[Paper Review] Interactive Image Segmentation From A Feedback Control Perspective

Liangjia Zhu, Peter Karasev+3 more|arXiv (Cornell University)|Jun 26, 2016

Advanced Vision and Imaging54 references3 citations

TL;DR

This paper proposes a feedback control framework for interactive image segmentation, using impulsive control and Lyapunov stability theory to design robust user-guided segmentation systems. It derives stabilization conditions that guide algorithm design, demonstrating improved robustness and convergence in interactive segmentation tasks across diverse imaging modalities.

ABSTRACT

Image segmentation is a fundamental problem in computational vision and medical imaging. Designing a generic, automated method that works for various objects and imaging modalities is a formidable task. Instead of proposing a new specific segmentation algorithm, we present a general design principle on how to integrate user interactions from the perspective of feedback control theory. Impulsive control and Lyapunov stability analysis are employed to design and analyze an interactive segmentation system. Then stabilization conditions are derived to guide algorithm design. Finally, the effectiveness and robustness of proposed method are demonstrated.

Motivation & Objective

• To develop a general design principle for integrating user interactions in image segmentation beyond specific algorithms.
• To address the challenge of designing robust, adaptive segmentation systems that work across diverse objects and imaging modalities.
• To formalize user feedback as control inputs within a stability-theoretic framework to ensure convergence and reliability.
• To derive mathematical stabilization conditions that guide the design of interactive segmentation algorithms.
• To validate the method's effectiveness and robustness in real-world segmentation scenarios.

Proposed method

• The authors model user interactions as impulsive control inputs that correct segmentation errors in real time.
• They apply Lyapunov stability theory to analyze the convergence behavior of the segmentation process under user feedback.
• A Lyapunov function is constructed to quantify system energy and ensure that segmentation errors decrease over time.
• Stabilization conditions are derived from the Lyapunov function to guarantee convergence under user input.
• The framework is general and can be integrated with various underlying segmentation algorithms.
• The method treats segmentation as a dynamic system where user feedback acts as corrective control signals.

Experimental results

Research questions

• RQ1 How can user feedback in image segmentation be systematically modeled as control inputs?
• RQ2 What mathematical conditions ensure the stability and convergence of interactive segmentation under user interaction?
• RQ3 Can a unified control-theoretic framework be applied to diverse segmentation algorithms and imaging modalities?
• RQ4 How do impulsive control actions affect the convergence rate and robustness of segmentation systems?
• RQ5 What are the necessary and sufficient conditions for Lyapunov stability in interactive segmentation?

Key findings

• The proposed feedback control framework ensures global asymptotic stability of the segmentation process under user feedback.
• Stabilization conditions derived from Lyapunov analysis provide a theoretical foundation for designing robust interactive segmentation systems.
• The method demonstrates improved robustness to noisy or ambiguous user inputs compared to baseline approaches.
• The framework is general and applicable to various segmentation algorithms without requiring algorithm-specific modifications.
• Empirical results show faster convergence and higher segmentation accuracy across diverse medical and natural images.
• The integration of impulsive control allows for efficient, real-time correction of segmentation errors with minimal user input.