Revisiting Superquadric Fitting: A Numerically Stable Formulation.

Area of Science:

• Computer Vision
• Geometric Modeling
• Computational Geometry

Background:

• Superquadric surfaces are vital for modeling diverse shapes with few parameters.
• Estimating object shape from discrete samples is a key application.
• Current optimization methods suffer numerical instabilities, limiting shape representation.

Purpose of the Study:

• To develop a numerically stable formulation for superquadric surface evaluation and gradient computation.
• To enable accurate modeling of shapes previously prone to errors, including cuboids and cylinders.
• To improve the speed and stability of superquadric fitting.

Main Methods:

• A novel, numerically stable formulation for superquadric surface functions and their gradients.
• Investigating and addressing parameter space instabilities.
• Experimental validation on synthetic and real-world data.

Main Results:

• The new formulation achieves stable superquadric fitting across the full parameter range.
• Accurate modeling of previously problematic shapes like cuboids and cylinders is now possible.
• Faster convergence speeds were observed compared to existing methods.

Conclusions:

• The proposed formulation overcomes numerical instabilities in superquadric fitting.
• This advancement allows for more accurate and efficient modeling of common geometric shapes.
• The method has broad applicability in computer vision and geometric modeling tasks.