Abstract

This paper applies a recently proposed dominant point detection method – precision and reliability optimization (PRO) – for representing shapes in the microscopy images of fabricated structures. This method uses both the local and the global nature of fit for dominant point detection. A smaller value of its control parameter better represents the local curvature properties of the shape while a larger value better indicates the global curvature properties. The applicability of this method to a wide range of microscopy images is demonstrated using four microscopy examples of brightness enhancement films, electromagnetic and photonic band gap materials, and aspherical mirror alignments. It is shown that PRO can clearly highlight several image effects and imperfections which may not be easily identifiable by human eye or may be difficult to analyze and assess. Further, for large scale arrays, it can be used to generate useful fabrication accuracy statistics and detect features with low fidelity or more imperfections.

© 2013 OSA

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2013 (3)

2011 (1)

T. P. Nguyen and I. Debled-Rennesson, “A discrete geometry approach for dominant point detection,” Pattern Recognit.44(1), 32–44 (2011).
[CrossRef]

2010 (4)

2009 (2)

2008 (3)

2007 (1)

2006 (1)

2005 (1)

2004 (1)

2001 (1)

1999 (1)

T. M. Cronin, “A boundary concavity code to support dominant point detection,” Pattern Recognit. Lett.20(6), 617–634 (1999).
[CrossRef]

1997 (1)

1992 (1)

B. K. Ray and K. S. Ray, “Detection of significant points and polygonal approximation of digitized curves,” Pattern Recognit. Lett.13(6), 443–452 (1992).
[CrossRef]

1973 (1)

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Cartographica: Int. J. Geograph. Inf. Geovisualization10(2), 112–122 (1973).
[CrossRef]

1972 (1)

U. Ramer, “An iterative procedure for the polygonal approximation of plane curves,” Comput. Graph. Image Process.1(3), 244–256 (1972).
[CrossRef]

Anderson, D.

Bao, G.

Baxter, G. W.

Bégin, G.

Blomstedt, K.

Brown, M. S.

Burge, J.

Cardenas, J.

Carmona-Poyato, A.

A. Carmona-Poyato, F. J. Madrid-Cuevas, R. Medina-Carnicer, and R. Muñoz-Salinas, “Polygonal approximation of digital planar curves through break point suppression,” Pattern Recognit.43(1), 14–25 (2010).
[CrossRef]

Collins, S.

Cotte, Y.

Cronin, T. M.

T. M. Cronin, “A boundary concavity code to support dominant point detection,” Pattern Recognit. Lett.20(6), 617–634 (1999).
[CrossRef]

Da, F.

Debled-Rennesson, I.

T. P. Nguyen and I. Debled-Rennesson, “A discrete geometry approach for dominant point detection,” Pattern Recognit.44(1), 32–44 (2011).
[CrossRef]

Depeursinge, C.

Douglas, D. H.

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Cartographica: Int. J. Geograph. Inf. Geovisualization10(2), 112–122 (1973).
[CrossRef]

Gai, S.

Gehm, M. E.

Indebetouw, G.

Jia, J.

Kallioniemi, I.

Kim, S.

Kinast, J.

Kitcher, D. J.

Kouskousis, B.

Lam, E. Y.

Leung, M. K. H.

D. K. Prasad, M. K. H. Leung, and C. Quek, “ElliFit: An unconstrained, non-iterative, least squares based geometric Ellipse Fitting method,” Pattern Recognit.46(5), 1449–1465 (2013).
[CrossRef]

D. K. Prasad and M. K. H. Leung, “Reliability/Precision Uncertainty in Shape Fitting Problems,” in IEEE International Conference on Image Processing(Hong Kong, 2010), 4277–4280.

Li, P.

Li, X.

Lin, Y.

Liu, J.

Madrid-Cuevas, F. J.

A. Carmona-Poyato, F. J. Madrid-Cuevas, R. Medina-Carnicer, and R. Muñoz-Salinas, “Polygonal approximation of digital planar curves through break point suppression,” Pattern Recognit.43(1), 14–25 (2010).
[CrossRef]

Masood, A.

A. Masood, “Dominant point detection by reverse polygonization of digital curves,” Image Vis. Comput.26(5), 702–715 (2008).
[CrossRef]

Medennikov, P. A.

Medina-Carnicer, R.

A. Carmona-Poyato, F. J. Madrid-Cuevas, R. Medina-Carnicer, and R. Muñoz-Salinas, “Polygonal approximation of digital planar curves through break point suppression,” Pattern Recognit.43(1), 14–25 (2010).
[CrossRef]

Muñoz-Salinas, R.

A. Carmona-Poyato, F. J. Madrid-Cuevas, R. Medina-Carnicer, and R. Muñoz-Salinas, “Polygonal approximation of digital planar curves through break point suppression,” Pattern Recognit.43(1), 14–25 (2010).
[CrossRef]

Nguyen, T. P.

T. P. Nguyen and I. Debled-Rennesson, “A discrete geometry approach for dominant point detection,” Pattern Recognit.44(1), 32–44 (2011).
[CrossRef]

Nordin, G. P.

Pan, F. Y.

Pan, Y.

Pavillon, N.

Peucker, T. K.

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Cartographica: Int. J. Geograph. Inf. Geovisualization10(2), 112–122 (1973).
[CrossRef]

Poleshchuk, A.

Poon, T.-C.

Prasad, D. K.

D. K. Prasad, M. K. H. Leung, and C. Quek, “ElliFit: An unconstrained, non-iterative, least squares based geometric Ellipse Fitting method,” Pattern Recognit.46(5), 1449–1465 (2013).
[CrossRef]

D. K. Prasad and M. S. Brown, “Online tracking of deformable objects under occlusion using dominant points,” J. Opt. Soc. Am. A30(8), 1484–1491 (2013).
[CrossRef]

D. K. Prasad and M. K. H. Leung, “Reliability/Precision Uncertainty in Shape Fitting Problems,” in IEEE International Conference on Image Processing(Hong Kong, 2010), 4277–4280.

Quek, C.

D. K. Prasad, M. K. H. Leung, and C. Quek, “ElliFit: An unconstrained, non-iterative, least squares based geometric Ellipse Fitting method,” Pattern Recognit.46(5), 1449–1465 (2013).
[CrossRef]

Ramer, U.

U. Ramer, “An iterative procedure for the polygonal approximation of plane curves,” Comput. Graph. Image Process.1(3), 244–256 (1972).
[CrossRef]

Ray, B. K.

B. K. Ray and K. S. Ray, “Detection of significant points and polygonal approximation of digitized curves,” Pattern Recognit. Lett.13(6), 443–452 (1992).
[CrossRef]

Ray, K. S.

B. K. Ray and K. S. Ray, “Detection of significant points and polygonal approximation of digitized curves,” Pattern Recognit. Lett.13(6), 443–452 (1992).
[CrossRef]

Réfrégier, P.

Roberts, A.

Ruch, O.

Saarinen, J.

Skorobogatiy, M.

Talneau, A.

Toy, M. F.

Tseng, C.-C.

Turunen, J.

Vo, H.

Wang, M.-W.

Wang, Y.

Wu, Z.

Xin, H.

Zhang, X.

Appl. Opt. (5)

Cartographica: Int. J. Geograph. Inf. Geovisualization (1)

D. H. Douglas and T. K. Peucker, “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” Cartographica: Int. J. Geograph. Inf. Geovisualization10(2), 112–122 (1973).
[CrossRef]

Comput. Graph. Image Process. (1)

U. Ramer, “An iterative procedure for the polygonal approximation of plane curves,” Comput. Graph. Image Process.1(3), 244–256 (1972).
[CrossRef]

Image Vis. Comput. (1)

A. Masood, “Dominant point detection by reverse polygonization of digital curves,” Image Vis. Comput.26(5), 702–715 (2008).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Technol. (1)

Opt. Express (6)

Opt. Lett. (2)

Pattern Recognit. (3)

D. K. Prasad, M. K. H. Leung, and C. Quek, “ElliFit: An unconstrained, non-iterative, least squares based geometric Ellipse Fitting method,” Pattern Recognit.46(5), 1449–1465 (2013).
[CrossRef]

A. Carmona-Poyato, F. J. Madrid-Cuevas, R. Medina-Carnicer, and R. Muñoz-Salinas, “Polygonal approximation of digital planar curves through break point suppression,” Pattern Recognit.43(1), 14–25 (2010).
[CrossRef]

T. P. Nguyen and I. Debled-Rennesson, “A discrete geometry approach for dominant point detection,” Pattern Recognit.44(1), 32–44 (2011).
[CrossRef]

Pattern Recognit. Lett. (2)

T. M. Cronin, “A boundary concavity code to support dominant point detection,” Pattern Recognit. Lett.20(6), 617–634 (1999).
[CrossRef]

B. K. Ray and K. S. Ray, “Detection of significant points and polygonal approximation of digitized curves,” Pattern Recognit. Lett.13(6), 443–452 (1992).
[CrossRef]

Other (3)

D. K. Prasad and M. K. H. Leung, “Polygonal representation of digital curves,” in Digital Image Processing, S. G. Stanciu, ed. (InTech, 2012), 71–90.

D. K. Prasad and M. K. H. Leung, “Reliability/Precision Uncertainty in Shape Fitting Problems,” in IEEE International Conference on Image Processing(Hong Kong, 2010), 4277–4280.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Pearson Prentice Hall, Delhi, 2008).

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Figures (9)

Fig. 1
Fig. 1

Pseudocode for PRO algorithm.

Fig. 2
Fig. 2

Results for the 17 snippets used in [19]. The lines fitted by various algorithms are shown for each snippet.

Fig. 3
Fig. 3

The digital curves used in Masood [13] and Carmona-Poyato [14] and the lines fitted using PRO0.2, PRO0.6, and PRO1.0.

Fig. 4
Fig. 4

Illustration of the computing average feature and statistics of a 2D planar array of circular photonic crystals. The original images are the copyright of the authors of [6] and have been used with their permission.

Fig. 5
Fig. 5

Two examples of photonic crystal array. In the middle column, the triangles denote the top 10 features with highest values of mean( d p /a ;p ) . The average ellipses are shown in white (overlapped with the original image) in the third column. The original images are the copyright of the authors of [6] and have been used with their permission.

Fig. 6
Fig. 6

The statistics of the two examples of photonic crystal array shown in Fig. 5. (a) statistics of individual features in example 1. (b) histogram and equivalent Gaussian distribution for the values of d p /a ;e,p for example 1. (c) and (d): same as (a) and (b) but for example 2.

Fig. 7
Fig. 7

Two examples of fabrication fidelity in brightness enhancement films with prism arrays fabricated using roll-to-roll process. The defects are highlighted using red arrows and red ellipse. The example images are taken from [7] with the permission of its authors.

Fig. 8
Fig. 8

Two examples of electromagnetic band gap structures. The defects not easily visible are highlighted using red arrows. The example images are taken from [8] with the permission of its authors.

Fig. 9
Fig. 9

Example images from [10] (taken with the authors’ permission) and the results of PRO. The images are shown in the upper row and PRO1.0 results are shown in the lower row. For the images 2 and 4, the center of the outer circle computed using [20] is shown in a red colored ‘ + ’ sign.

Tables (1)

Tables Icon

Table 1 The values of performance parameters for various algorithms. The entries with gray background are the minimum values of the performance parameters in a group of algorithms.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

X A ¯ = J ¯ ,
ε p = | J ¯ X A ¯ | / | A ¯ | ,
ε r = i | a x i +b y i 1 | / s max ,
x( y a y b )+y( x b x a )+ y b x a y a x b =0.
d i = | x i ( y 1 y N )+ y i ( x N x 1 )+ y N x 1 y 1 x N | ( x N x 1 ) 2 + ( y 1 y N ) 2 .
max( ε p , ε r )< ε 0 ,

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