Point Density Research Articles

Spatial–Temporal Reconstruction of Trajectories in Free Space Using Automatic Target Position Detection Data

The monitoring technology for targets such as aircraft and vehicles has rapidly developed in recent years and is widely used in national airspace security supervision, urban traffic supervision, and the tracking of special targets. However, the sparse trajectories of targets, primarily caused by the insufficient density of monitoring points, significantly reduce their usability. Therefore, it is important to reconstruct the target trajectories. Existing methods for the reconstruction of target trajectories often rely on topological data and convert trajectory reconstruction into a trajectory matching problem. Such methods heavily rely on topological data and cannot reconstruct trajectories in free space. To address this issue, we proposed a trajectory reconstruction method, named Prob-Attn, which does not rely on topological data and can accurately reconstruct target trajectories in free space. This method can be divided into two steps: first, a spatial trajectory construction module is proposed to determine the spatial trajectories of targets. Then, based on the reconstructed spatial trajectory of the target, this paper proposes a time series prediction model based on historical trajectories and an attention mechanism, which considers the impact of the target’s activity cycle and the surrounding status to predict the time series inside the trajectory. Finally, the proposed method is evaluated on real automatic vehicle detection datasets collected in Chongqing, China. The experimental results show that, compared with traditional methods, the proposed method can reconstruct the spatiotemporal trajectory of the target more accurately. The reconstructed trajectory data can be used for critical applications such as the intent and behavior analysis of key targets in national airspace and ground areas, providing valuable insights into security and safety.

Early Diabetic Retinopathy Evaluation With OCTA: A Study on Vascular Branching and Fragmentation.

The purpose of this study was to quantitatively evaluate the branching patterns and vascular fragmentation features in preclinical and early diabetic retinopathy (DR) using optical coherence tomography angiography (OCTA). OCTA metrics, including branch node number (BNN), branch node density (BND), end point number (EPN), end point density (EPD), fragmented vessel segment count (FVSC), and fragmented vascular length ratio (FVLR), were measured in foveal and parafoveal regions within superficial and deep vascular plexus (SVP and DVP) in the retina. Compared to healthy control (HCs), both BNN and BND exhibited a significant decrease in individuals with mild DR across both retinal layers, and also in diabetes mellitus without DR (no DR) within DVP. EPD showed a significant increase in mild DR cases compared to HCs, except for the foveal region in SVP; however, EPN did not demonstrate a significant difference among the three groups. Increases in both FVSC and FVLR were significant across all areas and in both layers of the retina. Notably, these metrics showed more pronounced differentiation in the DVP than the SVP. Foveal BND and BNN in DVP reveal vascular alterations indicative of preclinical DR. Indicators such as EPD, FVSC, and FVLR in DVP correlate with early DR changes and are useful for its early detection. These initial findings demonstrate the potential and benefits of these quantitative OCTA indices for delineating DR-associated alterations in the retinal microvasculature, indicating their potential clinical utility for improved DR screening.

Accuracy assessment of recent global ocean tide models in coastal waters of the European North West Shelf

The accuracy of global ocean tide models is assessed in coastal waters of the European North West Shelf to ascertain where higher resolution local (forecast) models are most needed for geophysical and navigational applications, and which global models are most suitable for providing boundary conditions for regional and local tide models. Five recent global ocean tide models (FES2014b, EOT20, TPXO9-atlas-v5, GOT4.10c, and DTU16) are considered, with the models first compared by interpolating them onto common grids and computing the mean absolute deviation at each grid point. Coastline tide gauge and offshore bottom pressure sensor data were collated from several sources to give a total of 279 observation sites for evaluating model accuracy, including observational values from 137 locations that have not previously been released and have therefore not been assimilated into any of the global models tested. The residual errors between each model’s predicted phasor and the corresponding observed phasor were calculated at each observation location, and quantified using the root mean square (RMS) and median absolute residual (MAR) for the eight tidal constituents M2, S2, N2, O1, K1, K2, P1, and Q1. To avoid RMS values being biased by observation point density, a Voronoi-weighted RMS based on the water area of the Voronoi polygon about each observation location was also developed and used. Four zones were defined based on ocean depth to gauge model performance, and model inaccuracy is again demonstrated in near-shore regions. Seven further zones were defined based on geographical areas, which reveals inhomogeneity among the global models. The smallest overall root sum square (RSS) RMS error across all eight constituents arises with FES2014b, although TPXO9-atlas-v5 has the best performance when using the MAR and Voronoi-weighted RMS metrics. Using only the 137 observation sites that have not been assimilated by any model and therefore provide an independent accuracy assessment, FES2014b exhibits the smallest errors at the coastline, with an RSS RMS of 24.46 cm. All models exhibit larger errors with the 137 independent observation sites than with all 279 observation sites, with an average overall increase in RSS RMS error of 12%, and an increase of 30% for coastline tide gauges, highlighting the need for local model development in these areas.

Control parameter layout of compressor airfoils and adaptive optimization method for boundary extension

Parameterized optimization methods are effective approaches for achieving high aerodynamic performance in compressors. Traditional parameterized optimization methods rely on a designer's preselected control parameter layout (including control frame orientation, point density distribution, control point displacement direction, number of variables, and variable ranges), which are purely based on empirical knowledge without sufficient theoretical basis. This paper selects the free-form deformation (FFD) method and Bayesian algorithm as the parameterization method and optimization algorithm for compressor airfoil optimization and studies the influence of FFD control parameter layouts on aerodynamic optimization performance. Additionally, an adaptive optimization method for control parameters based on FFD is proposed, where the orientation and density of the control framework can be incorporated as variables into the control parameters. During the optimization process, the range of design variables is adaptively expanded. A comparison between FFD optimization results based on B-spline and Bernstein basis functions shows that the former achieves an average performance improvement of 4% relative to the latter. Furthermore, an optimization method with an infinitely expandable boundary based on Bernstein basis FFD is proposed, which improves the performance by 12% compared to general adaptive boundary expansion methods.

A probabilistic approach driven credit card anomaly detection with CBLOF and isolation forest models

Businesses throughout the world are starting to accept more and more electronic payment alternatives for in-person and online purchases. Unusual behaviour such as internet fraud and payment defaults, which may lead to significant monetary losses, have become increasingly widespread as credit card use in online buying has expanded. To find a solution to this problem, researchers looked into a number of different machine learning classifiers that may identify irregularities in the data pertaining to credit card transactions. Overlapping class samples and an uneven distribution of classes make it hard to find outliers in this data. General learning algorithms may favour samples from the majority class, and the detection rate of anomalies in samples from minority classes is thus low. Our proposed Credit Card Outlier Detection (CCOD) model incorporates many machine learning algorithms to enhance the detection rates of credit card anomalies. Utilising the stratified sampling technique and the k-fold cross-validation process, we address data imbalance and overfitting. Working with optimized selected features rather than all features reduces the danger of overfitting and improves model performance. It has been noted that the findings of Cluster-Based Local Outlier Factor (CBLOF) classifier on European Credit Card Dataset and Isolation Forest classifier on German credit card dataset were superior to those of the other classifiers with Mathew correlation coefficient value of 0.95 and 0.97 respectively. The CBLOF, an advanced outlier detection method that evaluates the local density of data points within clusters. By comparing the density of a point to the densities of its surrounding clusters, CBLOF identifies outliers based on their deviation from normal cluster behaviour. In general, this CCOD model shows that it is better at dealing with issues like uneven class distribution, overfitting, and classes that overlap.

3D Reconstruction with Fast Dipole Sums

We introduce a method for high-quality 3D reconstruction from multi-view images. Our method uses a new point-based representation, the regularized dipole sum, which generalizes the winding number to allow for interpolation of per-point attributes in point clouds with noisy or outlier points. Using regularized dipole sums, we represent implicit geometry and radiance fields as per-point attributes of a dense point cloud, which we initialize from structure from motion. We additionally derive Barnes-Hut fast summation schemes for accelerated forward and adjoint dipole sum queries. These queries facilitate the use of ray tracing to efficiently and differentiably render images with our point-based representations, and thus update their point attributes to optimize scene geometry and appearance. We evaluate our method in inverse rendering applications against state-of-the-art alternatives, based on ray tracing of neural representations or rasterization of Gaussian point-based representations. Our method significantly improves 3D reconstruction quality and robustness at equal runtimes, while also supporting more general rendering methods such as shadow rays for direct illumination.

MVImgNet2.0: A Larger-scale Dataset of Multi-view Images

MVImgNet is a large-scale dataset that contains multi-view images of ~220k real-world objects in 238 classes. As a counterpart of ImageNet, it introduces 3D visual signals via multi-view shooting, making a soft bridge between 2D and 3D vision. This paper constructs the MVImgNet2.0 dataset that expands MVImgNet into a total of ~520k objects and 515 categories, which derives a 3D dataset with a larger scale that is more comparable to ones in the 2D domain. In addition to the expanded dataset scale and category range, MVImgNet2.0 is of a higher quality than MVImgNet owing to four new features: (i) most shoots capture 360° views of the objects, which can support the learning of object reconstruction with completeness; (ii) the segmentation manner is advanced to produce foreground object masks of higher accuracy; (iii) a more powerful structure-from-motion method is adopted to derive the camera pose for each frame of a lower estimation error; (iv) higher-quality dense point clouds are reconstructed via advanced methods for objects captured in 360 ° views, which can serve for downstream applications. Extensive experiments confirm the value of the proposed MVImgNet2.0 in boosting the performance of large 3D reconstruction models. MVImgNet2.0 will be public at luyues.github.io/mvimgnet2 , including multi-view images of all 520k objects, the reconstructed high-quality point clouds, and data annotation codes, hoping to inspire the broader vision community.

A dual-dimensionality reduction strategy for optimization-based parallel parking path planner

Optimization-based parking path planner has been attracting much more attention due to its capability to generate the optimal path rather than a feasible one. But when solving this optimal problem, it is difficult to make a good balance between the computational accuracy and efficiency. Because dense discretization points are necessary for accuracy, which conversely leads to a high dimensionality of optimization space. To deal with this challenge, this paper proposes a dual-dimensionality reduction strategy to accelerate the numerical optimization process of parallel parking path. One is to reduce the number of optimized parameters by approximating the optimal path with multiple circular arcs connected end to end, according to the numerical statistical analysis of the geometric features of the optimal path. The other is to reduce the number of nonlinear and non-convex constraints for obstacle avoidance by analyzing the geometry relationship between the parameterized arcs and the boundary lines of obstacles. This point-over-arc obstacle avoidance constraint can ensure that the planned path is collision-free by only checking the limitations at the endpoints of the circular arcs. The effectiveness of the proposed method on the improvement in computational efficiency is validated by several comparative simulation and experimental tests. Compared with the traditional numerical optimization methods, the presented algorithm improves the computational efficiency by nearly 40 times on average.

Mountain Landslide Monitoring Using a DS-InSAR Method Incorporating a Spatio-Temporal Atmospheric Phase Screen Correction Model

The detection of potential rural mountain landslide displacements using time-series interferometric Synthetic Aperture Radar has been challenged by both atmospheric phase screens and decoherence noise. In this study, we propose the use of a combined distributed scatterer (DS) and the Prophet_ZTD-NEF model to rapidly map the landslide surface displacements in Diqing Tibetan Autonomous Prefecture, China. We conducted tests on 28 full-resolution SENTINEL-1A images to validate the effectiveness of our methods. The conclusions are as follows: (1) Under the same sample conditions, confidence interval estimation demonstrated higher performance in identifying SHPs compared to generalized likelihood ratio test. The density of DS points was approximately eight times and five times higher than persistent scatterer interferometry and small baseline subset methods, respectively. (2) The proposed Prophet_ZTD-NEF model considers the spatial and temporal variability properties of tropospheric delays, and the root mean square error of measured values was approximately 1.19 cm instead of 1.58 cm (PZTD-NEF). (3) The proposed Prophet_ZTD-NEF method reduced the mean standard deviation of the corrected interferograms from 1.88 to 1.62 cm and improved the accuracy of the deformation velocity solution by approximately 8.27% compared to Global Position System (GPS) measurements. Finally, we summarized the driving factors contributing to landslide instability.

Spectra of solar shallow-water waves from bright point observations

Rossby waves, large-scale meandering patterns drifting in longitude, detected in the Sun, were recently shown to a play a crucial role in understanding “seasons” of space weather. Unlike Earth's purely classical atmospheric Rossby waves, the solar counterparts are strongly magnetized and most likely originate in the tachocline. Because of their deeper origin, detecting these magnetized Rossby waves is a challenging task that relies on careful observations of long-lived longitudinally drifting magnetic patterns at the surface and above. Here, we have utilized 3 years of global, synchronous observations of coronal bright point densities to obtain empirical signatures of dispersion relations that can be attributed to the simulated waves in the tachocline. By tracking the bright point densities at selected latitudes, we computed their wave-numbertimes frequency spectra. Wave-numbertimes frequency spectra were computed utilizing the Wheeler-Kiladis method. This method has been extensively used in the identification of equatorial waves in Earth's atmosphere by highlighting spectral peaks in the wave-numbertimes frequency space. Our results are compatible with the predictions of magneto-Rossby waves with typical periods of several months and inertio-gravity waves with typical periods of a few weeks, depending on the background magnetic field's strength and stratification at the convection zone base. Our analysis suggests that magnetized Rossby waves originate from the tachocline toroidal field of lesssim 15 kG. Global observations of bright points over extended periods will allow us to better constrain the stratification and magnetic field strength in the tachocline.

Study of the application of UAV and LiDAR to topographic survey of mountainous forest areas – Case study of Win 3 Wind Power Plant Project, Huong Hoa District, Quang Tri Province, Vietnam

Abstract Unmanned Aerial Vehicle (UAV) technology in conjunction with aerial photography and aerial Light Detection and Ranging (LiDAR) was used for topographic surveying of the Win 3 Wind Power Project area, a complex mountainous terrain situated in the Huong Hoa district of Quang Tri province, Vietnam with the primary objective to produce a map with a scale of 1:1,000 with a contour interval of 1.0 m, accompanied by 3D point clouds, a Digital Elevation Model (DEM), and an orthomosaic. Employing the UAV LiDAR system of DJI Matrice 300 RTK, we conduct ed survey flights, achieving a high point density laser scanning of 229 points/m2 and capturing ultra-high-resolution imagery at 4.22 cm/pixel. The integration of aerial LiDAR and photographic data results in a rich and detailed information repository regarding the surveyed terrain demonstrating that UAV LiDAR technology is a robust tool for geographic data collection, particularly in challenging terrain conditions in Vietnam. We also evaluated the accuracy of the created topographic map, achieving results that surpass the technical requirements and quality standards of the project. This underscores the potential and effectiveness of UAV LiDAR technology in the field of large-scale geographic data collection and mapping in Vietnam.

Evidence Map of Interventions to Reduce Alcohol ConsumptionMapa de la evidencia sobre intervenciones para reducir el consumo de alcohol

Systematize evidence on the effect of global interventions to reduce the consumption and/or sale of alcoholic beverages. Evidence map based on searches in nine bibliographic databases, including 182 studies of systematic reviews with or without meta-analysis, reviews of interventions, and reviews of reviews. The studies evaluated the effect of interventions grouped into comprehensive sets of actions: communication for behavior change; health-promoting environments; and systemic changes. Two outcomes of interest were considered: reduction in alcohol consumption and reduction in its purchase/sale. A total of 207 associations between different interventions and outcomes were recorded, with emphasis on communication for behavior change (81.64%) and reduction of consumption (98.55%). Most of the associations showed a positive (40.58%), inconclusive (28.99%), or potentially positive (26.57%) effect. The main interventions with positive or potentially positive results were: a government monopoly on the sale of alcoholic beverages, control of the density of points of sale, charging a minimum price per unit, health warnings on alcoholic beverage labels, and multiple integrated interventions. It is hoped that this map will help public policy makers and healthcare professionals adapt experiences to their own contexts, stimulating intersectoral actions to reduce alcohol consumption.

Integral points on a del Pezzo surface over imaginary quadratic fields

Chambert-Loir and Tschinkel constructed a framework for a geometric interpretation of the density of integral points on certain varieties, which was refined by Wilsch. By using harmonic analysis and the circle method, it was proved for some partial equivariant compactifications of vector groups over arbitrary number fields and high-dimensional complete intersections over Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Q}}$$\\end{document}. Further, there are some examples of using the torsor method for singular del Pezzo surfaces over Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Q}}$$\\end{document}. In this paper, we generalise the torsor method for integral points from Q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Q}}$$\\end{document} to imaginary quadratic number fields. As a first representative example, we characterise integral points of bounded log-anticanonical height on a quartic del Pezzo surface of singularity type A3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ extbf{A}}_3$$\\end{document} over imaginary quadratic fields with respect to its singularity and its lines. Furthermore, we count these integral points of bounded height by using universal torsors and interpret the count geometrically to prove an analogue of Manin’s conjecture for the set of integral points with respect to the singularity and to a line. Our results coincide with the predicted framework.

Physicochemical and electrical properties of DPPC bilayer membranes in the presence of oleanolic or asiatic acid

This study aimed to investigate the effect of selected compounds from the group of triterpene sapogenins on model phosphatidylcholine membranes. Two types of biological membrane model systems were used in the work, i.e., liposomes (microelectrophoresis method) and spherical bilayers (interfacial tension method). Each model was modified with the tested sapogenin compounds, and the change in their physicochemical and electrical parameters was analyzed. Parameters characterizing the equilibrium in the membrane of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC)-oleanolic acid (OA) and DPPC-asiatic acid (AA) were determined). Based on the Young-Laplace equation, the interfacial tensions of spherical lipid bilayers were measured. The formation of 1:1 complexes was assumed in the DPPC-OA and DPPC-AA membrane systems, and the parameters characterizing the interactions in the formed complexes were calculated. Microelectrophoresis was used to study the surface charge density of lipid membranes. These values were obtained from electrophoretic mobility data using Smoluchowsky’s equation. The influence of pH on the electrolyte solution and the composition of the membranes was investigated. The results indicate that modifying DPPC membranes with selected triterpene sapogenins, both OA and AA, causes changes in the surface charge density and shifts of the isoelectric point. Data presented in this work, obtained through mathematical derivation and confirmed experimentally, are of great importance for interpreting phenomena occurring in lipid membranes. A quantitative description of equilibria between phosphatidylcholine and sapogenins lets us understand the processes on the membrane surface. The equilibria are particularly significant from the standpoint of cell functioning. Phosphatidylcholine-sapogenin interactions modulate a range of physicochemical properties of membranes, and they are important in the course of the multiple processes involving membranes in the living cell (e.g., transport mechanism).

Enhancing environmental modeling and 3D point cloud construction for unmanned vehicles using laser SLAM and stereo vision with Convolutional Neural Networks

Abstract. This research presents an innovative SLAM algorithm that integrates Convolutional Neural Networks (CNNs) with LIDAR and stereo vision to significantly enhance the accuracy of environmental modeling and the construction of dense 3D point cloud maps in complex and dynamic surroundings. By processing pre-recorded video data and employing advanced image segmentation techniques, this study achieves a deep fusion of visual and geometric data, resulting in highly detailed and precise 3D representations of the environment. The experimental results demonstrate that this approach effectively detects and excludes dynamic objects, thereby significantly improving the overall quality, robustness, and reliability of the constructed maps. This work represents a substantial advancement in SLAM technology, particularly in its capability to model and capture intricate environmental details under varying conditions, making it a powerful tool for precise environmental mapping.

Clustering in point processes on linear networks using nearest neighbour volumes

This study introduces a novel method specifically designed to detect clusters of points within linear networks. This method extends a classification approach used for point processes in spatial contexts. Unlike traditional methods that operate on planar spaces, our approach adapts to the unique geometric challenges of linear networks, where classical properties of point processes are altered, and intuitive data visualisation becomes more complex. Our method utilises the distribution of the Kth nearest neighbour volumes, extending planar-based clustering techniques to identify regions of increased point density within a network. This approach is particularly effective for distinguishing overlapping Poisson processes within the same linear network. We demonstrate the practical utility of our method through applications to road traffic accident data from two Colombian cities, Bogota and Medellin. Our results reveal distinct clusters of high-density points in road segments where severe traffic accidents (resulting in injuries or fatalities) are most likely to occur, highlighting areas of increased risk. These clusters were primarily located on major arterial roads with high traffic volumes. In contrast, low-density points corresponded to areas with fewer accidents, likely due to lower traffic flow or other mitigating factors. Our findings provide valuable insights for urban planning and road safety management.

Influence of tree density and terrain slope on ground point density in LiDAR point clouds: a simulation-based study with Helios++

Influence of tree density and terrain slope on ground point density in LiDAR point clouds: a simulation-based study with Helios++

Machine learning-based optimization of photogrammetric JRC accuracy

To improve the accuracy of photogrammetric joint roughness coefficient (JRC) estimation, this study proposes two optimization models based on ground sample distance (GSD), point density, and the root mean square error (RMSE) of checkpoints. First, an algorithm that automatically generates spatial positions for equipment based on the convergence strategy was developed, using principles of Structure from Motion and Multi-View Stereo (SfM-MVS) and the shooting parameter selection algorithm (SPSA). Second, a portable positioning plate containing ground control points and checkpoints was designed based on optical principles, and a moving camera capture strategy guided by SPSA was proposed. Combining SPSA, portable positioning plate, and moving camera capture strategy, a photogrammetric experiment for small-scale rock samples in the field was conducted, collecting 48 datasets with different shooting parameters. Subsequently, a dataset incorporating GSD, point density, RMSE, and three JRC estimation metrics was established, revealing their correlations and sensitivities. Using seven machine learning algorithms, optimization models for photogrammetric JRC accuracy were developed, with Linear Multidimensional Regression and Gaussian Process Regression models improving JRC accuracy by an average of 85.73%. Finally, the applicability and limitations of the newly proposed method were further discussed.

Repeat airborne laser scanning to assess canopy height changes in tropical montane forests

Abstract. Tropical montane forests are vital ecosystems globally, preserving biodiversity, carbon stocks, and capturing moisture. We employed two airborne laser scanning (ALS) data sets to study changes in montane forest canopy heights in the Taita Hills, Kenya between 2014/2015 and 2022. We studied two forests, Ngangao (129 ha) and Yale (57 ha), which encompassed both indigenous montane forest and exotic plantations. First, forest types were mapped using field observations and aerial imagery, and then, canopy height changes were analysed using canopy height models at spatial resolution (i.e. the cell size) ranging from 1 m to 20 m. The results revealed overall increase in canopy height in the studied forests, with considerable spatial variation between the forest segments and main tree species. Planted exotic tree species, particularly eucalyptus but also pine and cypress, exhibited faster growth rates than native tree species. Point density differences between the ALS data sets can cause bias to estimation of canopy height changes. However, we observed that reducing the cell size of the canopy height models from 1 m to 10 m and 20 m, decreased the positive trend between point density difference and overestimation of canopy height change due to higher point density of more recent ALS data set. These findings contribute to our understanding on spatial complexity of montane forest ecosystems dynamics and help informing forest monitoring and development of management strategies for fragmented forests in montane regions.

ZygoPlanner: A three-stage graphics-based framework for optimal preoperative planning of zygomatic implant placement

Zygomatic implant surgery is an essential treatment option of oral rehabilitation for patients with severe maxillary defect, and preoperative planning is an important approach to enhance the surgical outcomes. However, the current planning still heavily relies on manual interventions, which is labor-intensive, experience-dependent, and poorly reproducible. Therefore, we propose ZygoPlanner, a pioneering efficient preoperative planning framework for zygomatic implantation, which may be the first solution that seamlessly involves the positioning zygomatic bones, the generation of alternative paths, and the computation of optimal implantation paths. To efficiently achieve robust planning, we developed a graphics-based interpretable method for zygomatic bone positioning leveraging the shape prior knowledge. Meanwhile, a surface-faithful point cloud filling algorithm that works for concave geometries was proposed to populate dense points within the zygomatic bones, facilitating generation of alternative paths. Finally, we innovatively realized a graphical representation of the medical bone-to-implant contact to obtain the optimal results under multiple constraints. Clinical experiments confirmed the superiority of our framework across different scenarios. The source code is available at https://github.com/Haitao-Lee/auto_zygomatic_implantation.