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Geometric observers for dynamically evolving curves.

Marc Niethammer1, Patricio A Vela, Allen Tannenbaum

  • 1Department of Computer Science, University of North Carolina, Chapel Hill, NC 27599-3175, USA. mn@cs.unc.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 19, 2008
PubMed
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This study introduces a novel deterministic observer for visual tracking using implicit level-set curves. The framework enables accurate, topologically adaptable curve tracking with subpixel precision.

Area of Science:

  • Computer Vision
  • Robotics
  • Image Processing

Background:

  • Accurate visual tracking of curves is crucial for various applications.
  • Existing methods often struggle with topological changes and subpixel accuracy.

Purpose of the Study:

  • To propose a deterministic observer framework for robust visual tracking.
  • To leverage non-parametric implicit (level-set) curve descriptions for enhanced tracking.
  • To achieve subpixel accuracy and handle topological changes in tracked curves.

Main Methods:

  • A continuous-discrete deterministic observer with continuous-time dynamics and discrete-time measurements.
  • State-space augmentation with curve position and point-wise velocities.
  • Integration of static segmentation and optical-flow for measurements.

Related Experiment Videos

  • Geometric formulation of the dynamical system.
  • Laplace-equation approach for establishing curve correspondences.
  • Implicit implementation using Eulerian solutions of transport equations.

    • Main Results:

    • The proposed observer framework effectively handles visual tracking tasks.
    • The implicit implementation naturally accommodates topological changes.
    • Subpixel accuracy is achieved on the computational grid.
    • Geometric curve interpolation and discrete-time filtering are addressed.

    Conclusions:

    • The deterministic observer framework provides a robust solution for visual curve tracking.
    • The implicit, level-set based approach offers significant advantages in accuracy and adaptability.
    • This method advances the state-of-the-art in dynamic curve estimation and tracking.