Methods for numerical integration of high-dimensional posterior densities with application to statistical image...

Area of Science:

• Applied Statistics
• Image Processing
• Computer Vision

Background:

• Bayesian posterior density computation is crucial in applied statistics and image processing.
• Existing literature is surveyed to identify efficient computational methods.
• Image models like Markov random fields (MRF) and polynomial surfaces are widely used.

Purpose of the Study:

• To present efficient methods for computing marginal density values for image models.
• To enable statistically based decisions in image analysis.
• To provide detailed descriptions and experimental validation.

Main Methods:

• Survey of previous literature on Bayesian computation.
• Development of efficient methods for marginal density computation.
• Application to Markov random field (MRF), implicit, and parametric polynomial surface models.

Main Results:

• Efficient methods for computing marginal density values are presented.
• Demonstrative experiments on real imagery showcase the methods' effectiveness.
• The computations support statistically based decisions.

Conclusions:

• The presented methods offer efficient solutions for Bayesian posterior density computation in image analysis.
• These techniques are valuable for tasks such as image segmentation and model selection.
• The study contributes to the advancement of computational statistics in computer vision.