Geodesic shape regression in the framework of currents.

Area of Science:

• Computational anatomy
• Statistical shape analysis
• Medical image analysis

Background:

• Statistical analysis of time-dependent shapes is crucial in various scientific fields.
• Existing shape regression methods often assume a fixed baseline shape, limiting their applicability.
• The large deformation diffeomorphic metric mapping (LDDMM) framework provides a robust way to model shape transformations.

Purpose of the Study:

• To develop a new generative model for shape regression that accounts for time-dependent shape changes.
• To extend linear regression principles to the space of shapes within the LDDMM framework.
• To overcome limitations of previous methods by not assuming a fixed baseline shape.

Main Methods:

• Developed a generative model by extending linear regression to shape spaces represented as currents in LDDMM.
• Introduced a control point formulation for discrete and low-dimensional parameterization of diffeomorphic transformations.
• Implemented a simultaneous optimization scheme using a single gradient descent algorithm to estimate baseline shape, control points, and initial momenta.

Main Results:

• The proposed model successfully estimates a baseline shape (intercept) and initial momenta (slope) to parameterize geodesic shape evolution.
• The control point formulation decouples deformation parameterization from shape representation, offering flexibility in dimensionality.
• Demonstrated the method's efficacy on both synthetic datasets and real anatomical shape complexes.

Conclusions:

• The novel shape regression model provides a powerful tool for statistical analysis of time-dependent shapes.
• The method offers a flexible and efficient approach to modeling complex shape changes over time.
• This work advances the field of computational anatomy by enabling more comprehensive analysis of evolving shapes.