A language of thought for the mental representation of geometric shapes

Why do geometric shapes such as lines, circles, zig-zags or spirals appear in all human cultures, but are never produced by other animals? Here, we formalize and test the hypothesis that all humans possess a compositional language of thought that can produce line drawings as recursive combinations of a minimal set of geometric primitives. We present a programming language, similar to Logo, that combines discrete numbers and continuous integration in higher-level structures based on repetition, concatenation and embedding, and show that the simplest programs in this language generate the fundamental geometric shapes observed in human cultures. On the perceptual side, we propose that shape perception in humans involves searching for the shortest program that correctly draws the image (program induction). A consequence of this framework is that the mental difficulty of remembering a shape should depend on its minimum description length (MDL) in the proposed language. In two experiments, we show that encoding and processing of geometric shapes is well predicted by MDL. Furthermore, our hypotheses predict additive laws for the psychological complexity of repeated, concatenated or embedded shapes, which are experimentally validated.

Voxelisation Algorithms and Data Structures: A Review

Voxel-based data structures, algorithms, frameworks, and interfaces have been used in computer graphics and many other applications for decades. There is a general necessity to seek adequate digital representations, such as voxels, that would secure unified data structures, multi-resolution options, robust validation procedures and flexible algorithms for different 3D tasks. In this review, we evaluate the most common properties and algorithms for voxelisation of 2D and 3D objects. Thus, many voxelisation algorithms and their characteristics are presented targeting points, lines, triangles, surfaces and solids as geometric primitives. For lines, we identify three groups of algorithms, where the first two achieve different voxelisation connectivity, while the third one presents voxelisation of curves. We can say that surface voxelisation is a more desired voxelisation type compared to solid voxelisation, as it can be achieved faster and requires less memory if voxels are stored in a sparse way. At the same time, we evaluate in the paper the available voxel data structures. We split all data structures into static and dynamic grids considering the frequency to update a data structure. Static grids are dominated by SVO-based data structures focusing on memory footprint reduction and attributes preservation, where SVDAG and SSVDAG are the most advanced methods. The state-of-the-art dynamic voxel data structure is NanoVDB which is superior to the rest in terms of speed as well as support for out-of-core processing and data management, which is the key to handling large dynamically changing scenes. Overall, we can say that this is the first review evaluating the available voxelisation algorithms for different geometric primitives as well as voxel data structures.

Automated near-field deformation detection from mobile laser scanning for the 2014 Mw 6.0 South Napa earthquake

Quantifying off-fault deformation in the near field remains a challenge for earthquake monitoring using geodetic observations. We propose an automated change detection strategy using geometric primitives generated using a deep neural network, random sample consensus and least squares adjustment. Using mobile laser scanning point clouds of vineyards acquired after the magnitude 6.0 2014 South Napa earthquake, our results reveal centimeter-level horizontal ground deformation over three kilometers along a segment of the West Napa Fault. A fault trace is detected from rows of vineyards modeled as planar primitives from the accumulated coseismic response, and the postseismic surface displacement field is revealed by tracking displacements of vineyard posts modeled as cylindrical primitives. Interpreted from the detected changes, we summarized distributions of deformation versus off-fault distances and found evidence of off-fault deformation. The proposed framework using geometric primitives is shown to be accurate and practical for detection of near-field off-fault deformation.

Multiple Cylinder Extraction from Organized Point Clouds

Most man-made objects are composed of a few basic geometric primitives (GPs) such as spheres, cylinders, planes, ellipsoids, or cones. Thus, the object recognition problem can be considered as one of geometric primitives extraction. Among the different geometric primitives, cylinders are the most frequently used GPs in real-world scenes. Therefore, cylinder detection and extraction are of great importance in 3D computer vision. Despite the rapid progress of cylinder detection algorithms, there are still two open problems in this area. First, a robust strategy is needed for the initial sample selection component of the cylinder extraction module. Second, detecting multiple cylinders simultaneously has not yet been investigated in depth. In this paper, a robust solution is provided to address these problems. The proposed solution is divided into three sub-modules. The first sub-module is a fast and accurate normal vector estimation algorithm from raw depth images. With the estimation method, a closed-form solution is provided for computing the normal vector at each point. The second sub-module benefits from the maximally stable extremal regions (MSER) feature detector to simultaneously detect cylinders present in the scene. Finally, the detected cylinders are extracted using the proposed cylinder extraction algorithm. Quantitative and qualitative results show that the proposed algorithm outperforms the baseline algorithms in each of the following areas: normal estimation, cylinder detection, and cylinder extraction.

PHOTOGRAMMETRY AND COMPUTED TOMOGRAPHY POINT CLOUD REGISTRATION USING VIRTUAL CONTROL POINTS

In this paper we propose a virtual control point based method for the registration of photogrammetry and computed tomography (CT) data. Because of the fundamentally different two data sources, conventional registration methods, such as manual control points registration or 3D local feature-based registration, are not suitable. The registration objective of our application is about 3D reconstructions of gyroscopes, which contain abundant geometric primitives to be fitted in the point clouds. In the first place, photogrammetry and CT scanning are applied, respectively, for 3D reconstructions. Secondly, our workflow implements a segmentation after obtaining the surface point cloud from the complete CT volumetric data. Then geometric primitives are fitted in this point cloud benefitting from the less complex cluster segments. In the next step, intersection operations of the parametrized primitives generates virtual points, which are utilized as control points for the transformation parameters estimation. A random sample consensus (RANSAC) method is applied to find the correspondences of both virtual control point sets using corresponding descriptors and calculates the transformation matrix as an initial alignment for further refining the registration. The workflow is invariant to pose, resolution, completeness and noise within our validation process.