Fourier encoding of closed planar boundaries.

Area of Science:

• Computer Vision
• Image Processing
• Information Theory

Background:

• Closed planar curves are fundamental in computer graphics and image analysis.
• Existing encoding schemes for curve data can be computationally intensive.
• The circular Gaussian autoregressive (CGAR) model offers a probabilistic approach to representing such curves.

Purpose of the Study:

• To develop efficient encoding schemes for closed planar curves modeled by CGAR sources.
• To establish theoretical bounds for data compression of curve representations.
• To propose a computationally efficient transform encoding scheme.

Main Methods:

• Utilizing rate-distortion theoretic techniques to derive optimal encoding bounds.
• Quantizing Fourier coefficients of the curve boundary separately.
• Developing and analyzing parametric equations for encoding bounds.

Main Results:

• Parametric equations for the optimal encoding bound were derived.
• A sampling criterion for efficient curve representation was established.
• A computationally efficient transform encoding scheme for the suboptimal class was proposed and evaluated.

Conclusions:

• The proposed transform encoding scheme provides an efficient method for compressing closed planar curves.
• The established sampling criterion aids in optimizing data representation.
• The study contributes to the theoretical understanding of encoding bounds for CGAR-modeled curves.