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Related Concept Videos

Probability Histograms01:17

Probability Histograms

A probability histogram is a visual representation of a probability distribution. Similar a typical histogram, the probability histogram consists of contiguous (adjoining) boxes. It has both a horizontal axis and a vertical axis. The horizontal axis is labeled with what the data represents. The vertical axis is labeled with probability. Each rectangular bar in the histogram is 1 unit wide, which suggests that the area under each bar equals the probability, P(x), where x is 1, 2, 3, and so on.
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
The Entropy as a State Function01:14

The Entropy as a State Function

Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...

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Related Experiment Video

Updated: Jun 8, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Point set registration using Havrda-Charvat-Tsallis entropy measures.

Nicholas J Tustison1, Suyash P Awate, Gang Song

  • 1University of Virginia, Radiology, Charlottesville, VA 22903, USA. ntustison@virginia.edu

IEEE Transactions on Medical Imaging
|October 13, 2010
PubMed
Summary

This study presents a new algorithm for labeled point set registration using Havrda-Charvat-Tsallis entropy for robust divergence measurement. The method, implemented in open-source software, shows utility in lung anatomy registration.

Related Experiment Videos

Last Updated: Jun 8, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

Area of Science:

  • Medical Image Analysis
  • Computational Geometry
  • Information Theory

Background:

  • Accurate registration of medical images is crucial for diagnosis and treatment planning.
  • Existing methods often struggle with robustness and fine-tuning for varying data characteristics.

Purpose of the Study:

  • To introduce a novel labeled point set registration algorithm.
  • To leverage generalized information-theoretic measures for improved robustness.
  • To demonstrate the algorithm's effectiveness in medical applications, specifically lung registration.

Main Methods:

  • Utilized a generalization of Shannon entropy: Havrda-Charvat-Tsallis entropy.
  • Employed a directly manipulated free-form deformation approach for transformation modeling.
  • Developed an open-source implementation using the National Institutes of Health Insight Toolkit.

Main Results:

  • The proposed algorithm offers tunable robustness in divergence measures between point sets.
  • Performance was characterized through comparisons with state-of-the-art kernel-based methods.
  • Demonstrated successful application in registering labeled point sets of lung anatomy.

Conclusions:

  • The novel information-theoretic approach provides a flexible and robust framework for labeled point set registration.
  • The open-source implementation facilitates wider adoption and further research.
  • The method shows significant potential for medical image analysis tasks, particularly in lung imaging.