A Method of Detecting End-To-End Curves of Limited Curvature

TL;DR

This paper introduces a dynamic programming-based method utilizing the Fast Hough Transform to detect limited-curvature end-to-end curves in images, achieving high approximation accuracy with efficient complexity.

Contribution

The paper presents a novel approach combining dynamic programming and Fast Hough Transform for detecting limited-curvature curves with proven asymptotic efficiency.

Findings

Effective detection on synthetic data

Successful application to real images

Complexity comparable to fast Fourier transform

Abstract

In this paper we consider a method for detecting end-to-end curves of limited curvature like the k-link polylines with bending angle between adjacent segments in a given range. The approximation accuracy is achieved by maximization of the quality function in the image matrix. The method is based on a dynamic programming scheme constructed over Fast Hough Transform calculation results for image bands. The proposed method asymptotic complexity is $O(h \cdot (w+ \frac{h}{k}) \cdot log(\frac{h}{k}))$, where $h$ and $w$ are the image size, and $k$ is the approximating polyline links number, which is an analogue of the complexity of the fast Fourier transform or the fast Hough transform. We also show the results of the proposed method on synthetic and real data.