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Related Concept Videos

Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Uncertainty: Confidence Intervals

The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor 't,' or...
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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Stochastic uncertainty models for the luminance consistency assumption.

Thomas Corpetti1, Etienne Mémin

  • 1Sino-French Laboratory on Computer Sciences, Automatics and Applied Mathematics (LIAMA), Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China. tcorpetti@gmail.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|July 28, 2011
PubMed
Summary

This study introduces a stochastic brightness consistency model for computer vision tasks like motion estimation. It accounts for image discretization uncertainties, improving motion estimation reliability and quality.

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Area of Science:

  • Computer Vision
  • Image Processing
  • Stochastic Calculus

Background:

  • Brightness consistency is crucial for dynamic scene analysis in computer vision.
  • Existing models often use a deterministic differential form of luminance constancy.
  • Image data is inherently discrete, introducing uncertainties not fully captured by deterministic models.

Purpose of the Study:

  • To propose a stochastic formulation of brightness consistency that incorporates discretization uncertainties.
  • To develop a more robust model for motion estimation and point tracking in dynamic scenes.
  • To enhance the reliability and accuracy of motion estimation algorithms.

Main Methods:

  • Formalizing image luminance as a continuous function transported by a flow with uncertainties.
  • Applying stochastic calculus to model luminance preservation under discretization.
  • Relaxing deterministic constraints by introducing weaker temporal assumptions and anisotropic uncertainties.
  • Computing uncertainty measures from image data to assess motion estimate reliability.

Main Results:

  • The proposed stochastic model generalizes the deterministic optical flow constraint equation.
  • Relaxing constraints leads to improved motion estimation.
  • Computed uncertainties provide insights into the reliability of motion estimates.
  • A novel local least-squares motion estimator using the stochastic constraint significantly enhances result quality.

Conclusions:

  • The stochastic formulation of brightness consistency offers a more accurate representation of image data.
  • This approach enhances the robustness and reliability of motion estimation in computer vision.
  • The method provides a principled way to quantify uncertainty in motion estimation.