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Related Concept Videos

Parametric Surfaces01:30

Parametric Surfaces

A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
Quadric Surfaces01:28

Quadric Surfaces

Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
Tangent Planes to a Parametric Surface01:22

Tangent Planes to a Parametric Surface

A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...
Methods of Obtaining Topography01:25

Methods of Obtaining Topography

Topography involves measuring and mapping land elevations, natural features, and artificial structures to create accurate representations of the terrain. Topographic surveying relies on traditional and modern methods, each with distinct advantages and limitations.Traditional Surveying Methods:Transit stadia surveys and plane table surveys were widely used traditional surveying methods. These techniques relied on instruments like theodolites and stadia rods for measuring distances and angles,...
Calculus with Parametric Curves: Surface Areas01:30

Calculus with Parametric Curves: Surface Areas

A parametric curve is a description of a path in the plane where both the x and y coordinates are functions of a single parameter, typically denoted t. When such a curve is revolved about an external axis lying in the same plane, it generates a surface of revolution in three dimensions. The surface area of this rotated shape depends fundamentally on two aspects: the geometry of the original curve and how far it lies from the chosen axis of rotation.A torus is a classical surface of revolution...
Cylinders in Three-Dimensional Space01:28

Cylinders in Three-Dimensional Space

A cylindrical surface is generated when a two-dimensional profile curve is translated along a straight line in three-dimensional space. The translated copies of the curve form a surface composed of parallel rulings, each oriented in the same fixed direction. This construction allows many three-dimensional forms to be described using relatively simple planar equations.In Cartesian coordinates, a cylindrical surface is often recognized by an equation that omits one of the three variables. For...

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Data Processing Methods for 3D Seismic Imaging of Subsurface Volcanoes: Applications to the Tarim Flood Basalt
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Data Processing Methods for 3D Seismic Imaging of Subsurface Volcanoes: Applications to the Tarim Flood Basalt

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Three-dimensional surface relief completion via nonparametric techniques.

Toby P Breckon1, Robert B Fisher

  • 1Applied Mathematics and Computing Group, School of Engineering, Cranfield University, Bedford, UK. toby.breckon@cranfield.ac.uk

IEEE Transactions on Pattern Analysis and Machine Intelligence
|November 8, 2008
PubMed
Summary
This summary is machine-generated.

This study presents a novel method for completing missing 3D scene data, improving 3D reconstruction from 2.5D scans. The technique uses existing visible data to infer and fill in hidden areas for more complete 3D models.

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Area of Science:

  • Computer Vision
  • 3D Reconstruction
  • Geometric Modeling

Background:

  • Current 3D acquisition methods like laser scanning and stereo capture often result in 2.5D data, leaving hidden or missing portions of scenes.
  • Incomplete 3D data poses challenges for applications requiring full scene representation.

Purpose of the Study:

  • To develop an automated approach for completing missing or hidden regions in 3D scenes captured using 2.5D techniques.
  • To enhance the completeness and accuracy of 3D scene reconstructions.

Main Methods:

  • Proposed an automated method for 3D scene completion.
  • Utilized non-parametric propagation of scene knowledge from visible areas to invisible regions.
  • Incorporated initial underlying geometric surface completion.

Main Results:

  • Successfully demonstrated automated completion of hidden and missing 3D scene portions.
  • The approach effectively leverages available scene data to infer and reconstruct unseen areas.
  • Achieved enhanced geometric accuracy in the completed 3D models.

Conclusions:

  • The proposed method offers a robust solution for addressing data gaps in 2.5D 3D captures.
  • This technique advances automated 3D reconstruction by enabling the generation of complete scene representations.
  • The approach has potential applications in various fields requiring detailed 3D scene analysis.