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Attributes Attributes

Point Cloud and Mesh Attributes

Overview​

Attributes are geometric and statistical properties computed for vertices (points) or triangles in a 3D model. These attributes are derived by analyzing the local neighborhood either using a search radius or by specifying the number of nearest neighbors.

Vertex Attributes​

Vertex attributes are properties computed for each point in a point cloud based on its local neighborhood.

Eigenvalue-Based Attributes​

These attributes are derived from eigenvalue analysis of the local point neighborhood, producing three eigenvalues (λ₁ ≥ λ₂ ≥ λ₃) that describe the geometric distribution of points.

  • Eigen Values x3: The three eigenvalues (λ₁, λ₂, λ₃) computed from the local neighborhood. These describe the variance along principal directions
  • Sum of Eigenvalues: Sum of all three eigenvalues (Σλᵢ). Represents the total variance in the local neighborhood
  • Omnivariance: Cubic root of the product of eigenvalues: (λ₁ × λ₂ × λ₃)^(1/3). Measures the 3D spread of the local point distribution
  • Eigenentropy: Entropy measure of eigenvalue distribution: −Σλᵢ ln(λᵢ). Indicates the disorder or randomness in the local geometry

Dimensionality Features​

These attributes characterize the local surface.

  • Linearity: (λ₁ − λ₂)/λ₁. Measures how linear the local feature is. Values close to 1 indicate linear features
  • Planarity: (λ₂ − λ₃)/λ₁. Measures how planar the local feature is. Values close to 1 indicate flat surfaces
  • Sphericity: λ₃/λ₁. Measures how 3D the local feature is. Values close to 1 indicate scattered point distributions
  • Colinearity: How linear the surface is. Indicates the degree to which points are arranged along a line
  • Coplanarity: How planar the surface is. Indicates the degree to which points lie on a flat plane

Geometric Properties​

  • Elevation: The Z coordinate value of the vertex in the project coordinate system
  • Range: Distance from the scanner origin to the point. Only applicable to spherical scan datasets where sensor position is known
  • Dip: The dip angle of the local surface orientation. Measures the angle of inclination from horizontal (0-90 degrees)
  • Azimuth: The azimuth or strike direction of the local surface. Measures the compass direction (0-360 degrees)
  • Pole x3: The X, Y, and Z components of the pole vector (normal vector perpendicular to the local surface). Three separate attributes

Curvature and Surface Complexity​

  • Change of Curvature: λ₃/(λ₁ + λ₂ + λ₃). Estimates the local surface curvature. Higher values indicate more curved surfaces
  • Verticality (x2): Two attributes measuring the angle between eigenvectors and the vertical (Z) axis: −angle(eᵢ, eᵧ). Used to detect vertical structures

Statistical Moments​

  • Absolute Moment (x6): Six attributes representing absolute moments of the point distribution. Used for shape characterization
  • Vertical Moment (x2): Two attributes representing vertical moments of the point distribution

Point Count and Color​

  • Number of Points: The count (N) of neighboring points used in the attribute calculation. Indicates the local point density
  • Average Color (x3): Three attributes for the average red, green, and blue color values in the local neighborhood
  • Color Variance (x3): Three attributes for the variance of red, green, and blue color values in the local neighborhood. Indicates color heterogeneity

Triangle Attributes​

Triangle attributes are properties computed for each triangular face in a mesh surface.

Orientation Attributes​

  • Dip: The dip angle of the triangle face. Measures the angle of inclination from horizontal (0-90 degrees)
  • Azimuth: The azimuth or strike direction of the triangle face. Measures the compass direction (0-360 degrees)

Statistical and Geometric Measures​

  • Fisher K Value: The Fisher concentration parameter (K) computed from connected triangles. Higher K values indicate more clustered or consistent orientations in the local area. Used for assessing surface orientation consistency
  • Triangle Area: The surface area of the triangle. Measured in square units of the project coordinate system
  • Max Edge Length: The length of the longest edge of the triangle. Useful for identifying elongated or poor-quality triangles

Fracture Analysis​

  • P21 Map: A fracture intensity attribute derived from trace analysis. P21 represents the fracture intensity as total trace length per unit area. Used for fracture network characterization

Computation Methods​

Attributes can be computed using two neighborhood selection methods:

  1. Search Radius: Include all points/triangles within a specified distance from the target point/triangle
  2. K-Nearest Neighbors: Include the K closest points/triangles to the target point/triangle

The choice of method and parameter values (radius size or K value) significantly affects the scale of features detected.

References​

Fernández, O. (2005). Obtaining a best fitting plane through 3D georeferenced data. Journal of Structural Geology, 27, 855-858. https://www.sciencedirect.com/science/article/abs/pii/S0191814105000143

Weinmann, M., Jutzi, B., & Mallet, C. (2013). Feature relevance assessment for the semantic interpretation of 3D point cloud data. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume II-5/W2, 313-318. https://www.isprs-ann-photogramm-remote-sens-spatial-inf-sci.net/II-5-W2/313/2013/isprsannals-II-5-W2-313-2013.pdf

Hackel, T., Wegner, J. D., & Schindler, K. (2016). Fast Semantic Segmentation of 3D Point Clouds with Strongly Varying Density. ISPRS Annual Congress of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Prague, Czech Republic, July 12-19, 2016. https://ethz.ch/content/dam/ethz/special-interest/baug/igp/photogrammetry-remote-sensing-dam/documents/pdf/timo-jan-isprs2016.pdf

Demantké, J., Mallet, C., David, N., & Vallet, B. (2012). Dimensionality based scale selection in 3D LiDAR point clouds. ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. http://recherche.ign.fr/labos/matis/pdf/articles_conf/2011/laserscanning2011_demantke_final.pdf