The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images

Sean Matz

doi:doi:10.11648/j.mcs.20210601.14

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The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images

Sean Matz

Published in Mathematics and Computer Science (Volume 6, Issue 1)

Received: 9 January 2021 Accepted: 1 March 2021 Published: 1 April 2021

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Abstract

This paper considers the idea of using the Radon transform to extract the orientation features of lines in binary images. The Radon transform sends a line at a particular orientation in image space to a point in feature space. The ensuing set of points in feature space is called a sinogram. This computation is usually performed for a large group of angles (over the interval [0,179] degrees taken in integer increments in this paper). Therefore, linear features at specific orientations will be mapped to points having maximum value at particular angles. For angular spacing of at least 5 degrees, the peaks of the sinogram at the angles corresponding to the orientations of the lines will be clearly visible (in a bar plot of sinogram peaks) above sinogram values at other angles. The mapping from image space to feature space accomplished by the Radon transform which maps rectangular coordinates (x,y) to coordinates (range, angle) provides for the garnering of the orientation of the linear features in binary images. In particular, the coordinates (range, angle) in the sinogram allow for distinguishing between lines oriented at one angle versus lines oriented at another angle or angles. This particular property of the sinogram allows for the extraction of the orientation features of lines in an image.

Published in	Mathematics and Computer Science (Volume 6, Issue 1)
DOI	10.11648/j.mcs.20210601.14
Page(s)	24-29
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Angles, Lines, Orientation, Radon Transform, Sinogram

References

[1]	Lesley M. Murphy. “Linear feature detection and enhancement in noisy images via the Radon transform.” In: Pattern Recognition Letters Issue 10, September 1986, pp. 279-284.
[2]	Kourosh Jafari-Khouzani and Hamid Soltanian- Zadeh “Radon Transform Orientation Estimation for Rotation Invariant Texture Analysis”. In: IEEE Transactions on Pattern Analysis and Machine Intelligence (June. 2005),27(6) pp. 1004-1008. URL : https://doi.org/10.1109/TPAMI.2005.126
[3]	N. Aggarwal and W.C. Karl. “Line Detection in images through regularized hough transform” In: IEEE Transactions on Image Processing (Volume: 15, Issue: 3, March 2006),pp. 582-591. URL : https://doi.org/10.1109/TIP.2005.863021
[4]	Philipp Fischer, Alexey Dosovitskiy, and Thomas Brox “Image Orientation Estimation with Convolutional Networks” In: Gall J., Gehler P., Leibe B. (eds) Pattern Recognition. DAGM 2015. Lecture Notes in Computer Science, vol 9358. Springer, Cham URL: https://doi.org/10.1007/978-3-319-24947-6
[5]	Youngran Jo, Jinbeum Jang, Minwoo Shin, and Joonki Paik “Camera orientation estimation using voting approach on the Gaussian sphere for in-vehicle camera” In: Optics Express, Vol. 27, No. 19, 16 Sep 2019.
[6]	AbdulSattar M. Khidhir “Use of Radon Transform in Orientation Estimation of Printed Text” In: The 5th International Conference on Information Technology (ICIT) 2011.
[7]	Lalita Kumari, Swapan Debbarma, and Radhey Shyam “Text Orientation Detection from Document Image of Indian Scripts” In: International Journal of Computer Communication and Information System (IJCCIS) Vol 2. No. 1. July-Dec 2010.
[8]	Rengarajan Pelapur, Filiz Bunyak, Kannappan Palaniappan, and Gunasekaran Seetharaman. “Vehicle Detection and Orientation Estimation Using the Radon Transform.” In: Proc. of SPIE vol. 8747, 2013 URL: https:/doi.org/10.1117/12.2016407
[9]	Hitesh Rajput, Tanmoy Som, and Soumitra Kar. “Using Radon Transform to Recognize Skewed Images of Vehicular License Plates.” In: Computer Vol 49, Issue 1, January 2016, pp. 59-65 URL: https:/doi.org/10.1109/MC.2016.14 Mathematics and Computer Science 2021; 6(1): 24-29 29
[10]	Satyabrata Sahu, Santosh Kumar Nanda, and Tanushree Mohapatra. “Digital Image Texture Classification and Detection Using Radon Transform.” In: International Journal of Image, Graphics and Signal Processing (IJIGSP), vol. 5, No. 12, October 2013.
[11]	Gianluigi Ciocca, Claudio Cusano, and Raimondo Schettini. “Image orientation detection using LBP-based features and logistic regression.” In: Multimedia Tools and Applications 74, pp 3013-3034, 2015.
[12]	Diwakar Tiwary, K. Srinivasulu, and Anveshraj. “Fingerprint Identification Using Radon Transform.” In: International Refereed Journal of Engineering and Science (IRJES) Vol 3, Issue 10, October 2014, pp. 106- 110.
[13]	Cong Yao, Xin Zhang, Xiang Bai, Wenyu Liu, Yi Ma, and Zhuowen Tu. “Rotation-Invariant Features for Multi- Oriented Text Detection in Natural Images” In: PLoS ONE 8(8): e70173 URL: https://doi.org/10.1371/journal- pone-0070173
[14]	Sean Matz “Orientation Detection of Lines in Binary Images Using the Radon Transform” In: 6th Annual Conference on Computational Science and Computational Intelligence (CSCI) December 05-07, 2019.
[15]	Sean Matz “Orientation and Line Thickness Determination in Binary Images” In: The 2020 World Congress in Computer Science, Computer Engineering, and Applied Computing (CSCE) July 27-30, 2020.

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Sean Matz. (2021). The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images. Mathematics and Computer Science, 6(1), 24-29. https://doi.org/10.11648/j.mcs.20210601.14

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ACS Style

Sean Matz. The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images. Math. Comput. Sci. 2021, 6(1), 24-29. doi: 10.11648/j.mcs.20210601.14

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AMA Style

Sean Matz. The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images. Math Comput Sci. 2021;6(1):24-29. doi: 10.11648/j.mcs.20210601.14

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@article{10.11648/j.mcs.20210601.14,
  author = {Sean Matz},
  title = {The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {1},
  pages = {24-29},
  doi = {10.11648/j.mcs.20210601.14},
  url = {https://doi.org/10.11648/j.mcs.20210601.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210601.14},
  abstract = {This paper considers the idea of using the Radon transform to extract the orientation features of lines in binary images. The Radon transform sends a line at a particular orientation in image space to a point in feature space. The ensuing set of points in feature space is called a sinogram. This computation is usually performed for a large group of angles (over the interval [0,179] degrees taken in integer increments in this paper). Therefore, linear features at specific orientations will be mapped to points having maximum value at particular angles. For angular spacing of at least 5 degrees, the peaks of the sinogram at the angles corresponding to the orientations of the lines will be clearly visible (in a bar plot of sinogram peaks) above sinogram values at other angles. The mapping from image space to feature space accomplished by the Radon transform which maps rectangular coordinates (x,y) to coordinates (range, angle) provides for the garnering of the orientation of the linear features in binary images. In particular, the coordinates (range, angle) in the sinogram allow for distinguishing between lines oriented at one angle versus lines oriented at another angle or angles. This particular property of the sinogram allows for the extraction of the orientation features of lines in an image.},
 year = {2021}
}

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TY  - JOUR
T1  - The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images
AU  - Sean Matz
Y1  - 2021/04/01
PY  - 2021
N1  - https://doi.org/10.11648/j.mcs.20210601.14
DO  - 10.11648/j.mcs.20210601.14
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JO  - Mathematics and Computer Science
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EP  - 29
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20210601.14
AB  - This paper considers the idea of using the Radon transform to extract the orientation features of lines in binary images. The Radon transform sends a line at a particular orientation in image space to a point in feature space. The ensuing set of points in feature space is called a sinogram. This computation is usually performed for a large group of angles (over the interval [0,179] degrees taken in integer increments in this paper). Therefore, linear features at specific orientations will be mapped to points having maximum value at particular angles. For angular spacing of at least 5 degrees, the peaks of the sinogram at the angles corresponding to the orientations of the lines will be clearly visible (in a bar plot of sinogram peaks) above sinogram values at other angles. The mapping from image space to feature space accomplished by the Radon transform which maps rectangular coordinates (x,y) to coordinates (range, angle) provides for the garnering of the orientation of the linear features in binary images. In particular, the coordinates (range, angle) in the sinogram allow for distinguishing between lines oriented at one angle versus lines oriented at another angle or angles. This particular property of the sinogram allows for the extraction of the orientation features of lines in an image.
VL  - 6
IS  - 1
ER  -

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Author Information

Sean Matz

Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, United States

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APA Style

Sean Matz. (2021). The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images. Mathematics and Computer Science, 6(1), 24-29. https://doi.org/10.11648/j.mcs.20210601.14

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ACS Style

Sean Matz. The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images. Math. Comput. Sci. 2021, 6(1), 24-29. doi: 10.11648/j.mcs.20210601.14

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AMA Style

Sean Matz. The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images. Math Comput Sci. 2021;6(1):24-29. doi: 10.11648/j.mcs.20210601.14

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@article{10.11648/j.mcs.20210601.14,
  author = {Sean Matz},
  title = {The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images},
  journal = {Mathematics and Computer Science},
  volume = {6},
  number = {1},
  pages = {24-29},
  doi = {10.11648/j.mcs.20210601.14},
  url = {https://doi.org/10.11648/j.mcs.20210601.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20210601.14},
  abstract = {This paper considers the idea of using the Radon transform to extract the orientation features of lines in binary images. The Radon transform sends a line at a particular orientation in image space to a point in feature space. The ensuing set of points in feature space is called a sinogram. This computation is usually performed for a large group of angles (over the interval [0,179] degrees taken in integer increments in this paper). Therefore, linear features at specific orientations will be mapped to points having maximum value at particular angles. For angular spacing of at least 5 degrees, the peaks of the sinogram at the angles corresponding to the orientations of the lines will be clearly visible (in a bar plot of sinogram peaks) above sinogram values at other angles. The mapping from image space to feature space accomplished by the Radon transform which maps rectangular coordinates (x,y) to coordinates (range, angle) provides for the garnering of the orientation of the linear features in binary images. In particular, the coordinates (range, angle) in the sinogram allow for distinguishing between lines oriented at one angle versus lines oriented at another angle or angles. This particular property of the sinogram allows for the extraction of the orientation features of lines in an image.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - The Utilization of the Radon Transform for the Extraction of the Orientation of Linear Features in Binary Images
AU  - Sean Matz
Y1  - 2021/04/01
PY  - 2021
N1  - https://doi.org/10.11648/j.mcs.20210601.14
DO  - 10.11648/j.mcs.20210601.14
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 24
EP  - 29
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20210601.14
AB  - This paper considers the idea of using the Radon transform to extract the orientation features of lines in binary images. The Radon transform sends a line at a particular orientation in image space to a point in feature space. The ensuing set of points in feature space is called a sinogram. This computation is usually performed for a large group of angles (over the interval [0,179] degrees taken in integer increments in this paper). Therefore, linear features at specific orientations will be mapped to points having maximum value at particular angles. For angular spacing of at least 5 degrees, the peaks of the sinogram at the angles corresponding to the orientations of the lines will be clearly visible (in a bar plot of sinogram peaks) above sinogram values at other angles. The mapping from image space to feature space accomplished by the Radon transform which maps rectangular coordinates (x,y) to coordinates (range, angle) provides for the garnering of the orientation of the linear features in binary images. In particular, the coordinates (range, angle) in the sinogram allow for distinguishing between lines oriented at one angle versus lines oriented at another angle or angles. This particular property of the sinogram allows for the extraction of the orientation features of lines in an image.
VL  - 6
IS  - 1
ER  -

Copy | Download