Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Histogram01:05

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data represents (for instance, distance from your home to school). The vertical y-axis is labeled either frequency or relative frequency (or percent frequency or probability).
A histogram graph consists of contiguous (adjoining) boxes. The heights of the bars correspond to frequency values. The graph will have the same shape with respective labels. The...
Line, Surface, and Volume Integrals01:15

Line, Surface, and Volume Integrals

A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a prescribed path. If the prescribed path is closed, the integrals reduce to a closed-line integral. The closed-contour integral of the vector field is referred to in terms of the circulation of the vector field around the closed path. A vector with zero circulation around every closed path is called a conservative field, while one with non-zero...
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.
Area Between Curves: Integrating With Respect to x01:25

Area Between Curves: Integrating With Respect to x

Consider two continuous functions defined on a closed interval from a to b. The region between these curves is bounded vertically by their graphs and horizontally by the endpoints of the interval. The objective is to measure the area of this region.An initial estimate of the area can be obtained by dividing the interval into a large number of narrow vertical strips of equal width. Each strip is approximated by a rectangle whose height is given by the vertical difference between the two...
Statgraphics01:10

Statgraphics

Statgraphics is a comprehensive statistical software suite designed for both basic and advanced data analysis. Originating in 1980 at Princeton University under Dr. Neil W. Polhemus, it was one of the pioneering tools for statistical computing on personal computers, with its public release in 1982 marking an early milestone in data science software. Over the years, it has evolved into a robust platform for data science, offering tools for regression analysis, ANOVA, multivariate statistics,...
Area Between Curves: Integrating With Respect to y01:29

Area Between Curves: Integrating With Respect to y

Consider a planar region bounded by two curves that are both written as functions of the vertical variable, y. The left and right boundary curves are continuous between y = c and y = d, and these two horizontal lines define the vertical limits of the region. Because the boundaries depend on y rather than x, the area is most appropriately evaluated using horizontal slices.The area is obtained using the Riemann sum method. The region is divided into many thin horizontal strips, each having an...

You might also read

Related Articles

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

Sort by
Same author

PLUTO: A Public Value Assessment Tool.

IEEE computer graphics and applications·2026
Same author

A Multidimensional Assessment Method for Visualization Understanding (MdamV).

IEEE transactions on visualization and computer graphics·2026
Same author

Untangling Rhetoric, Pathos, and Aesthetics in Data Visualization.

IEEE transactions on visualization and computer graphics·2025
Same author

The Importance of Being Thorough: How Data Analysis Choices Impact the Perceived Relationship between Pollutants and Predictors.

Water research·2025
Same author

Visual Data Analysis of Time-Based Transport Optimizations.

IEEE computer graphics and applications·2025
Same author

Multi-Field Visualization: Trait Design and Trait-Induced Merge Trees.

IEEE transactions on visualization and computer graphics·2025
Same journal

Blue Noise Dithering for Reservoir-based Spatio-temporal Importance Resampling.

IEEE transactions on visualization and computer graphics·2026
Same journal

ROS-GS: Relightable Outdoor Scenes With Gaussian Splatting.

IEEE transactions on visualization and computer graphics·2026
Same journal

MesoSplats: Texture Synthesis with Gaussian Splatting.

IEEE transactions on visualization and computer graphics·2026
Same journal

GLLA: A Unified Force-Directed Graph Layout Framework Supporting Local Adjustments.

IEEE transactions on visualization and computer graphics·2026
Same journal

Multi-Perception Crowd: Learning to combine entity and implicit perception for diverse crowd simulation.

IEEE transactions on visualization and computer graphics·2026
Same journal

Hiding in Plain Sight: Camouflaging Real-world Objects.

IEEE transactions on visualization and computer graphics·2026
See all related articles

Related Experiment Video

Updated: May 22, 2026

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
09:37

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

Integrating Isosurface Statistics and Histograms.

Brian Duffy, Hamish Carr, Torsten Möller

    IEEE Transactions on Visualization and Computer Graphics
    |May 9, 2012
    PubMed
    Summary
    This summary is machine-generated.

    This study introduces a mathematical model for quantized statistics of continuous functions sampled on regular lattices. It reconciles existing theories and proves convergence for geometric approximations, offering guidance on computational costs.

    More Related Videos

    Analysis of Astrocyte Territory Volume and Tiling in Thick Free-Floating Tissue Sections
    10:53

    Analysis of Astrocyte Territory Volume and Tiling in Thick Free-Floating Tissue Sections

    Published on: April 20, 2022

    Analyzing Cellular Internalization of Nanoparticles and Bacteria by Multi-spectral Imaging Flow Cytometry
    18:07

    Analyzing Cellular Internalization of Nanoparticles and Bacteria by Multi-spectral Imaging Flow Cytometry

    Published on: June 8, 2012

    Related Experiment Videos

    Last Updated: May 22, 2026

    Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
    09:37

    Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

    Published on: April 26, 2016

    Analysis of Astrocyte Territory Volume and Tiling in Thick Free-Floating Tissue Sections
    10:53

    Analysis of Astrocyte Territory Volume and Tiling in Thick Free-Floating Tissue Sections

    Published on: April 20, 2022

    Analyzing Cellular Internalization of Nanoparticles and Bacteria by Multi-spectral Imaging Flow Cytometry
    18:07

    Analyzing Cellular Internalization of Nanoparticles and Bacteria by Multi-spectral Imaging Flow Cytometry

    Published on: June 8, 2012

    Area of Science:

    • Data Science
    • Applied Mathematics
    • Statistical Modeling

    Background:

    • Data sets are often sampled on regular lattices in multiple dimensions.
    • Previous work highlighted the importance of underlying physical phenomena continuity for statistical properties.
    • The impact of quantization on these statistics remained unaddressed.

    Purpose of the Study:

    • To reconcile previous statistical findings with underlying mathematical theory.
    • To develop a mathematical model for quantized statistics of continuous functions.
    • To analyze the computational cost of different statistical approaches.

    Main Methods:

    • Developed a mathematical model for quantized statistics.
    • Proved convergence of geometric approximations to continuous statistics for regular sampling lattices.
    • Evaluated the computational expense of various statistical methods.

    Main Results:

    • Established a unified mathematical framework for quantized statistics.
    • Demonstrated the convergence of geometric approximations for lattice-sampled data.
    • Provided recommendations on the selection of statistical methods based on computational efficiency.

    Conclusions:

    • The developed model accurately represents quantized statistics for continuous functions on regular lattices.
    • Geometric approximations are shown to converge to continuous statistics.
    • Guidance is provided for choosing appropriate statistical methods considering computational trade-offs.