Building 3-D statistical shape models by direct optimization.

Area of Science:

• Medical image analysis
• Computer vision
• Computational geometry

Background:

• Statistical shape models (SSMs) are crucial for image interpretation and shape analysis.
• Current SSMs often rely on manual landmarking for correspondence, which is time-consuming and subjective, especially in 3D.
• Establishing dense correspondence across training datasets is a significant challenge.

Purpose of the Study:

• To develop an automated method for establishing dense correspondence in training datasets for SSMs.
• To utilize the Minimum Description Length (MDL) principle for optimizing correspondence and model quality.
• To provide quantitative measures for comparing different SSM building methods.

Main Methods:

• Correspondence is treated as an optimization problem, automatically established across the training set.
• Reparameterization of training shapes is used to manipulate correspondence.
• An explicit representation for 3D surface reparameterization prevents illegal correspondences.
• Large-scale optimization strategies are employed for model building.

Main Results:

• The Minimum Description Length (MDL) principle is proposed as an objective function for building compact, specific, and generalizable SSMs.
• Quantitative measures for model quality are derived for meaningful comparisons.
• Experiments on 3D shape datasets demonstrate superior performance of MDL-based models over other approaches.

Conclusions:

• Automated dense correspondence using optimization significantly improves SSM building.
• MDL-based optimization leads to statistically superior shape models.
• The proposed methods offer a robust and efficient alternative to manual landmarking for SSM construction.