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Maximum likelihood wavelet density estimation with applications to image and shape matching.

A M Peter¹, A Rangarajan

¹Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|April 9, 2008

Summary

This study introduces a novel wavelet density estimation method that ensures non-negative densities. The approach uses maximum likelihood estimation for accurate density approximation in various applications.

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Area of Science:

Statistical modeling
Signal processing
Machine learning

Background:

Density estimation is crucial for data analysis and image registration.
Wavelet estimators are popular for approximating complex functions and handling abrupt changes.
Practical wavelet density estimation faces challenges like non-negativity and coefficient computation.

Purpose of the Study:

To present a new method for accurate non-negative density estimation using wavelets.
To address theoretical and empirical issues in practical wavelet density estimation.
To provide a robust and efficient density estimation technique.

Main Methods:

A maximum likelihood framework is employed to estimate the square root of the density.
The method ensures a non-negative density representation (sqrt(p))^2.

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Theoretical analysis reveals a connection to Fisher information, enabling constrained optimization for wavelet coefficients.

Main Results:

The proposed method accurately estimates non-negative densities.
It demonstrates effectiveness in mutual information-based image registration and shape point set alignment.
Performance is empirically compared against known densities and kernel density estimators.

Conclusions:

The new wavelet-based density estimation method is effective and addresses practical challenges.
The approach offers a theoretically grounded and computationally efficient solution.
This method advances density estimation for observational data in diverse applications.