Closed form line-segment extraction using the Hough transform


by Z Xu, B-S Shin, R Klette
Abstract:
This paper proposes a novel closed-form solution to complete line-segment extraction. Given a voting angle in image space, the voting distribution is analyzed and two functional relationships are deduced. Regarding the corresponding column in Hough space, voting along the distance axis is considered as being a random variable, and voting values in cells are considered as forming a probability distribution. Statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve. Direction, length, and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves. The midpoint of a line segment is determined based on the fitted linear curve. The method is tested on simulated and real-world images; results show that the proposed closed-form solution is feasible in the presence of quantization errors or image noise.
Reference:
Closed form line-segment extraction using the Hough transform (Z Xu, B-S Shin, R Klette), In Pattern Recognition, Elsevier Ltd, volume 48, 2015.
Bibtex Entry:
@article{xu2015closedtransform,
author = "Xu, Z and Shin, B-S and Klette, R",
journal = "Pattern Recognition",
month = "Jan",
pages = "412--423",
publisher = "Elsevier Ltd",
title = "Closed form line-segment extraction using the Hough transform",
volume = "48",
year = "2015",
abstract = "This paper proposes a novel closed-form solution to complete line-segment extraction. Given a voting angle in image space, the voting distribution is analyzed and two functional relationships are deduced. Regarding the corresponding column in Hough space, voting along the distance axis is considered as being a random variable, and voting values in cells are considered as forming a probability distribution. Statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve. Direction, length, and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves. The midpoint of a line segment is determined based on the fitted linear curve. The method is tested on simulated and real-world images; results show that the proposed closed-form solution is feasible in the presence of quantization errors or image noise.",
doi = "10.1016/j.patcog.2015.06.008",
issn = "0031-3203",
issue = "12",
keyword = "Curve fitting",
keyword = "Hough transform",
keyword = "Line-segment extraction",
keyword = "Line-segment parameters",
keyword = "Pattern analysis",
language = "eng",
pii = "S0031-3203(15)00230-7",
day = "19",
publicationstatus = "accepted",
}