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Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

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A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
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Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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Glassware Calibration01:11

Glassware Calibration

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Accurate calibration of glassware, such as volumetric flasks, pipettes, and burettes, is essential to ensure accurate measurements in the analytical laboratory. Calibration helps maintain consistency across measurements and prevents errors arising from inaccurate volumes.
Volumetric flasks: Volumetric flasks are designed to prepare aqueous solutions of precise volumes accurately with a calibration line on the neck. To calibrate a volumetric flask, it is important to fill it with distilled...
1.3K
Instrument Calibration01:12

Instrument Calibration

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Instrument calibration is essential for ensuring that instruments produce accurate and consistent results. It is vital in manufacturing, healthcare, testing laboratories, and scientific research. Calibration processes are specific to each instrument and help enhance data accuracy. Each instrument has a unique calibration process tailored to its design and function to improve data accuracy.
Analytical Balance Calibration
An analytical balance measures mass and requires regular calibration to...
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Regression Toward the Mean01:52

Regression Toward the Mean

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

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Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
Here, in order to determine the magnitude of velocity and acceleration for point...
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Related Experiment Video

Updated: Jan 10, 2026

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery
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Knowledge-Guided Symbolic Regression for Interpretable Camera Calibration.

Rui Pimentel de Figueiredo1

  • 1Department of Mechanical and Production Engineering, Aarhus University, 8200 Aarhus, Denmark.

Journal of Imaging
|November 26, 2025
PubMed
Summary
This summary is machine-generated.

This study introduces a novel symbolic model discovery framework for camera calibration, offering an interpretable and efficient alternative to traditional and neural methods. It accurately identifies lens distortion models, even with limited data.

Keywords:
calibrationcameradistortion modelsgenetic programmingmodel selectionsymbolic regression

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Area of Science:

  • Computer Vision
  • Optical Engineering
  • Machine Learning

Background:

  • Accurate camera calibration is crucial for applications like autonomous navigation and robotics.
  • Existing models (pinhole, radial-tangential) and neural methods have limitations in handling complex distortions, data requirements, and computational cost.

Purpose of the Study:

  • To develop a flexible, interpretable, and resource-efficient symbolic model discovery framework for camera calibration.
  • To identify lens-specific projection and distortion models that accurately represent optical deviations.

Main Methods:

  • Utilized symbolic regression and genetic programming (GP) guided by physical knowledge.
  • Incorporated established distortion models (Brown-Conrady, Mei-Rives, Kannala-Brandt, double-sphere) as modular components.
  • Embedded models into the symbolic search to constrain the solution space for efficient parameter fitting and model selection.

Main Results:

  • The framework successfully identified calibration models for various lens types (fisheye, omnidirectional, catadioptric, traditional).
  • Achieved comparable or superior results to existing calibration techniques.
  • Demonstrated robustness against overfitting and efficiency in parameter fitting.

Conclusions:

  • The proposed symbolic model discovery framework offers a flexible and interpretable alternative for camera calibration.
  • It is particularly suitable for scenarios with scarce calibration data or limited computational resources.
  • The method provides accurate and efficient lens distortion modeling.