Machine Vision and Applications (2013) 24:447–459 DOI 10.1007/s00138-012-0433-5 ORIGINAL PAPER Robust and accurate pattern matching in fuzzy space for fiducial mark alignment Xuenan Cui · Hakil Kim · Eunsoo Park · Hyohoon Choi Received: 2 April 2011 / Revised: 9 December 2011 / Accepted: 27 April 2012 / Published online: 24 May 2012 © Springer-Verlag 2012 Abstract This paper presents a new pattern matching method for fiducial mark alignment in a fuzzy space. The membership functions of fuzzy sets are designed by distance transforms, and their levels are set in the fuzzy space for fast matching of a specific fiducial mark. After the fuzzification, a sub-pixel level translation is estimated by a fuzzy similar- ity measure and an interpolation using fuzzified model and target images. This paper also proposes a method of coarse- to-fine rotation estimation in sub-pixel level. Experiments show that the proposed fuzzy space pattern matching algo- rithm outperforms commercial pattern matching algorithms based on correlation or edge. Keywords Fiducial mark · Alignment · Pattern matching · Distance transform · Fuzzy space 1 Introduction Automated optical inspection (AOI) systems are, as per its name, automatic systems that use machine vision techniques to detect defects on intermediate or final products in a man- X. Cui (B ) · H. Kim · E. Park School of Information and Communication Engineering, INHA University, 253 Yonghyun-Dong, Nam-Gu, Incheon 402-751, Korea e-mail: xncui@vision.inha.ac.kr H. Kim e-mail: hikim@inha.ac.kr E. Park e-mail: espark@inha.ac.kr H. Choi Electro-Mechanics, 314 Maetan3-Dong, Yeongtong-Gu, Suwon 443-743, Korea e-mail: hyohoon.choi@samsung.com ufacturing process. Alignment is a crucial issue in AOI, because the accuracy of the alignment directly affects the performance of the overall AOI system. Two types of fidu- cial marks are used for alignment between a reference image and a test image in the AOI system. The first is the origi- nal fiducial mark provided by computer-aided design (CAD) data (Fig.1a). The second is a modified fiducial mark that makes use of the characteristics of the grab image (Fig.1b). Engineers need additional tasks to estimate the properties of the grab image when the modified fiducial mark is utilized. In practice, this is a very difficult task, because the images from different products have their own properties. Therefore, AOI systems need a robust alignment algorithm based on the original fiducial mark. Pattern matching algorithms are very essential for object recognition, stereo matching etc. Not only simple algorithms, such as Sum of Absolute Difference (SAD), Sum of Squared Difference (SSD)and Normalized Cross Correlation (NCC) [1, 2], but also advanced algorithms for pattern matching have been developed by researchers. In [3], the integral image based on the pattern matching algorithm was developed to accelerate the matching speed. In [4–9], the edge, shape, and local scale-invariant information are used for matching various objects. The distance transform (DT)-based pattern matching can be considered as feature-based pattern match- ing approach. The DT uses diverse distance measures (such as Euclidean, chessboard, cityblock and dead reckoning [10–12]), usually over binary image. However, it can be extended to be applied to gray-scale images, as presented by Ikonen [13, 14]. Wright et al. [15] proposed a distance transform-based method for skeletonization, and Holzer et al. [16] proposed a method for object recognition and pose estimation using DTs. The goal of fiducial mark alignment is to locate robustly and accurately a given fiducial mark in an input grab image, 123