and recognition of foreground instances and background regions in high-resolution remote sensing images without the need for prompt input, while providing smooth segmentation boundaries with a panoptic segmentation quality (PQ) of 57.2, outperforming current mainstream methods.

Mamba- and ResNet-Based Dual-Branch Network for Ultrasound Thyroid Nodule Segmentation.

Accurate segmentation of thyroid nodules in ultrasound images is crucial for the diagnosis of thyroid cancer and preoperative planning. However, the segmentation of thyroid nodules is challenging due to their irregular shape, blurred boundary, and uneven echo texture. To address these challenges, a novel Mamba- and ResNet-based dual-branch network (MRDB) is proposed. Specifically, the visual state space block (VSSB) from Mamba and ResNet-34 are utilized to construct a dual encoder for extracting global semantics and local details, and establishing multi-dimensional feature connections. Meanwhile, an upsampling-convolution strategy is employed in the left decoder focusing on image size and detail reconstruction. A convolution-upsampling strategy is used in the right decoder to emphasize gradual feature refinement and recovery. To facilitate the interaction between local details and global context within the encoder and decoder, cross-skip connection is introduced. Additionally, a novel hybrid loss function is proposed to improve the boundary segmentation performance of thyroid nodules. Experimental results show that MRDB outperforms the state-of-the-art approaches with DSC of 90.02% and 80.6% on two public thyroid nodule datasets, TN3K and TNUI-2021, respectively. Furthermore, experiments on a third external dataset, DDTI, demonstrate that our method improves the DSC by 10.8% compared to baseline and exhibits good generalization to clinical small-scale thyroid nodule datasets. The proposed MRDB can effectively improve thyroid nodule segmentation accuracy and has great potential for clinical applications.

Enhancing Brain Tumor Diagnosis with L-Net: A Novel Deep Learning Approach for MRI Image Segmentation and Classification.

Background: Brain tumors are highly complex, making their detection and classification a significant challenge in modern medical diagnostics. The accurate segmentation and classification of brain tumors from MRI images are crucial for effective treatment planning. This study aims to develop an advanced neural network architecture that addresses these challenges. Methods: We propose L-net, a novel architecture combining U-net for tumor boundary segmentation and a convolutional neural network (CNN) for tumor classification. These two units are coupled such a way that the CNN classifies the MRI images based on the features extracted by the U-net while segmenting the tumor, instead of relying on the original input images. The model is trained on a dataset of 3064 high-resolution MRI images, encompassing gliomas, meningiomas, and pituitary tumors, ensuring robust performance across different tumor types. Results: L-net achieved a classification accuracy of up to 99.6%, surpassing existing models in both segmentation and classification tasks. The model demonstrated effectiveness even with lower image resolutions, making it suitable for diverse clinical settings. Conclusions: The proposed L-net model provides an accurate and unified approach to brain tumor segmentation and classification. Its enhanced performance contributes to more reliable and precise diagnosis, supporting early detection and treatment in clinical applications.

Trusted microelectronics: reverse engineering chip die using U-Net convolutional network

In the field of integrated circuits (IC) reverse engineering, accurate IC die image segmentation is critical for ensuring trust and detecting counterfeits. This study introduces a deep learning-based methodology utilizing a U-Net Convolutional Neural Network (CNN) tailored for IC image segmentation. Our model excels in processing complex IC images with noise, achieving superior segmentation accuracy. The model was evaluated on a dataset of 512 × 512 pixel IC die images, achieving a mean Intersection over Union (IoU) of 81.2%, which is a significant improvement over traditional image processing techniques that achieve an IoU around 65.3%. During training, the model’s Dice Loss showed a sharp decrease, as depicted in the provided graph, highlighting the model’s ability to effectively learn and refine segmentation boundaries. Simultaneously, the training accuracy, as illustrated in the accompanying accuracy graph, improved steadily, reaching approximately 60% but still rising. This convergence of Dice Loss and the upward trend in accuracy demonstrate the model’s robust performance across varying noise levels and its effectiveness in producing precise segmentation outputs. This work underscores the effectiveness of CNNs, particularly the U-Net architecture, in enhancing the accuracy and reliability of IC die image analysis, paving the way for improved IC manufacturing quality assurance.

Segmentation of Glacier Area Using U-Net through Landsat Satellite Imagery for Quantification of Glacier Recession and Its Impact on Marine Systems

Glaciers have experienced a global trend of recession within the past century. Quantification of glacier variations using satellite imagery has been of great interest due to the importance of glaciers as freshwater resources and as indicators of climate change. Spatiotemporal glacier dynamics must be monitored to quantify glacier variations. The potential methods to quantify spatiotemporal glacier dynamics with increasing complexity levels include detecting the terminus location, measuring the length of the glacier from the accumulation zone to the terminus, quantifying the glacier surface area, and measuring glacier volume. Although some deep learning methods designed purposefully for glacier boundary segmentation have achieved acceptable results, these models are often localized to the region where their training data were acquired and further rely on the training sets that were often curated manually to highlight glacial regions. Due to the very large number of glaciers, it is practically impossible to perform a worldwide study of glacier dynamics using manual methods. As a result, an automated or semi-automated method is highly desirable. The current study has built upon our previous works moving towards identification methods of the 2D glacier profile for glacier area segmentation. In this study, a deep learning method is proposed for segmentation of temporal Landsat images to quantify the glacial region within the Mount Cook/Aoraki massif located in the Southern Alps/Kā Tiritiri o te Moana of New Zealand/Aotearoa. Segmented glacial regions can be further utilized to determine the relationship of their variations due to climate change. This model has demonstrated promising performance while trained on a relatively small dataset. The permanent ice and snow class was accurately segmented at a 92% rate by the proposed model.

IC-IE-AKS-O: an automatic recognition method for coastal slope landslide areas

Automatically and accurately identifying the deformation zone of coastal slope landslides is crucial for exploring the mechanism of landslides and predicting landslide disasters. To this end, this study proposes an integrated automatic recognition method combining Image Clipping (IC), Image Information Enhancement (IE), Adaptive K-means Clustering Segmentation (AKS), and Optimization (O): IC-IE-AKS-O, which achieves precise extraction of the deformation area in coastal slope landslide images. Firstly, due to the more complex natural environment of field slopes, to extend the monitoring duration, we introduce a hierarchical operation algorithm based on the HSV color model, which effectively mitigates the impact of sunlight, rain, and foggy weather on image recognition accuracy. Secondly, this study proposes a 2D landslide image segmentation technique that combines K-means clustering with global threshold segmentation for landslide images, enabling the segmentation of small image regions with precision. Finally, we combine image information enhancement technology with image segmentation technology. To verify its effectiveness, we identify a landslide image of a coastal slope in Pingtan. The method displays an average relative error of 5.20% and 5.14% in the X and Y directions, respectively. Its advantages are threefold: (1) The combination of image information enhancement and segmentation techniques can more accurately identify landslide areas that appear blurred in the image; (2) expanding the temporal dimension of coastal slope monitoring; (3) providing excellent boundary conditions and segmentation results. The practical application of this method ensures the stable and accurate operation of the coastal slope monitoring system, providing a safeguard for the sustainable development of marine safety.

Updimensioning strategy derived from synthetic equiaxed grain structures for approximating 3D grain size distributions from 2D visualizations with 1D parameters

We generated synthetic equiaxed grain structures using computer graphics software to explore the relationship between various grain size determination methods and true three-dimensional (3D) grain diameters. Mirroring grain measurement techniques, the synthetic 3D grain structures are imaged as 2D micrographs which are measured to yield 1D grain size parameters. Synthetic grain structures provide data at a mass scale and permit exploration of both polished and fractured surface micrographs, revealing one-to-one correspondence between exposed 2D grain cross-sections and individual 3D grains. Analysis of this correspondence yielded a procedure to approximate 3D equiaxed grain size and volume distributions based on the mode of the 2D fractograph grain size distribution. The 3D approximation procedure is shown to be less susceptible to different imaging conditions that affect small, undiscernible grains compared to the standard planimetric and linear intercept methods, which by design also tend to underestimate the 3D grain diameter. The procedure requires larger sample sizes to lower variance and a deeper analysis which could become more practical with machine learning (ML) models for grain boundary segmentation, which synthetic grain structures can help train. This work lays the foundation for analyzing other grain distributions such as columnar and composite grains in similar depth.

Research on coastline extraction and dynamic change from remote sensing images based on deep learning

Accurate coastline extraction is crucial for the scientific management and protection of coastal zones. Due to the diversity of ground object details and the complexity of terrain in remote sensing images, the segmentation of sea and land faces challenges such as unclear segmentation boundaries and discontinuous coastline contours. To address these issues, this study improve the accuracy and efficiency of coastline extraction by improving the DeepLabv3+ model. Specifically, this study constructs a sea-land segmentation network, DeepSA-Net, based on strip pooling and coordinate attention mechanisms. By introducing dynamic feature connections and strip pooling, the connection between different branches is enhanced, capturing a broader context. The introduction of coordinate attention allows the model to integrate coordinate information during feature extraction, thereby allowing the model to capture longer-distance spatial dependencies. Experimental results has shown that the model can achieves a land-sea segmentation mean intersection over union (mIoU) ration and Recall of over 99% on all datasets. Visual assessment results show more complete edge details of sea-land segmentation, confirming the model’s effectiveness in complex coastal environments. Finally, using remote sensing data from a coastal area in China as an application instance, coastline extraction and dynamic change analysis were implemented, providing new methods for the scientific management and protection of coastal zones.

A method framework of semi-automatic knee bone segmentation and reconstruction from computed tomography (CT) images.

Accurate delineation of knee bone boundaries is crucial for computer-aided diagnosis (CAD) and effective treatment planning in knee diseases. Current methods often struggle with precise segmentation due to the knee joint's complexity, which includes intricate bone structures and overlapping soft tissues. These challenges are further complicated by variations in patient anatomy and image quality, highlighting the need for improved techniques. This paper presents a novel semi-automatic segmentation method for extracting knee bones from sequential computed tomography (CT) images. Our approach integrates the fuzzy C-means (FCM) algorithm with an adaptive region-based active contour model (ACM). Initially, the FCM algorithm assigns membership degrees to each voxel, distinguishing bone regions from surrounding soft tissues based on their likelihood of belonging to specific bone regions. Subsequently, the adaptive region-based ACM utilizes these membership degrees to guide the contour evolution and refine segmentation boundaries. To ensure clinical applicability, we further enhance our method using the marching cubes algorithm to reconstruct a three-dimensional (3D) model. We evaluated the method on six randomly selected knee joints. We evaluated the method using quantitative metrics such as the Dice coefficient, sensitivity, specificity, and geometrical assessment. Our method achieved high Dice scores for the femur (98.95%), tibia (98.10%), and patella (97.14%), demonstrating superior accuracy. Remarkably low root mean square distance (RSD) values were obtained for the tibia and femur (0.5±0.14 mm) and patella (0.6±0.13 mm), indicating precise segmentation. The proposed method offers significant advancements in CAD systems for knee pathologies. Our approach demonstrates superior performance in achieving precise and accurate segmentation of knee bones, providing valuable insights for anatomical analysis, surgical planning, and patient-specific prostheses.

Physically-guided open vocabulary segmentation with weighted patched alignment loss

Open vocabulary segmentation is a challenging task that aims to segment out the thousands of unseen categories. Directly applying CLIP to open-vocabulary semantic segmentation is challenging due to the granularity gap between its image-level contrastive learning and the pixel-level recognition required for segmentation. To address these challenges, we propose a unified pipeline that leverages physical structure regularization to enhance the generalizability and robustness of open vocabulary segmentation. By incorporating physical structure information, which is independent of the training data, we aim to reduce bias and improve the model’s performance on unseen classes. We utilize low-level structures such as edges and keypoints as regularization terms, as they are easier to obtain and strongly correlated with segmentation boundary information. These structures are used as pseudo-ground truth to supervise the model. Furthermore, inspired by the effectiveness of comparative learning in human cognition, we introduce the weighted patched alignment loss. This loss function contrasts similar and dissimilar samples to acquire low-dimensional representations that capture the distinctions between different object classes. By incorporating physical knowledge and leveraging weighted patched alignment loss, we aim to improve the model’s generalizability, robustness, and capability to recognize diverse object classes. The experiments on the COCO Stuff, Pascal VOC, Pascal Context-59, Pascal Context-459, ADE20K-150, and ADE20K-847 datasets demonstrate that our proposed method consistently improves baselines and achieves new state-of-the-art in the open vocabulary segmentation task.

3D Point Cloud Semantic Segmentation based on Multi-scale Dense Nested Networks

Aiming at the problem that the relationship between geometric features and semantic features is ignored in the point cloud data downsampling process, which leads to inaccurate segmentation of object boundaries and structural details, this paper proposes a 3D point cloud semantic segmentation network based on multi-scale dense nested type. Firstly, a dense nested network architecture is constructed by nesting multiple multi-scale feature fusion modules to fuse multi-scale features of different directions between encoder-decoder paths, so as to effectively propagate local ge-ometric context information and enhance the ability of cross-scale information interaction. Secondly, a local feature aggregation unit is constructed in the multi-scale feature fusion module, which strengthens the structural awareness within the local point set based on graph convolution and attention mechanism, and promotes the complementarity of local geometric features and abstract semantic information. Then, the cross-layer multi-loss supervision module is combined to further optimize the multi-scale feature propagation, which makes the network training more stable and improves the point cloud segmentation accuracy. Finally, this paper verified the proposed network on the S3DIS dataset. The experimental results show that the proposed network has the mean intersection over Union of 71.2% and the overall accuracy of 88.7%, which is 1.2 and 0.7 percentage points higher than RandLA-Net, respectively, which proves that the proposed network can effectively improve the accuracy of 3D point cloud semantic segmentation.

Fault geometry and kinematics at the intersection of the Zemuhe, Daliangshan and Xiaojiang Faults

The complexity of strike-slip fault segmentation affects the initiation, propagation, and termination of earthquake ruptures and the earthquake magnitude. Studying the fault geometry, kinematics, and segmentation provides fundamental knowledge for mitigating earthquake hazards along faults. The Zemuhe, Daliangshan, and Xiaojiang Faults intersect along the eastern boundary of the Tibetan Plateau in the area from Ningnan in Sichuan Province to Qiaojia in Yunnan Province. Although few large earthquakes have occurred on these faults, the relationships between the intersections of these three faults and earthquake rupture behavior in this region are poorly constrained. The interpretation of aerial photographs and detailed field surveys revealed the geometric pattern and fault kinematics in the area of intersection. The distribution patterns and focal depths near the faults were obtained via analysis of seismic data in the area of intersection. The northern segment of the Xiaojiang Fault deviates approximately 25° northwest of Qiaojia, forming a conspicuous bend. The Xiaojiang Fault continues to extend southeast of the Ningnan Basin, where it intersects with the southern segment of the Zemuhe Fault, forming a pull-apart basin approximately 4.5 km wide. The bend and Ningnan pull-apart basin mark the segmented boundary between the Zemuhe Fault and the Xiaojiang Fault, which may prevent the propagation of large earthquake ruptures along the eastern boundary fault. Moreover, the lack of obvious geometric complexity between the Daliangshan Fault and Xiaojiang Fault might hinder the prevention of earthquake rupture propagation. Additionally, our results suggest that different earthquake prevention and disaster reduction measures should be taken for different cities in the region.

TBConvL-Net: A hybrid deep learning architecture for robust medical image segmentation

Deep learning has shown great potential for automated medical image segmentation to improve the precision and speed of disease diagnostics. However, the task presents significant difficulties due to variations in the scale, shape, texture, and contrast of the pathologies. Traditional convolutional neural network (CNN) models have certain limitations when it comes to effectively modelling multiscale context information and facilitating information interaction between skip connections across levels. To overcome these limitations, a novel deep learning architecture is introduced for medical image segmentation, which takes advantage of CNNs and vision transformers. Our proposed model, named TBConvL-Net, involves a hybrid network that combines the local features of a CNN encoder–decoder architecture with long-range and temporal dependencies using biconvolutional long-short-term memory (LSTM) networks and vision transformers (ViT). This enables the model to capture contextual channel relationships in the data and account for the uncertainty of the segmentation over time. Additionally, we introduce a novel composite loss function that considers both segmentation robustness and boundary agreement of the predicted output with the gold standard. Our proposed model shows consistent improvement over the state of the art on ten publicly available datasets of seven different medical imaging modalities.

Computing the cut locus, Voronoi diagram, and signed distance function of polygons

This paper presents a new method for the computation of the generalized Voronoi diagram of planar polygons. First, we show that the vertices of the cut locus can be computed efficiently. This is achieved by enumerating the tripoints of the polygon, a superset of the cut locus vertices. This is the set of all points that are of equal distance to three distinct topological entities. Then our algorithm identifies and connects the appropriate tripoints to form the cut locus vertex connectivity graph, where edges define linear or parabolic boundary segments between the Voronoi regions, resulting in the generalized Voronoi diagram. Our proposed method is validated on complex polygon soups. We apply the algorithm to represent the exact signed distance function of the polygon by augmenting the Voronoi regions with linear and radial functions, calculating the cut locus both inside and outside.

GeGra: Approaching a generic model for quantitative grain size analysis from materials microscopy data using deep learning

Grain size has a significant impact on the properties of materials, and is crucial for predicting material properties. Traditional grain size measurement relies heavily on human operators, leading to subjective results, and existing machine learning methods are typically material-specific, requiring significant labeling and training efforts for each new material. This paper provides insight into developing a deep learning-based generic grain boundary detection model (GeGra) from different material micrographs. The model is trained on 1006 images from various microscopy techniques such as light optical, Kerr, and scanning electron microscopy, acquired at different magnifications for different materials such as copper, austenite, brass, sintered hard magnet, hard metal, bronze, nickel silver, and aluminum. The developed GeGra model effectively handles visual artifacts and substructures such as twin grains, which often pose challenges for material-specific, state-of-the-art grain boundary segmentation models. The developed model achieved an IoU score of 69 % on a diverse test set and enables accurate grain size analysis using external image analysis software in less than one minute, according to ASTM standards, which is more than 5 times faster than the manual method. The developed model prioritizes generality with objective that it can have broader applicability for various materials instead of high-precision grain boundary detection. Additionally, the model has the potential to be a foundational tool for generalized grain size analysis in material microscopy, reducing the effort required for such analysis and assisting both material science experts and machine learning users.

Isoperimetric Control of an Expanding Set

Consider a contaminated region in a 2-dimensional plane that is expanding with unit normal speed. Our goal is to apply a control function (e.g. pesticide) along the boundary of this region to reduce the contaminated area to zero in the shortest possible time, while consistently clearing a fixed amount of land per unit time. It has been proven that when the initial contamination forms a convex set, an optimal eradication strategy requires applying pesticide to the boundary segments with the highest curvature at each moment. This is equivalent to adopting a myopic strategy that minimizes the perimeter of the contaminated region at each time step. This result provided insight for developing numerical methods to compute approximations of these optimal strategies for convex sets. Namely, our simulation consists in alternating between computing the isoperimetric (perimeter-minimizing) profile with a convex constraint and then dilating the resulting set by a radius equal to the time mesh. This process is repeated until the shape reaches a circle, which can then be trivially scaled down to a point. The isoperimetric profile is obtained through morphological opening, an erosion-dilation operator commonly used in image processing for noise removal. A major open problem remains: a full characterization of optimal eradication strategies for initial contaminations of general shapes. We have applied the above numerical scheme with non-convex constraints to gain some intuition in this broader context. This may entail replacing the morphological opening operator with a more general algorithm relying on the medial axis of a shape. It turns out that, in some configurations, it is more effective to split the contamination into several components and shrink them separately.