Projection Operators and Moment Invariants to Image Blurring

Area of Science:

• Computer Vision
• Image Processing
• Geometric Invariance

Background:

• Image blurring is a common challenge in computer vision, degrading feature distinctiveness.
• Existing methods struggle with recognizing objects in significantly blurred or transformed images.

Purpose of the Study:

• Introduce a novel theory of blur invariants for robust image feature representation.
• Develop methods for computing and utilizing these invariants for object recognition.

Main Methods:

• Defined blur invariants invariant to convolution with N-fold symmetric point-spread functions (PSFs).
• Introduced a primordial image concept in the spectral domain using projection operators.
• Derived recursive formulae for computing primordial image moments without explicit construction.

Main Results:

• Proved that primordial image moments are invariant to blur and form a complete set of invariants.
• Demonstrated extension of invariance to translation, rotation, and scaling.
• Validated invariance and recognition power using simulated and real-world blurred image data.

Conclusions:

• The proposed blur invariants offer a powerful tool for object recognition in degraded image conditions.
• This method has broad applicability in various fields requiring reliable object identification from blurred imagery.