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Updated: Jun 2, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

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Published on: November 14, 2019

Revisiting complex moments for 2-D shape representation and image normalization.

João B F P Crespo1, Pedro M Q Aguiar

  • 1Institute for Systems and Robotics/Instituto Superior Técnico, Lisboa 1049-001, Portugal.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|April 27, 2011
PubMed
Summary
This summary is machine-generated.

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This study introduces Principal Moments for uniquely defining 2-D shape orientation, overcoming limitations of prior methods. Principal Moment Analysis offers a robust and efficient solution for shape normalization and image processing.

Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Geometry

Background:

  • Normalization of 2-D shapes is crucial for comparison, with translation and scale easily handled.
  • Defining and computing the orientation of general 2-D shapes remains a significant challenge.
  • Existing methods fail to accurately compute orientation for simple shapes, even without noise.

Purpose of the Study:

  • To uniquely define the orientation of arbitrary 2-D shapes.
  • To develop a compact representation for 2-D shapes using Principal Moments.
  • To introduce an efficient method for computing shape orientation and its application in image normalization.

Main Methods:

  • Defining shape orientation using Principal Moments.
  • Demonstrating that a subset of Principal Moments provides a compact shape representation.

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  • Proposing Principal Moment Analysis for efficient orientation computation.
  • Exploring applications in gray-level image normalization.

    • Main Results:

    • Successfully defined a unique orientation for arbitrary 2-D shapes.
    • Showcased the compactness of Principal Moments for large-scale databases.
    • Developed Principal Moment Analysis, an efficient method for shape orientation.
    • Demonstrated robustness to noise and effectiveness on real images.

    Conclusions:

    • Principal Moments offer a novel and effective way to define 2-D shape orientation.
    • Principal Moment Analysis provides an efficient and robust solution for shape normalization.
    • The method has practical applications in processing real-world gray-level images.