Alpha-shape Algorithm Research Articles

Evaluation of novel precision viticulture tool for canopy biomass estimation and missing plant detection based on 2.5D and 3D approaches using RGB images acquired by UAV platform

BackgroundThe knowledge of vine vegetative status within a vineyard plays a key role in canopy management in order to achieve a correct vine balance and reach the final desired yield/quality. Detailed information about canopy architecture and missing plants distribution provides useful support for farmers/winegrowers to optimize canopy management practices and the replanting process, respectively. In the last decade, there has been a progressive diffusion of UAV (Unmanned Aerial Vehicles) technologies for Precision Viticulture purposes, as fast and accurate methodologies for spatial variability of geometric plant parameters. The aim of this study was to implement an unsupervised and integrated procedure of biomass estimation and missing plants detection, using both the 2.5D-surface and 3D-alphashape methods.ResultsBoth methods showed good overall accuracy respect to ground truth biomass measurements with high values of R2 (0.71 and 0.80 for 2.5D and 3D, respectively). The 2.5D method led to an overestimation since it is derived by considering the vine as rectangular cuboid form. On the contrary, the 3D method provided more accurate results as a consequence of the alphashape algorithm, which is capable to detect each single shoot and holes within the canopy. Regarding the missing plants detection, the 3D approach confirmed better performance in cases of hidden conditions by shoots of adjacent plants or sparse canopy with some empty spaces along the row, where the 2.5D method based on the length of section of the row with lower thickness than the threshold used (0.10 m), tended to return false negatives and false positives, respectively.ConclusionsThis paper describes a rapid and objective tool for the farmer to promptly identify canopy management strategies and drive replanting decisions. The 3D approach provided results closer to real canopy volume and higher performance in missing plant detection. However, the dense cloud based analysis required more processing time. In a future perspective, given the continuous technological evolution in terms of computing performance, the overcoming of the current limit represented by the pre- and post-processing phases of the large image dataset should mainstream this methodology.

Building outline extraction from ALS point clouds using medial axis transform descriptors

Automatic building extraction and delineation from airborne LiDAR point cloud data of urban environments is still a challenging task due to the variety and complexity at which buildings appear. The Medial Axis Transform (MAT) is able to describe the geometric shape and topology of an object, but has never been applied for building roof outline extraction. It represents the shape of an object by its centerline, or skeleton structure instead of its boundary. Notably, end points of the MAT in principle coincide with corner points of building outlines. However, the MAT is sensitive to small boundary irregularities, which makes shape detection in airborne point clouds challenging. We propose a robust MAT-based method for detecting building corner points, which are then connected to form a building boundary polygon. First, we approximate the 2D MAT of a set of building edge points acquired by the alpha-shape algorithm to derive a so-called building roof skeleton. We then propose a hierarchical corner-aware segmentation to cluster skeleton points based on their properties which are the so-called separation angle, radius of the maximally inscribe circle, and defining edge point indices. From each segment, a corner point is then estimated by extrapolating the position of the zero radius inscribed circle based on the skeleton point positions within the segment. Our experiment uses point cloud datasets of Makassar, Indonesia and EYE-Amsterdam, The Netherlands. The average positional accuracy of the building outline results for Makassar and EYE-Amsterdam is 65 cm and 70 cm, respectively, which meet one-meter base map accuracy criteria. The results imply that skeletonization is a promising tool to extract relevant geometric information on e.g. building outlines even from far from perfect geographical point cloud data.

Point cloud-based estimation of effective payload volume for earthmoving loaders

Construction and mining require high levels of planning and productivity. Planning and management of operational targets and performance requires taking into account several variables, among which the amount of moved, loaded and unloaded material is one the main ones. This motivates the development of an approach for the estimation of the volume of material transported in field operations by loader trucks. The proposed methodology employs a three-dimensional point cloud representation of the volume and is tested using a skid-steer loader. The volume estimation process involves the segmentation of the loader's bucket from the raw point cloud using machine learning techniques. The segmented point cloud is associated with a pre-constructed reference model of the empty bucket. The volume is computed from a surface model built using the alpha shape algorithm applied to the Delaunay triangulation of the segmented point cloud. Several field experiments were carried out using a stereo camera for five different volumes of material and the bucket at different heights. A 95% accuracy was obtained on average. The encouraging results suggest that effective volume estimation for different bucket types would be possible using the proposed methodology.

Extraction of Building Roof Boundaries From LiDAR Data Using an Adaptive Alpha-Shape Algorithm

The alpha-shape algorithm was developed to extract object shapes in 2-D space; however, the accuracy of the result depends on an appropriate choice of the parameter $\alpha $ . This parameter is directly related to point density and the level of detail of the boundary. Similar approaches usually consider a unique parameter $\alpha $ to extract all buildings in the data set. However, as the point density can vary along the cloud and also along the building, using a global parameter may not be suitable in some situations. This letter proposes an adaptive method to overcome this limitation. It estimates a local parameter $\alpha $ for each edge based on local point spacing. The experiments were performed considering buildings with different levels of complexity, which were selected from two different LiDAR data sets and three densities. Qualitative and quantitative analysis enabled verification of the proposed method, showing good results in cases where significant density variation occurs along the building, and in the extraction of complex buildings such as those composed of convex and concave segments and/or the presence of inner boundaries. The proposed adaptive solution can overcome most limitations of simpler approaches, such as the use of a global parameter or only one parameter per building.

Solving the conjugate tooth profile of screw compressor rotors using edge detection method based on Alpha Shape algorithm

While designing a screw compressor, the design of the rotor profiles is the most important because rotor profiles essentially determine the overall performance of the screw compressor. In the field of rotor design, the mutual solution of male and female rotors is characterized by shortcomings such as complex and error-prone calculation, and unsolvable interference. In this study, an edge detection method based on the Alpha Shape algorithm was proposed to avoid the complex calculation process in the traditional planar meshing theory and quickly obtain the point cloud data with singularity points removed. The results show that, with relatively high accuracy and fast processing speed, this algorithm can extract comparatively desirable edges so as to obtain data of the female (male) rotor profile based on the conjugate male (female) rotor profile. The analytical method and the experimental method were used to compare the data of the conjugate rotors, verifying the correctness of the design, which efficiently and highly accurately overcame the problems in mutual solution of male and female rotors. This method can also be applied to design similar conjugate products such as gears, worms, and milling cutters.

Apple orchard inventory with a LiDAR equipped unmanned aerial system

Knowledge about the number of trees in an orchard and their geometric parameters is beneficial in precise farming and together with other information may be used to predict the yield. These parameters can be obtained based on time-consuming field measurements or more effectively, from very high resolution 3D data collected with Unmanned Aerial Vehicles (UAV). Numerous UAV experiments have been conducted in agricultural areas; however, most of studies are limited to the use of a passive optical sensor (camera). This study demonstrates an experiment on the novel remote sensing approach of determining selected geometric parameters of trees in an apple orchard, based on a high-density point cloud obtained from a Velodyne HDL-32E laser scanner mounted on a small UAV platform Leica Aibot X6 V2. Reference data of selected geometric parameters of trees was obtained from orthophotomap and with geodetic surveying methods. Original and robust methodology is proposed for the point cloud processing, which is the inventive combination of an alpha-shape algorithm, principal component analysis and detection of local minima on crown profiles. The developed approach allowed for the correct identification of 99% of the trees in the test orchard. The root mean square error of determined crown areas was equal to 0.98 m2. The accuracy of tree top identification, tree height and crown base height determination was equal to 0.38, 0.09 and 0.09 m, respectively.

Power Pylon Reconstruction Based on Abstract Template Structures Using Airborne LiDAR Data

As an important power facility for transmission corridors, automatic three-dimensional (3D) reconstruction of the pylon plays an important role in the development of smart grid. In this study, a novel three-dimensional reconstruction method using airborne LiDAR (Light Detection And Ranging) point cloud is developed and tested. First, a principal component analysis (PCA) algorithm is performed for pylon redirection based on the structural feature of the upper part of a pylon. Then, based on the structural similarity of a pylon, a pylon is divided into three parts that are inverted triangular pyramid lower structures, quadrangular frustum pyramid middle structures, and complex upper or lateral structures. The reconstruction of the inverted triangular pyramid structures and quadrangular frustum pyramid structures is based on prior knowledge and a data-driven strategy, where the 2D alpha shape algorithm is used to obtain contour points and 2D linear fitting is carried out based on the random sample consensus (RANSAC) method. Complex structures’ reconstruction is based on the priori abstract template structure and a data-driven strategy, where the abstract template structure is used to determine the topological relationship among corner points and the image processing method is used to extract corner points of the abstract template structure. The main advantages in the proposed method include: (1) Improving the accuracy of the pylon decomposition method through introducing a new feature to identify segmentation positions; (2) performing the internal structure of quadrangular frustum pyramids reconstruction; (3) establishing the abstract template structure and using image processing methods to improve computational efficiency of pylon reconstruction. Eight types of pylons are tested in this study, and the average error of pylon reconstruction is 0.32 m and the average of computational time is 0.8 s. These results provide evidence that the pylon reconstruction method developed in this study has high accuracy, efficiency, and applicability.

Solving the screw compressor rotor-forming grinding wheel using the edge detection method based on the graphic method

As a complex grinding wheel for special use, the screw compressor rotor-forming grinding wheel needs to be designed according to the specific profile of the workpiece. The design process is complicated and difficult to grasp, and various design issues are likely to occur. This study is based on the design theory of helical rotor-forming grinding wheels. Here, disc-shaped forming grinding wheels for machining a helical surface were studied, with discrete point workpiece cross-sections as examples. MATLAB was used as the development tool, and the Unigraphics motion simulation function was applied to establish a 3D model of screw rotors and design the forming grinding wheel for machining the helical surface. Additionally, the edge shape of the grinding wheel obtained with the analytical method and the edge shape obtained with the edge detection method based on the graphic method and the alpha-shape algorithm were compared. The results of this comparison show that the edge shape of the grinding wheel obtained by the edge detection method had high precision and was easy to solve. This method can also be used for the design of other similar conjugated products such as gears, worms, and grinding wheels. The research findings provide important reference value for the design and machining of screw rotors and grinding wheels.

DETERMINING GEOMETRIC PARAMETERS OF AGRICULTURAL TREES FROM LASER SCANNING DATA OBTAINED WITH UNMANNED AERIAL VEHICLE

Abstract. The estimation of dendrometric parameters has become an important issue for agriculture planning and for the efficient management of orchards. Airborne Laser Scanning (ALS) data is widely used in forestry and many algorithms for automatic estimation of dendrometric parameters of individual forest trees were developed. Unfortunately, due to significant differences between forest and fruit trees, some contradictions exist against adopting the achievements of forestry science to agricultural studies indiscriminately. In this study we present the methodology to identify individual trees in apple orchard and estimate heights of individual trees, using high-density LiDAR data (3200 points/m2) obtained with Unmanned Aerial Vehicle (UAV) equipped with Velodyne HDL32-E sensor. The processing strategy combines the alpha-shape algorithm, principal component analysis (PCA) and detection of local minima. The alpha-shape algorithm is used to separate tree rows. In order to separate trees in a single row, we detect local minima on the canopy profile and slice polygons from alpha-shape results. We successfully separated 92 % of trees in the test area. 6 % of trees in orchard were not separated from each other and 2 % were sliced into two polygons. The RMSE of tree heights determined from the point clouds compared to field measurements was equal to 0.09 m, and the correlation coefficient was equal to 0.96. The results confirm the usefulness of LiDAR data from UAV platform in orchard inventory.

Computing Algorithm for the Gear Tooth Space Points Cloud Envelope Generated by the Mixed Cad Method

Abstract The task of the mixed pure CAD generating method developed by the authors consists in finding only the points situated on the gear tooth surface. The use of the mixed CAD gear generating method results in a very large and particular type of Points Cloud: This contains points situated both in the tooth space, and on the tooth surface. The existing filtering programs and methods, as it was presented in previous papers, cannot deal with these particular point sets. The development of the named particular generating method claims an algorithm and a computer software which can find the envelope of the Points Cloud. This papers presents an Alpha Shape algorithm based filtering algorithm, adapted and developed to be used together with the mixed CAD generating software.

AUTOMATIC MONITORING OF TUNNEL DEFORMATION BASED ON HIGH DENSITY POINT CLOUDS DATA

Abstract. An automated method for tunnel deformation monitoring using high density point clouds data is presented. Firstly, the 3D point clouds data are converted to two-dimensional surface by projection on the XOY plane, the projection point set of central axis on XOY plane named Uxoy is calculated by combining the Alpha Shape algorithm with RANSAC (Random Sampling Consistency) algorithm, and then the projection point set of central axis on YOZ plane named Uyoz is obtained by highest and lowest points which are extracted by intersecting straight lines that through each point of Uxoy and perpendicular to the two -dimensional surface with the tunnel point clouds, Uxoy and Uyoz together form the 3D center axis finally. Secondly, the buffer of each cross section is calculated by K-Nearest neighbor algorithm, and the initial cross-sectional point set is quickly constructed by projection method. Finally, the cross sections are denoised and the section lines are fitted using the method of iterative ellipse fitting. In order to improve the accuracy of the cross section, a fine adjustment method is proposed to rotate the initial sectional plane around the intercept point in the horizontal and vertical direction within the buffer. The proposed method is used in Shanghai subway tunnel, and the deformation of each section in the direction of 0 to 360 degrees is calculated. The result shows that the cross sections becomes flat circles from regular circles due to the great pressure at the top of the tunnel

A Method to Obtain Orange Crop Geometry Information Using a Mobile Terrestrial Laser Scanner and 3D Modeling

LiDAR (Light Detection and Ranging) technology has been used to obtain geometrical attributes of tree crops in small field plots, sometimes using manual steps in data processing. The objective of this study was to develop a method for estimating canopy volume and height based on a mobile terrestrial laser scanner suited for large commercial orange groves. A 2D LiDAR sensor and a GNSS (Global Navigation Satellite System) receiver were mounted on a vehicle for data acquisition. A georeferenced point cloud representing the laser beam impacts on the crop was created and later classified into transversal sections along the row or into individual trees. The convex-hull and the alpha-shape reconstruction algorithms were used to reproduce the shape of the tree crowns. Maps of canopy volume and height were generated for a 25 ha orange grove. The different options of data processing resulted in different values of canopy volume. The alpha-shape algorithm was considered a good option to represent individual trees whereas the convex-hull was better when representing transversal sections of the row. Nevertheless, the canopy volume and height maps produced by those two methods were similar. The proposed system is useful for site-specific management in orange groves.

Automatic estimation of olive tree dendrometric parameters based on airborne laser scanning data using alpha-shape and principal component analysis

The aim of this study is to present an automatic approach for olive tree dendrometric parameter estimation from airborne laser scanning (ALS) data. The proposed method is based on a unique combination of the alpha-shape algorithm applied to normalized point cloud and principal component analysis. A key issue of the alpha-shape algorithm is to define the α parameter, as it directly affects the crown delineation results. We propose to adjust this parameter based on a group of representative trees in an orchard for which the classical field measurements were performed. The best value of the α parameter is one whose correlation coefficient of dendrometric parameters between field measurements and estimated values is the highest. We determined crown diameters as principal components of ALS points representing a delineated crown. The method was applied to a test area of an olive orchard in Spain. The tree dendrometric parameters estimated from ALS data were compared with field measurements to assess the quality of the developed approach. We found the method to be equally good or even superior to previously investigated semi-automatic methods. The average error is 19% for tree height, 53% for crown base height, and 13% and 9% for the length of the longer diameter and perpendicular diameter, respectively.

Verification and Updating of the Database of Topographic Objects with Geometric Information About Buildings by Means of Airborne Laser Scanning Data

Abstract Airborne laser scanning data (ALS) are used mainly for creation of precise digital elevation models. However, it appears that the informative potential stored in ALS data can be also used for updating spatial databases, including the Database of Topographic Objects (BDOT10k). Typically, geometric representations of buildings in the BDOT10k are equal to their entities in the Land and Property Register (EGiB). In this study ALS is considered as supporting data source. The thresholding method of original ALS data with the use of the alpha shape algorithm, proposed in this paper, allows for extraction of points that represent horizontal cross section of building walls, leading to creation of vector, geometric models of buildings that can be then used for updating the BDOT10k. This method gives also the possibility of an easy verification of up-to-dateness of both the BDOT10k and the district EGiB databases within geometric information about buildings. For verification of the proposed methodology there have been used the classified ALS data acquired with a density of 4 points/m2. The accuracy assessment of the identified building outlines has been carried out by their comparison to the corresponding EGiB objects. The RMSE values for 78 buildings are from a few to tens of centimeters and the average value is about 0,5 m. At the same time for several objects there have been revealed huge geometric discrepancies. Further analyses have shown that these discrepancies could be resulted from incorrect representations of buildings in the EGiB database.

AUTOMATIC EXTRACTION AND REGULARIZATION OF BUILDING OUTLINES FROM AIRBORNE LIDAR POINT CLOUDS

Building outlines are needed for various applications like urban planning, 3D city modelling and updating cadaster. Their automatic reconstruction, e.g. from airborne laser scanning data, as regularized shapes is therefore of high relevance. Today’s airborne laser scanning technology can produce dense 3D point clouds with high accuracy, which makes it an eligible data source to reconstruct 2D building outlines or even 3D building models. In this paper, we propose an automatic building outline extraction and regularization method that implements a trade-off between enforcing strict shape restriction and allowing flexible angles using an energy minimization approach. The proposed procedure can be summarized for each building as follows: (1) an initial building outline is created from a given set of building points with the alpha shape algorithm; (2) a Hough transform is used to determine the main directions of the building and to extract line segments which are oriented accordingly; (3) the alpha shape boundary points are then repositioned to both follow these segments, but also to respect their original location, favoring long line segments and certain angles. The energy function that guides this trade-off is evaluated with the Viterbi algorithm.

AUTOMATIC EXTRACTION AND REGULARIZATION OF BUILDING OUTLINES FROM AIRBORNE LIDAR POINT CLOUDS

Abstract. Building outlines are needed for various applications like urban planning, 3D city modelling and updating cadaster. Their automatic reconstruction, e.g. from airborne laser scanning data, as regularized shapes is therefore of high relevance. Today’s airborne laser scanning technology can produce dense 3D point clouds with high accuracy, which makes it an eligible data source to reconstruct 2D building outlines or even 3D building models. In this paper, we propose an automatic building outline extraction and regularization method that implements a trade-off between enforcing strict shape restriction and allowing flexible angles using an energy minimization approach. The proposed procedure can be summarized for each building as follows: (1) an initial building outline is created from a given set of building points with the alpha shape algorithm; (2) a Hough transform is used to determine the main directions of the building and to extract line segments which are oriented accordingly; (3) the alpha shape boundary points are then repositioned to both follow these segments, but also to respect their original location, favoring long line segments and certain angles. The energy function that guides this trade-off is evaluated with the Viterbi algorithm.

Robust Object Tracking with Mutualism between Particle Filter and Geometric Active Contour

Robust object tracking is important in many real applications. This study proposes a novel robust object tracking algorithm that combines particle filter and geometric active contour. In contrast to conventional combinations, the proposed algorithm establishes mutualism, wherein the particle filter provides curve initialization for the active contour by using the alpha shape algorithm, and the active contour provides evolved boundary for particle filter classification. The refined particles are used to estimate the states which reduce the distance error. Discriminable object feature is proposed to enhance the tracking robustness, and prior information-based curve evolution is used to improve the accuracy of boundary segmentation. Comparable experiments are performed using a stand particle filter and continuously adaptive mean-shift methods. The proposed algorithm is found to be highly robust for long video sequences with non-linear motion, scale changes and clutter background.

Automatic Extraction of Facade Details of Heritage Building Using Terrestrial Laser Scanning Data

The Terrestrial Laser Scanning (TLS) has become an interesting technology in various fields. The architecture and heritage fields benefit more and more of this technology. In the heritage field, TLS data and derived products are used to complete the digital archive of cultural sites all over the world. Among these cultural sites, we deal with the historical Moroccan sites, especially the old Medina. The rehabilitation of the old Medina requires the reconstruction of facade planes. For that purpose, Moroccan authorities need a precise inventory of all facades. The planes extracted from 3D point cloud provide the desired results. However, the manual process is too long and sometimes difficult. Automatic methods of plane recognition including the point cloud segmentation are generally based on geometric approaches which fail to identify some facade details of such heritage buildings. In this context, we propose a new automatic approach of point cloud segmentation. This approach relies on all the components of a colored point--both geometric and radiometric--combining the RGB values, laser intensity and geometric data. Our approach also includes a new method to filter the segmentation result through Delaunay triangulation. The last step of our processing is the facade and detail contour detection that is based on alpha-shape algorithm to find interior and exterior boundaries. Experiments are performed on facades presenting an example of old Medina architecture located in Casablanca’s Medina. Results show the importance of integrating all point cloud components for the detail facades extraction and planes establishment.

The endangered maned sloth Bradypus torquatus of the Brazilian Atlantic forest: a review and update of geographical distribution and habitat preferences

ABSTRACT The endemic maned sloth Bradypus torquatus is globally threatened due to deforestation, habitat fragmentation and isolation of populations. Despite increased interest in the species in recent years, information on its geographic distribution is limited and is derived mainly from a few museum species and from a survey based mostly on interviews carried out more than 20 years ago. Information on its habitat and altitudinal preferences is lacking. We therefore compile, update and review all occurrence records of this species using geographical information system (GIS) tools and produce a distribution map for the species. Our compilation totalled 188 occurrence records, of which 130 (69%) were considered confirmed (museum specimens or individuals captured or seen in the field), most of which (62%) were restricted to the states of Bahia and central‐south Espírito Santo (29%). The species occurs predominantly in ombrophilous forest (80%), from sea level to 1290m, but mainly (79%) below 200m altitude. We used GIS techniques and the alpha shape algorithm to calculate the extent of occurrence of the species and compared the resulting map with distribution maps available in the literature. We found a great deal of variation in distribution area shape and an almost two‐fold variation in distribution area size among sources. We confirmed the existence of a main distribution gap between southern Bahia and northern Espírito Santo and discovered a second smaller gap between southern Espírito Santo and northern Rio de Janeiro. We also confirmed that B. torquatus is sympatric with the common three‐toed sloth Bradypus variegatus in a large part of the Atlantic forest and that the two species are syntopic in at least 11 locations.

Segmentation, Reconstruction, and Analysis of Blood Thrombus Formation in 3D 2-Photon Microscopy Images

We study the problem of segmenting, reconstructing, and analyzing the structure growth of thrombi (clots) in blood vessels in vivo based on 2-photon microscopic image data. First, we develop an algorithm for segmenting clots in 3D microscopic images based on density-based clustering and methods for dealing with imaging artifacts. Next, we apply the union-of-balls (or alpha-shape) algorithm to reconstruct the boundary of clots in 3D. Finally, we perform experimental studies and analysis on the reconstructed clots and obtain quantitative data of thrombus growth and structures. We conduct experiments on laser-induced injuries in vessels of two types of mice (the wild type and the type with low levels of coagulation factor VII) and analyze and compare the developing clot structures based on their reconstructed clots from image data. The results we obtain are of biomedical significance. Our quantitative analysis of the clot composition leads to better understanding of the thrombus development, and is valuable to the modeling and verification of computational simulation of thrombogenesis.