On the identification of the convex hull of a finite set of points in the plane
References (1)
- R.L. Graham
An Efficient Algorithm for Determining the Convex Hull of a Finite Planar Set
Information Processing Letters
(1972)
Cited by (541)
An evaluation of GPU filters for accelerating the 2D convex hull
2024, Journal of Parallel and Distributed ComputingThe Convex Hull is one of the most relevant structures in computational geometry, with many applications such as in computer graphics, robotics, and data mining. Despite the advances in the new algorithms in this area, it is often needed to improve the performance to solve more significant problems quickly or in real-time processing. This work presents an experimental evaluation of GPU filters to reduce the cost of computing the 2D convex hull. The techniques first perform a preprocessing of the input set, filtering all points within an eight-vertex polygon to obtain a reduced set of candidate points. We use parallel computation and the use of the Manhattan distance as a metric to find the vertices of the polygon and perform the point filtering. For the filtering stage we study different approaches; from custom CUDA kernels to libraries such as Thrust and Cub. Four types of point distributions are tested: a normal distribution (favorable case), uniform (favorable case), circumference (the worst case), and a case where points are shifted randomly from the circumference (intermediate case). The experimental evaluation shows that the GPU filtering algorithm can be up to 17.5× faster than a sequential CPU implementation, and the whole convex hull computation can be up to 160× faster than the fastest implementation provided by the CGAL library for a uniform distribution and 23× for a normal distribution.
A semi-supervised generative adversarial network for amodal instance segmentation of piglets in farrowing pens
2023, Computers and Electronics in AgricultureOcclusions, such as farrowing pens in piggeries, hinder computer vision applications for automated animal monitoring. Amodal instance segmentation (AIS), aiming to predict a complete mask of an occluded target, is a promising solution. However, AIS usually requires amodal datasets, which are challenging to create and limit the application of AIS. To solve this problem, we proposed a novel semi-supervised generative adversarial network (GAN) for AIS, denoted “the AISGAN”. Our AISGAN only requires a regular modal dataset and generate amodal samples by random occlusions, making the AIS method more applicable. A corresponding segmentation loss was added to overcome mode collapse of GAN. The results showed that the AISGAN achieved a mean Intersection of Union (mIoU) of 0.823 and outperformed the mIoUs of Mask RCNN, Raw, and Convex Hull (0.801, 0.780, and 0.778, respectively). As a semi-supervised method, the mIoU of our AISGAN was further enhanced (by 0.6%) when we fine-tuned it with unlabeled new data, showing its extensibility to new unseen scenarios. The visualization demonstrates that the AISGAN can produce realistic masks of piglets, including details of their noses and legs, even under heavily occluded conditions. With the AISGAN, we achieved an occlusion-resistant spatial distribution analysis of the piglets in farrowing pens. Thus, the AISGAN is a promising tool to manage occlusion problems for automated animal monitoring in complex housing environments.
Cargo transport properties are enhanced by cylindrical microtubule geometry and elliptical contact zone on cargo surface
2023, Journal of Theoretical BiologyMolecular motors are responsible for carrying cellular transport of various membranous vesicles or organelles along cytoskeletal tracks. Transport of cellular cargos require high forces that are generated by motors working in groups. Hence, the properties of cargo transport can be modulated by varying various parameters such as cargo size and shape, microtubule geometry, motor number and their arrangement on cargo surface. Only those motors which are present in the contact zone on cargo surface have potential to bind to microtubule. Although earlier studies revealed the importance of cargo size, total motors attached to microtubule and their arrangement on cargo transport, yet how the contact zone influences binding of motors to microtubule largely remains unexplored. Here, it has been shown that contact zone is elliptical in shape for a spherical cargo and increases with cargo size for Kinesin-1 motors. To further understand the combined effect of elliptical contact zone and microtubule geometry on cargo transport, 3D mean-field model with uniform and clustered arrangement of motors for different cargo sizes and motor number has been used. Our findings indicate that cylindrical microtubule geometry maximizes the microtubule-bound motors which enhances the runlength and velocity of cargo transport. Our results show that microtubule-bound motors decrease with cargo size for uniform arrangement of motors on cargo thus decreasing its runlength and velocity, whereas in clustered arrangement, the number of microtubule-bound motors increase with cargo size which leads to increase in runlength and velocity.
Finite Algebras for Solid Modeling using Julia's Sparse Arrays
2023, CAD Computer Aided DesignAn early research in solid modeling led by Herbert Voelcker at the University of Rochester and later at Cornell suggested that every solid representation scheme corresponds to an algebra, where the elements of the algebra are solid representations constructed and edited using operations in the algebra. For example, every CSG representation describes an element in a finite Boolean algebra of closed regular sets, whereas every boundary representation describes an element of a vector space of 2-chains in an algebraic topological chain complex. In this paper, we elucidate the precise relationships (functors) between all algebras used for CSG and boundary representations of solids. Based on these properties, we show that many solid modeling operations, including boundary evaluation, reduce to straightforward algebraic operations or application of identified functors that are efficiently implemented using point membership tests and sparse matrix operations. To fully exploit the efficacy of the new algebraic approach to solid modeling, all algorithms are fully implemented in Julia, the modern language of choice for numerical and scientific computing.
ECKM: An improved K-means clustering based on computational geometry
2023, Expert Systems with ApplicationsA modified version of traditional k-means clustering algorithm applying computational geometry for initialization of cluster centers has been presented in this paper. It is well known that the quality of k-means clustering depends on its random initialization of centers. This paper shows that when the initial cluster centers are selected from the list of circumference points of the empty circles sorted in non-increasing order of their corresponding radii, it can significantly improv
ethe performance. The proposed algorithm is named as Empty Circles based k-means (ECKM) Clustering, which was successfully implemented with PYTHON. Extensive experimentation was carried out on various benchmark data sets that includes both artificial and real data sets having different shapes, sizes and features. In order to minimize the size of this paper, we presented the results for seven of such benchmark datasets, viz., iris, wine, hepta, flame compound, breast_cancer and DS577 although in reality we experimented for more than fifteen data sets in order to validate our ECKM. Results establish the superiority of the ECKM clustering over standard techniques.