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

Gaussian Elimination: Problem Solving01:30

Gaussian Elimination: Problem Solving

Systems of linear equations in several variables are pivotal in modeling complex scenarios involving multiple unknowns and constraints. Such systems are widely used in various fields to represent relationships where several conditions must be simultaneously satisfied. Each variable in the system corresponds to an unknown quantity, while each equation imposes a linear constraint, leading to a structured approach for analyzing and solving real-world problems.A system of three equations with three...
Synthetic Disvision of Polynomials01:28

Synthetic Disvision of Polynomials

Synthetic division is an efficient algorithmic approach for dividing a polynomial by a linear binomial of the form x - c, where c is a real number. This method is helpful due to its streamlined process, which avoids the more cumbersome steps involved in the traditional long division of polynomials. It simplifies computation and serves as a practical tool for evaluating polynomials and identifying their factors.To perform synthetic division, one begins by listing the coefficients of the...
Systems of Linear Equations in Two Variables01:25

Systems of Linear Equations in Two Variables

Solving a system of linear equations is a fundamental concept in algebra. A system of equations consists of two or more linear equations involving the same set of variables. One of the most efficient algebraic methods for solving such systems is the substitution method. This technique involves expressing one variable in terms of the other from one equation and substituting it into the second equation. This method is particularly useful when one of the equations is easily rearranged.Consider the...
Real Zeros of Polynomials01:27

Real Zeros of Polynomials

Polynomials are algebraic expressions of terms with variables raised to non-negative integer powers. A central aspect of analyzing polynomial functions is determining their real zeros—values of the variable for which the polynomial evaluates to zero. These values represent the x-intercepts of the polynomial’s graph.The Rational Zeros Theorem lists possible rational solutions for a polynomial equation with integer coefficients. If f(x)=anxn+....+a0​, then every rational zero is of the form p/q​,...
Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the Complete Factorization...
Introduction to Polynomial Functions01:26

Introduction to Polynomial Functions

Polynomial functions are fundamental elements in algebra and calculus, defined by expressions that combine variables and constants through addition, subtraction, and multiplication, with the variable raised to nonnegative integer exponents. A general polynomial function of degree n is given byWhere an ≠ 0. The term anxn is the leading term, and an is the leading coefficient, while a0 is referred to as the constant term.Characteristics and ClassificationPolynomials are categorized by their...

You might also read

Related Articles

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

Sort by
Same author

A Guide to Structureless Visual Localization.

International journal of computer vision·2026
Same author

An Algebraic Geometry Approach to Viewing Graph Solvability.

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

Are Minimal Radial Distortion Solvers Really Necessary for Relative Pose Estimation?

International journal of computer vision·2026
Same author

CoVAMPnet: Comparative Markov State Analysis for Studying Effects of Drug Candidates on Disordered Biomolecules.

JACS Au·2024
Same author

PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility.

IEEE transactions on pattern analysis and machine intelligence·2023
Same author

Trifocal Relative Pose From Lines at Points.

IEEE transactions on pattern analysis and machine intelligence·2023
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
Same journal

Task-KV: Task-aware KV Cache Optimization via Semantic Differentiation of Attention Heads.

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

Achieving Text-based Person Retrieval with Any Granularity.

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

Related Experiment Video

Updated: May 26, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Polynomial Eigenvalue Solutions to Minimal Problems in Computer Vision.

Zuzana Kukelova1, Martin Bujnak, Tomas Pajdla

  • 1Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Prague, Karlovo namesti 13, 121-35 Praha 2, Czech Republic. kukelova@cmp.felk.cvut.cz

IEEE Transactions on Pattern Analysis and Machine Intelligence
|December 7, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a new polynomial eigenvalue problem (PEP) method for solving computer vision polynomial equations. It offers a simpler, more efficient alternative to Gröbner basis methods for relative pose problems.

Related Experiment Videos

Last Updated: May 26, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

Area of Science:

  • Computer Vision
  • Algebraic Geometry
  • Numerical Analysis

Background:

  • Solving systems of polynomial equations is crucial in computer vision.
  • Existing methods like Gröbner bases can be complex and computationally intensive.
  • There is a need for more straightforward and efficient solvers.

Purpose of the Study:

  • To present a novel method for solving polynomial systems in computer vision using polynomial eigenvalue solvers.
  • To characterize problems solvable as polynomial eigenvalue problems (PEPs).
  • To demonstrate the method's applicability to minimal relative pose problems.

Main Methods:

  • Utilizing polynomial eigenvalue solvers as the core computational tool.
  • Developing a resultant-based approach to transform polynomial systems into PEPs.
  • Implementing techniques to reduce the size of the resulting PEPs.

Main Results:

  • A characterization of systems amenable to PEP solutions is provided.
  • A resultant-based transformation method is presented.
  • The method is successfully applied to solve several minimal relative pose problems.

Conclusions:

  • The proposed polynomial eigenvalue method is a more straightforward and implementable alternative to Gröbner basis methods.
  • The PEP approach offers efficiency and robustness for solving specific polynomial systems in computer vision.
  • This method has practical applications in solving fundamental problems like minimal relative pose estimation.