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The problem faced in this paper concerns the recognition of simple and complex geometric primitives in point clouds resulting from scans of mechanical CAD objects. A large number of points, the presence of noise, outliers, missing or redundant parts and uneven distribution are the main problems to be addressed to meet this need. In this article we propose a solution, based on the Hough transform, that can recognize simple and complex geometric primitives and is robust to noise, outliers, and missing parts. Additionally, we can extract a series of geometric descriptors that uniquely characterize a primitive and, based on them, aggregate the output into maximal or compound primitives, thus reducing oversegmentation. The results presented in the paper demonstrate the robustness of the method and its competitiveness with respect to other solutions proposed in the literature.

Voltage-gated sodium (Nav) channels constitute a prime target for drug design and discovery, given their implication in various diseases such as epilepsy, migraine and ataxia to name a few. In this regard, performing morphological analysis is a crucial step in comprehensively understanding their biological function and mechanism, as well as in uncovering subtle details of their mechanism that may be elusive to experimental observations. Despite their tremendous therapeutic potential, drug design resources are deficient, particularly in terms of accurate and comprehensive geometric information. This paper presents a geometric dataset of molecular surfaces that are representative of Nav channels in mammals. For each structure we provide three representations and a number of geometric measures, including length, volume and straightness of the recognized channels. To demonstrate the effective use of GEO-Nav, we have tested it on two methods belonging to two different categories of approaches: a sphere-based and a tessellation-based method.

This paper presents the methods that have participated in the SHREC 2022 track on the fitting and recognition of simple geometric primitives on point clouds. As simple primitives we mean the classical surface primitives derived from constructive solid geometry, i.e., planes, spheres, cylinders, cones and tori. The aim of the track is to evaluate the quality of automatic algorithms for fitting and recognising geometric primitives on point clouds. Specifically, the goal is to identify, for each point cloud, its primitive type and some geometric descriptors. For this purpose, we created a synthetic dataset, divided into a training set and a test set, containing segments perturbed with different kinds of point cloud artifacts. Among the six participants to this track, two are based on direct methods, while four are either fully based on deep learning or combine direct and neural approaches. The performance of the methods is evaluated using various classification and approximation measures.

The automatic creation of geometric models from point clouds has numerous applications in CAD (e.g., reverse engineering, manufacturing, assembling) and, more in general, in shape modelling and processing. Given a segmented point cloud representing a man-made object, we propose a method for recognizing simple geometric primitives and their interrelationships. Our approach is based on the Hough transform (HT) for its ability to deal with noise, missing parts and outliers. In our method we introduce a novel technique for processing segmented point clouds that, through a voting procedure, is able to provide an initial estimate of the geometric parameters characterizing each primitive type. By using these estimates, we localize the search of the optimal solution in a dimensionally-reduced parameter space thus making it efficient to extend the HT to more primitives than those that are generally found in the literature, i.e. planes and spheres. Then, we extract a number of geometric descriptors that uniquely characterize a segment, and, on the basis of these descriptors, we show how to aggregate parts of primitives (segments). Experiments on both synthetic and industrial scans reveal the robustness of the primitive fitting method and its effectiveness for inferring relations among segments.

This paper presents the methods that have participated in the SHREC 2021 contest on retrieval and classification of protein surfaces on the basis of their geometry and physicochemical properties. The goal of the contest is to assess the capability of different computational approaches to identify different conformations of the same protein, or the presence of common sub-parts, starting from a set of molecular surfaces. We addressed two problems: defining the similarity solely based on the surface geometry or with the inclusion of physicochemical information, such as electrostatic potential, amino acid hydrophobicity, and the presence of hydrogen bond donors and acceptors. Retrieval and classification performances, with respect to the single protein or the existence of common sub-sequences, are analysed according to a number of information retrieval indicators.

This paper presents the methods that have participated in the SHREC 2021 contest on retrieval and classification of protein surfaces on the basis of their geometry and physicochemical properties. The goal of the contest is to assess the capability of different computational approaches to identify different conformations of the same protein, or the presence of common sub-parts, starting from a set of molecular surfaces. We addressed two problems: defining the similarity solely based on the surface geometry or with the inclusion of physicochemical information, such as electrostatic potential, amino acid hydrophobicity, and the presence of hydrogen bond donors and acceptors. Retrieval and classification performances, with respect to the single protein or the existence of common sub-sequences, are analysed according to a number of information retrieval indicators.

We propose Fit4CAD, a benchmark for the evaluation and comparison of methods for fitting simple geometric primitives in point clouds representing CAD objects. This benchmark is meant to help both method developers and those who want to identify the best performing tools. The Fit4CAD dataset is composed by 225 high quality point clouds, each of which has been obtained by sampling a CAD object. The way these elements were created by using existing platforms and datasets makes the benchmark easily expandable. The dataset is already split into a training set and a test set. To assess performance and accuracy of the different primitive fitting methods, various measures are defined. To demonstrate the effective use of Fit4CAD, we have tested it on two methods belonging to two different categories of approaches to the primitive fitting problem: a clustering method based on a primitive growing framework and a parametric method based on the Hough transform.

Continuous representations are fundamental for modeling sampled data and performing computations and numerical simulations directly on the model or its elements. To effectively and efficiently address the approximation of point clouds we propose the Weighted Quasi Interpolant Spline Approximation method (wQISA). We provide global and local bounds of the method and discuss how it still preserves the shape properties of the classical quasi-interpolation scheme. This approach is particularly useful when the data noise can be represented as a probabilistic distribution: from the point of view of nonparametric regression, the wQISA estimator is robust to random perturbations, such as noise and outliers. Finally, we show the effectiveness of the method with several numerical simulations on real data, including curve fitting on images, surface approximation and simulation of rainfall precipitations.

In this paper we investigate a local surface approximation, the Weighted Quasi Interpolant Spline Approximation (wQISA), specifically designed for large and noisy point clouds. We briefly describe the properties of the wQISA representation and introduce a novel data-driven implementation, which combines prediction capability and complexity efficiency. We provide an extended comparative analysis with other continuous approximations on real data, including different types of surfaces and levels of noise, such as 3D models, terrain data and digital environmental data.

In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is of interest to extract information about the underlying geometry through reverse engineering. In this work we develop a novel method to determine these primitive shapes by combining clustering analysis with approximate implicitization. The proposed method is automatic and can recover algebraic hypersurfaces of any degree in any dimension. In exact arithmetic, the algorithm returns exact results. All the required parameters, such as the implicit degree of the patches and the number of clusters of the model, are inferred using numerical approaches in order to obtain an algorithm that requires as little manual input as possible. The effectiveness, efficiency and robustness of the method are shown both in a theoretical analysis and in numerical examples implemented in Python.