Template matching via densities on the roto-translation group

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Abstract

We propose a template matching method for the detection of 2D image objects that are characterized by orientation patterns. Our method is based on data representations via orientation scores, which are functions on the space of positions and orientations, and which are obtained via a wavelet-type transform. This new representation allows us to detect orientation patterns in an intuitive and direct way, namely via cross-correlations. Additionally, we propose a generalized linear regression framework for the construction of suitable templates using smoothing splines. Here, it is important to recognize a curved geometry on the position-orientation domain, which we identify with the Lie group SE(2): the roto-translation group. Templates are then optimized in a B-spline basis, and smoothness is defined with respect to the curved geometry. We achieve state-of-the-art results on three different applications: detection of the optic nerve head in the retina (99.83% success rate on 1737 images), of the fovea in the retina (99.32% success rate on 1616 images), and of the pupil in regular camera images (95:86% on 1521 images). The high performance is due to inclusion of both intensity and orientation features with effective geometric priors in the template matching. Moreover, our method is fast due to a cross-correlation based matching approach.
Original languageEnglish
Pages (from-to)452-466
Number of pages15
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Volume40
Issue number2
DOIs
Publication statusPublished - 2018

Fingerprint

Template matching
Template Matching
Splines
Lie groups
Geometry
Linear regression
Retina
Optics
Cross-correlation
Cameras
Template
Smoothing Splines
Nerve
B-spline
Intuitive
Smoothness
Wavelets
High Performance
Inclusion
Camera

Keywords

  • Linear regression
  • Pattern matching
  • Retina
  • Smoothing methods
  • Splines (mathematics)
  • Wavelet transforms
  • fovea
  • invertible orientation scores
  • multi-orientation
  • optic nerve head
  • retina
  • template matching

Cite this

@article{9ea2f7669ceb4645a9cdac48c8020884,
title = "Template matching via densities on the roto-translation group",
abstract = "We propose a template matching method for the detection of 2D image objects that are characterized by orientation patterns. Our method is based on data representations via orientation scores, which are functions on the space of positions and orientations, and which are obtained via a wavelet-type transform. This new representation allows us to detect orientation patterns in an intuitive and direct way, namely via cross-correlations. Additionally, we propose a generalized linear regression framework for the construction of suitable templates using smoothing splines. Here, it is important to recognize a curved geometry on the position-orientation domain, which we identify with the Lie group SE(2): the roto-translation group. Templates are then optimized in a B-spline basis, and smoothness is defined with respect to the curved geometry. We achieve state-of-the-art results on three different applications: detection of the optic nerve head in the retina (99.83{\%} success rate on 1737 images), of the fovea in the retina (99.32{\%} success rate on 1616 images), and of the pupil in regular camera images (95:86{\%} on 1521 images). The high performance is due to inclusion of both intensity and orientation features with effective geometric priors in the template matching. Moreover, our method is fast due to a cross-correlation based matching approach.",
keywords = "Linear regression, Pattern matching, Retina, Smoothing methods, Splines (mathematics), Wavelet transforms, fovea, invertible orientation scores, multi-orientation, optic nerve head, retina, template matching",
author = "E. Bekkers and M. Loog and Romeny, {B. ter Haar} and R. Duits",
year = "2018",
doi = "10.1109/TPAMI.2017.2652452",
language = "English",
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pages = "452--466",
journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",
issn = "0162-8828",
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}

Template matching via densities on the roto-translation group. / Bekkers, E.; Loog, M.; Romeny, B. ter Haar; Duits, R.

In: IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 40, No. 2, 2018, p. 452-466.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Template matching via densities on the roto-translation group

AU - Bekkers, E.

AU - Loog, M.

AU - Romeny, B. ter Haar

AU - Duits, R.

PY - 2018

Y1 - 2018

N2 - We propose a template matching method for the detection of 2D image objects that are characterized by orientation patterns. Our method is based on data representations via orientation scores, which are functions on the space of positions and orientations, and which are obtained via a wavelet-type transform. This new representation allows us to detect orientation patterns in an intuitive and direct way, namely via cross-correlations. Additionally, we propose a generalized linear regression framework for the construction of suitable templates using smoothing splines. Here, it is important to recognize a curved geometry on the position-orientation domain, which we identify with the Lie group SE(2): the roto-translation group. Templates are then optimized in a B-spline basis, and smoothness is defined with respect to the curved geometry. We achieve state-of-the-art results on three different applications: detection of the optic nerve head in the retina (99.83% success rate on 1737 images), of the fovea in the retina (99.32% success rate on 1616 images), and of the pupil in regular camera images (95:86% on 1521 images). The high performance is due to inclusion of both intensity and orientation features with effective geometric priors in the template matching. Moreover, our method is fast due to a cross-correlation based matching approach.

AB - We propose a template matching method for the detection of 2D image objects that are characterized by orientation patterns. Our method is based on data representations via orientation scores, which are functions on the space of positions and orientations, and which are obtained via a wavelet-type transform. This new representation allows us to detect orientation patterns in an intuitive and direct way, namely via cross-correlations. Additionally, we propose a generalized linear regression framework for the construction of suitable templates using smoothing splines. Here, it is important to recognize a curved geometry on the position-orientation domain, which we identify with the Lie group SE(2): the roto-translation group. Templates are then optimized in a B-spline basis, and smoothness is defined with respect to the curved geometry. We achieve state-of-the-art results on three different applications: detection of the optic nerve head in the retina (99.83% success rate on 1737 images), of the fovea in the retina (99.32% success rate on 1616 images), and of the pupil in regular camera images (95:86% on 1521 images). The high performance is due to inclusion of both intensity and orientation features with effective geometric priors in the template matching. Moreover, our method is fast due to a cross-correlation based matching approach.

KW - Linear regression

KW - Pattern matching

KW - Retina

KW - Smoothing methods

KW - Splines (mathematics)

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KW - fovea

KW - invertible orientation scores

KW - multi-orientation

KW - optic nerve head

KW - retina

KW - template matching

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