Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Search research articles

Related Experiment Video

Updated: Sep 15, 2025

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Published on: May 10, 2020

Employing variance component estimation for point cloud based geometric surface representation by B-splines.

Elisabeth Ötsch¹, Corinna Harmening², Hans Neuner¹

¹Research Group Engineering Geodesy, Geodesy and Geoinformation, TU Vienna, Vienna, Austria.

Journal of Applied Geodesy

|July 16, 2025

Summary

This summary is machine-generated.

Related Concept Videos

Variance

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the...

Curvilinear Motion: Normal and Tangential Components

Curvilinear Motion: Normal and Tangential Components

When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of...

Curvilinear Motion: Rectangular Components

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
As the car advances, its position evolves over time. Quantifying the car's velocity involves computing the...

Vector Components in the Cartesian Coordinate System

Vector Components in the Cartesian Coordinate System

Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if someone gives you directions for a particular location, you will be told to go a few km in a direction like east, west, north, or south, along with the angle in which you are supposed to move. In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is...

Vector Algebra: Method of Components

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...

Variation

Variation

An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

A Review on UAS Trajectory Estimation Using Decentralized Multi-Sensor Systems Based on Robotic Total Stations.

Sensors (Basel, Switzerland)·2025

Same journal

An approach for considering the object surface properties in a TLS stochastic model.

Journal of applied geodesy·2023

See all related articles

This study uses variance component estimation (VCE) to separate measurement and model uncertainties in geometric surface approximation. Realistic separation is achievable when model uncertainty surpasses measurement uncertainty.

Area of Science:

Geodesy
Computational Geometry
Statistical Modeling

Background:

Assessing interepochal displacements relies heavily on stochastic information from point clouds for geometric surface representation.
Uncertainties in point clouds can arise from instrumentation, environment, or object-specific factors, alongside model uncertainty from approximation methods.

Purpose of the Study:

To investigate the realistic estimation and separation of measurement and model uncertainties using variance component estimation (VCE).
To evaluate the effectiveness of VCE in distinguishing between measurement (distance, angular) and model uncertainties (covariance functions).

Main Methods:

Employed variance component estimation (VCE) with the BIQUE-estimation method for tensor product B-spline surface approximation.
Generated a more complex B-spline surface to simulate model uncertainty by artificially altering points.

Keywords:

B-spline approximation TLS measurement uncertainty model uncertainty variance component estimation

More Related Videos

Precision Measurements and Parametric Models of Vertebral Endplates

Precision Measurements and Parametric Models of Vertebral Endplates

Published on: September 17, 2019

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Related Experiment Videos

Last Updated: Sep 15, 2025

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Surface Mapping of Earth-like Exoplanets using Single Point Light Curves

Published on: May 10, 2020

Precision Measurements and Parametric Models of Vertebral Endplates

Precision Measurements and Parametric Models of Vertebral Endplates

Published on: September 17, 2019

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

Separated overlapping variance components related to measurement and model uncertainties.

Main Results:

Variance components were found to be separable and estimable under specific conditions.
Successful separation occurred when model uncertainty exceeded measurement uncertainty.
Inclusion of only points affected by model deviations in the variance-covariance matrix (VCM) setup was crucial.

Conclusions:

VCE is a viable method for disentangling measurement and model uncertainties in geometric point cloud approximation.
The study demonstrates the importance of the relative magnitudes of uncertainties and data selection for accurate VCE.
Findings contribute to more reliable significance assessments of surface changes over time.