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The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He mathematically...

Propagation of Uncertainty from Random Error

Propagation of Uncertainty from Random Error

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...

Propagation of Uncertainty from Systematic Error

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...

Uncertainty: Overview

Uncertainty: Overview

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.

Uncertainty in Measurement: Accuracy and Precision

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.

Uncertainty in Measurement: Reading Instruments

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such measurements result in exact numbers. By counting the eggs in a carton, for instance, one can determine exactly how many eggs are there in the carton. Similarly, the numbers of defined quantities are also exact. For example, 1 foot is exactly 12 inches, 1 inch is exactly 2.54 centimeters, and 1 gram is exactly 0.001 kilograms. Quantities...

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Related Experiment Video

Updated: May 23, 2026

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

The uncertainty principle in image processing.

R Wilson¹, G H Granlund

¹Department of Electrical Engineering, Linköping University, Linköping, Sweden; Department of Electrical and Electronic Engineering, The University of Aston in Birmingham, Birmingha.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|April 14, 2012

Summary

This summary is machine-generated.

The uncertainty principle, fundamental in signal processing, is crucial for image processing inference. It impacts vision

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Time Multiplexing Super Resolving Technique for Imaging from a Moving Platform

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Last Updated: May 23, 2026

Picometer-Precision Atomic Position Tracking through Electron Microscopy

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Published on: February 12, 2014

Area of Science:

Image Processing
Signal Processing
Computer Vision

Background:

The uncertainty principle is a cornerstone of quantum mechanics and signal processing.
Its application in image processing inference is not widely recognized.
Vision involves fundamental constraints like shift-invariance and illumination insensitivity.

Purpose of the Study:

To unify the understanding of uncertainty in image processing.
To demonstrate the link between vision constraints and uncertainty.
To highlight the role of uncertainty in the 'language' of vision.

Main Methods:

Deriving uncertainty from fundamental constraints of vision.
Analyzing requirements for class-defining operations (shift-invariant, illumination-insensitive).
Connecting uncertainty to the choice of elementary signals (alphabet) and inferential structure (syntax).

Main Results:

Uncertainty in image processing can be derived from basic vision constraints.
These constraints necessitate uncertainty in defining visual elements and their relationships.
Uncertainty influences both the basic components (signals) and the processing logic (inference) in vision.

Conclusions:

Uncertainty is a key factor in image processing and computer vision.
It fundamentally shapes how visual information is represented and interpreted.
Practical applications include image enhancement, data compression, and segmentation.