An improved Hough Transform neighborhood map for straight line segments

Area of Science:

• Computer Vision
• Image Processing
• Pattern Recognition

Background:

• Accurate detection of straight line segments is crucial in image analysis.
• Existing Hough Transform (HT) variations often rely on less robust neighborhood definitions for line segments.
• The performance of line detection can be sensitive to segment length and precision requirements.

Purpose of the Study:

• To propose a novel distance metric for straight line segments in image space.
• To define and map the neighborhood of a line segment into parameter space.
• To develop an improved line segment neighborhood technique for the Hough Transform.

Main Methods:

• A new distance is defined between a straight line and a line segment in image space.
• This distance is used to define a line segment's neighborhood, which is then mapped to parameter space.
• The mapped parameter space neighborhood is analytically derived and approximated by a quadrangle.

Main Results:

• The proposed neighborhood mapping is a one-to-one reversible map between image and parameter spaces.
• The technique demonstrates superior performance compared to conventional methods in Hough Transform variations.
• Detection error is independent of line segment length, and precision requirements are explicitly resolvable.

Conclusions:

• The proposed straight line segment neighborhood technique offers significant advantages for Hough Transform.
• It provides robustness against segment length variations and allows explicit control over precision.
• The method effectively distinguishes between segments belonging to the same straight line, showing high practical value.