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

Area Between Curves: Problem Solving01:27

Area Between Curves: Problem Solving

A region can be enclosed by three curves: a square root function, a reflected cube root function, and a linear function. The linear function intersects each of the other two curves, and these intersection points determine where the boundary of the enclosed region changes. Because different curves serve as the upper and lower boundaries in different parts of the graph, the area cannot be found using a single setup over the entire interval.To compute the area, the region is first divided into two...
Area Problem01:26

Area Problem

Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
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...
Areas Within Irregular Boundaries01:26

Areas Within Irregular Boundaries

Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and environmental management. Surveyors often begin by creating a traverse, a connected series of straight lines approximating the area's boundary. The coordinates of each traverse point are essential for calculating the enclosed area. The double meridian distance formula is a widely used technique for this purpose. This method utilizes the...
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...
Area Computation by the Alternative Coordinate Method01:24

Area Computation by the Alternative Coordinate Method

The alternative coordinate method, also known as the Shoelace Formula, is a technique for determining the area of a traverse using Cartesian coordinates. This method relies on the sequential arrangement of x and y coordinates for each point of the shape, ensuring accuracy and ease of application.In this approach, each corner's x and y coordinates are listed as fractions, with the x-coordinate as the numerator and the y-coordinate as the denominator. These coordinates are arranged sequentially...

You might also read

Related Articles

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

Sort by
Same author

CARL: A Framework for Equivariant Image Registration.

Proceedings. IEEE Computer Society Conference on Computer Vision and Pattern Recognition·2026
Same author

Inverse Consistency by Construction for Multistep Deep Registration.

Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention·2026
Same author

LiftReg: Limited Angle 2D/3D Deformable Registration.

Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention·2026
Same author

Erratum for: Prediction of Lobar Emphysema Progression with a CT-Based Foundational Model.

Radiology·2026
Same author

uniGradICON: A Foundation Model for Medical Image Registration.

Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention·2026
Same author

Prediction of Lobar Emphysema Progression with a CT-Based Foundational Model.

Radiology·2026
Same journal

ContiMorph: An unsupervised learning framework for cardiac motion tracking with time-continuous diffeomorphism.

Medical image analysis·2026
Same journal

MedP-CLIP: Medical CLIP with region-aware prompt integration.

Medical image analysis·2026
Same journal

Multi-organ guided diagnosis of mild cognitive impairment via hierarchical alignment and knowledge distillation.

Medical image analysis·2026
Same journal

SUDA: Simultaneous unsupervised knowledge distillation and adaptation of foundation models for efficient pathological image analysis.

Medical image analysis·2026
Same journal

Beyond the LUMIR challenge: The pathway to foundational registration models.

Medical image analysis·2026
Same journal

Annotation-efficient medical image segmentation via cross-latent graphs and vector-quantized memory.

Medical image analysis·2026
See all related articles

Related Experiment Video

Updated: May 17, 2026

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data
12:08

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data

Published on: August 13, 2014

Segmentation with area constraints.

Marc Niethammer1, Christopher Zach

  • 1Department of Computer Science, University of North Carolina-UNC, Chapel Hill, USA. mn@cs.unc.edu

Medical Image Analysis
|October 23, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a novel image segmentation method with explicit area constraints. This approach overcomes limitations of traditional methods, enabling more accurate segmentation of structures like vesicles in electron tomography images.

Related Experiment Videos

Last Updated: May 17, 2026

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data
12:08

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data

Published on: August 13, 2014

Area of Science:

  • Medical Imaging
  • Computational Biology
  • Computer Vision

Background:

  • Traditional image segmentation methods rely on implicit shape or boundary information.
  • Explicit control over segmentation area or volume is often lacking.
  • Length-based regularization can introduce a shrinking bias in segmentation results.

Purpose of the Study:

  • To develop an image segmentation method with explicit area constraints.
  • To address the limitations of convex relaxations for size-constrained segmentation.
  • To enable soft selection of meaningful solutions and counteract shrinking bias.

Main Methods:

  • Formulation of area-constrained segmentation as a mixed integer program.
  • Development of a branch and bound method for exact minimization.
  • Utilization of convex relaxations for lower energy bounds and a numerical scheme for subproblems.

Main Results:

  • A novel method for area-constrained image segmentation was developed.
  • The method effectively counteracts the shrinking bias of length-based regularization.
  • Demonstrated successful segmentation of vesicles in electron tomography images.

Conclusions:

  • Explicit area constraints provide a powerful tool for image segmentation.
  • The proposed mixed integer programming approach offers exact minimization.
  • This method enhances the accuracy and reliability of segmenting biological structures.