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 Experiment Video

Updated: May 29, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

Filtering closed curves.

B K Horn1, E J Weldon

  • 1Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

Introduction to Horizontal Curves01:19

Introduction to Horizontal Curves

Horizontal curves are essential in highway and railroad design, ensuring smooth and safe transitions between straight path segments, or tangents. These curves allow vehicles to maintain speed without abrupt changes, minimizing accidents and improving travel efficiency.A horizontal curve is typically defined by its geometric relationship to two tangents that meet at an intersection point (P.I.), where a simple curve is introduced to connect them. The back tangent refers to the initial tangent...
Horizontal Curve: Problem Solving01:03

Horizontal Curve: Problem Solving

A horizontal curve is characterized by its radius, intersection angle, and stationing of key points. In this case, the radius is 400 meters, and the angle of intersection is 30 degrees, with the station of the point of curvature (P.C.) at 0 + 150 meters. The goal is to determine the station values at the point of intersection (P.I.), point of tangency (P.T.), and midpoint of the curve, as well as the length of the long chord.The process begins with calculating the tangent distance (T) and the...
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...
Curve Sketching and Derivatives01:22

Curve Sketching and Derivatives

Understanding the behavior of a function through its first and second derivatives is essential for analyzing its graph. Derivatives provide insight into where a function increases or decreases, where it attains local maxima or minima, and how its curvature behaves across different intervals.The first derivative of a function reveals the slope of the tangent line at any given point. Points where the derivative is zero or undefined are considered critical, as they often indicate potential extrema...
Guidelines for Sketching a Curve01:23

Guidelines for Sketching a Curve

Curve sketching is a systematic method for understanding the overall behavior of a function by analyzing its key mathematical features. A function defines a curve on the coordinate plane, where the horizontal axis represents the input variable and the vertical axis represents the output. The process begins by determining the domain, which specifies the set of input values for which the function is defined and establishes the horizontal extent of the graph.Intercepts with the horizontal and...
Introduction to Vertical Curves01:24

Introduction to Vertical Curves

Vertical curves are parabolic transitions that connect different grades on highways and railroads, ensuring a smooth alignment between back and forward tangents. The back tangent represents the initial grade, while the forward tangent defines the subsequent grade. These curves can be symmetrical, with equal tangent lengths, or nonsymmetrical, with varying lengths. The key points defining a vertical curve include the Point of Vertical Intersection (P.V.I.), where the tangents meet; the Point of...

You might also read

Related Articles

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

Sort by
Same author

Direct passive navigation.

IEEE transactions on pattern analysis and machine intelligence·2011
Same author

Calculating the reflectance map.

Applied optics·2010
Same author

Intrinsic stability of unused and retrieved polyethylene glenoid components.

Journal of shoulder and elbow surgery·2001
Same author

Upper extremity overuse injuries in swimming. A discussion of swimmer's shoulder.

Clinics in sports medicine·2001
Same author

Atmospheric effects in satellite imaging of mountainous terrain.

Applied optics·1983
Same author

The volumetric measurement of gastric emptying and gastric secretion by a radioisotope method.

The American journal of digestive diseases·1976
Same journal

TraGraph-GS: Trajectory Graph-based Gaussian Splatting for Arbitrary Large-Scale Scene Rendering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

SWIFT: A Small-World Interaction Framework for Flow-Aware Trajectory Prediction in Autonomous Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

HardFlow: Hard-Constrained Sampling for Flow-Matching Models Via Trajectory Optimization.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Industrial Brain: Self-Evolving Neuro-Symbolic Autonomy with Causal Resilience for Cyber-Physical Systems.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Adaptive Hardness-Driven Dictionary Distillation for Incomplete Streaming View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Mixture of Global and Local Experts with Diffusion Transformer for Controllable Face Generation.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

A novel curve representation using radius of curvature offers advantages for digital image processing. Convolutional filtering of this representation reliably generates closed curves, unlike other methods.

Area of Science:

  • Geometry
  • Computer Vision
  • Digital Image Processing

Background:

  • Representing curves digitally is crucial for various applications.
  • Existing methods for curve representation have limitations in preserving topological properties like closure.

Purpose of the Study:

  • To introduce a new representation for closed curves in the plane.
  • To evaluate the effectiveness of convolutional filtering on this new representation for curve closure.

Main Methods:

  • Developing a curve representation based on radius of curvature versus normal direction.
  • Applying convolutional filtering to this extended circular image representation.
  • Comparing results with filtering applied to alternative curve representations.

More Related Videos

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis
09:36

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

Published on: August 12, 2025

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

Related Experiment Videos

Last Updated: May 29, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
13:04

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation

Published on: January 18, 2022

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis
09:36

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

Published on: August 12, 2025

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

Main Results:

  • Convolutional filtering of the proposed representation reliably produces a closed curve.
  • Filtering other curve representations does not guarantee closure, and sometimes results in smaller curves.

Conclusions:

  • The radius of curvature versus normal direction representation is advantageous for digital curve processing.
  • Convolutional filtering on this representation is a robust method for generating closed curves.