Convexity Shape Prior for Binary Segmentation.

Area of Science:

• Computer Vision
• Image Processing
• Computational Geometry

Background:

• Convexity is a significant feature in human visual perception.
• Image segmentation algorithms often benefit from incorporating shape priors.
• Existing regularization methods may introduce biases like shrinking.

Purpose of the Study:

• To propose shape convexity as a novel high-order regularization constraint for binary image segmentation.
• To develop an efficient optimization method for convexity-based potentials in discrete settings.
• To evaluate the performance and advantages of the convexity prior against traditional methods.

Main Methods:

• Representing object convexity as sum of three-clique potentials in discrete optimization.
• Employing an iterative trust region approach for optimizing non-submodular potentials.
• Utilizing dynamic programming for efficient evaluation and approximation of cliques.
• Developing a second-order approximation model for enhanced accuracy.

Main Results:

• The proposed method efficiently optimizes non-submodular potentials using an iterative trust region approach.
• Dynamic programming enables linear-time evaluation and approximation of three-cliques.
• Experiments show the convexity prior's general usefulness on synthetic and real image data.
• The convexity prior demonstrates robustness to scale changes and parameter selection, avoiding shrinking bias.

Conclusions:

• Shape convexity is an effective high-order regularization for binary image segmentation.
• The developed optimization technique efficiently handles non-submodular potentials.
• The convexity prior offers advantages over standard length regularization, including no shrinking bias and scale robustness.