Optimal edge-based shape detection.

Area of Science:

• Computer Vision
• Image Processing
• Pattern Recognition

Background:

• Accurate detection of two-dimensional (2-D) shapes is crucial in various image analysis tasks.
• Existing methods often struggle with noise and complex shape geometries.
• Modeling shape boundaries as step functions provides a robust foundation for detection.

Purpose of the Study:

• To develop an accurate and robust method for 2-D shape detection.
• To extend 1-D edge detection principles to global contour detection.
• To analyze and predict the performance of the proposed shape detection operator.

Main Methods:

• Derived a 1-D optimal step edge operator (Derivative of Double Exponential - DODE) minimizing noise and mean squared error.
• Extended the DODE filter along shape contours for 2-D shape detection.
• Accumulated filter responses at the centroid to estimate shape presence likelihood.

Main Results:

• The DODE operator effectively models shape boundaries as step functions.
• The proposed method extends pixel-level edge detection to global contour detection.
• Statistical properties of the response were computed, enabling performance prediction and parameter adjustment.

Conclusions:

• The DODE-based shape detection approach offers a systematic tool for edge-based shape analysis.
• The method demonstrates predictable localization and detection performance under general assumptions.
• Successfully applied to vehicle detection, facial feature detection, and contour tracking.