Related Experiment Video
Updated: Aug 4, 2026

Optical Scatter Microscopy Based on Two-Dimensional Gabor Filters
Published on: June 2, 2010
Maximum likelihood localization of 2-D patterns in the Gauss-Laguerre Transform domain: theoretic framework and
Alessandro Neri1, Giovanni Jacovitti
1Applied Electronics Department, University of Rome III, 00146 Rome, Italy. neri@uniroma3.it
Abstract:
Usual approaches to localization, i.e., joint estimation of position, orientation and scale of a bidimensional pattern employ suboptimum techniques based on invariant signatures, which allow for position estimation independent of scale and orientation. In this paper a Maximum Likelihood method for pattern localization working in the Gauss-Laguerre Transform (GLT) domain is presented. The GLT is based on an orthogonal family of Circular Harmonic Functions with specific radial profiles, which permits optimum joint estimation of position and scale/rotation parameters looking at the maxima of a "Gauss-Laguerre Likelihood Map." The Fisher information matrix for any given pattern is given and the theoretical asymptotic accuracy of the parameter estimates is calculated through the Cramer Rao Lower Bound. Application of the ML estimation method is discussed and an example is provided.
Related Concept Videos
Gauss's Law
Region of Convergence of Laplace Tarnsform
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Time and frequency -Domain Interpretation of Phase-lag Control
Phase-lag controllers do not place a pole at zero, but instead influence the steady-state error by amplifying any finite,...
Application of Linearization and Approximation

