Invariant 2D object recognition using KRA and GRA

Abstract

Computer vision has been extensively adopted in industry for the last two decades. It enhances productivity and quality management, and is flexibility, efficient, fast, inexpensive, reliable and robust. This study presents a new translation, rotation and scaling-free object recognition method for 2D objects. The proposed method comprises two parts: KRA feature extractor and GRA classifier. The KRA feature extractor employs K-curvature, re-sampling, and autocorrelation transformation to extract unique features of objects, and then gray relational analysis (GRA) classifies the extracted invariant features. The boundary of the digital object was first represented as the form of the K-curvature over a given region of support, and was then re-sampled and transformed with autocorrelation function. After that, the extracted features own the unique property that is invariant to translation, rotation and scaling. To verify and validate the proposed method, 50 synthetic and 50 real objects were digitized as standard patterns, and 10 extra images of each object (test images) which were taken at different positions, orientations and scales, were acquired and compared with the standard patterns. The experimental results reveal that the proposed method with either GRA or MD methods is effective and reliable for part recognition.

Introduction

Various working environments suggest that automatic part recognition with invariant properties is of priority concern issue. Ullman (1996) noted that part recognition is the most difficult of these tasks owing to the varying positions, orientations and scales of parts. Hence, recognizing parts plays a critical role that first determines which process plan should be adopted for the manufactured work piece particularly in a flexible manufacturing system (FMS) or a robot system. Many invariant object recognition methods have been developed in the last decade. Lee, Moon, and Lee (1997) used signature and autocorrelation to extract features and used backpropagation neural networks to automatically recognize 2D parts. Jones and Bhanu (2001) developed an invariant SAR (Synthetic aperture radar) recognition method using SAR scattering center locations and magnitudes as features. Wöhler and Anlauf (2001) presented an object detection and recognition system in the traffic environment based on the adaptable time delay neural network. Khalil and Bayoumi (2002a) developed a 2D invariant object recognition method using continuous wavelet transform and neural networks. Furthermore, they defined three invariant functions with dyadic wavelet transformation of the object boundary to object recognition (Khalil & Bayoumi, 2002b). Zhang, Zhang, Krim, and Walter (2003) proposed an invariant 2D object recognition approach by measuring the geodesic distance between the observed object and a model in the shape space. Cao, Hao, and Wang (2004) employed the direction basis function (DBF) neural networks for successful invariant object recognition. Kyrki, Kamarainen, and Kavianen (2004) utilized a Gabor filter to extract invariant features for object recognition. Li and Lee (2004) presented a Hopfield neural network model for invariant object recognition using projective transformations and the projective invariance was embedded into the compatibility constraint for finding point correspondences such that the problem was formulated by minimizing the predefined energy function through a Hopfield network. Huang, Wang, and Zhang (2005) proposed a scheme based on independent component analysis (ICA) for object recognition with affine transformation and for affine motion estimation between video frames. Sookhanaphibarn and Lursinsap (2006) proposed a method for extracting the invariant features of a color image based on the concept of principal component analysis and a competitive learning algorithm. Yu and Bennamoun (2007) developed two complete sets of similarity invariant descriptors using Fourier–Mellin transform and the analytical Fourier–Mellin transform frameworks, and then adopted 2D-PCA to simplify the invariant descriptor for face recognition. Sun and Tien (2008) proposed an invariant object recognition method by incorporating the eigenvalue of covariance matrix and autocorrelation with backpropagation neural networks.

Using object profiles for object recognition is one of the major fields in pattern recognition. Therefore, boundary descriptor becomes an important role to represent objects’ profiles. Various boundary descriptors, such as chain code, curvature, and Fourier Descriptor (FD), have been developed. The Freeman chain code (Freeman & Davis, 1977), which can be treated as a polygonal approximation of a contour, is easy to use, but it is less efficient and accurate. Fourier descriptors have been successfully applied to contour enhancement and object inspection, providing position, orientation and scale invariant properties by normalization. (Bandera et al., 1999, Sánchez-Marín, 2000). However, performing forward and backward transformations requires heavy computation when calculating the complex equations. Curvature, defined as the change rate of the slope, has been widely employed in different applications such as shape representation, feature extraction, corner detection and object recognition (Byun and Nagata, 1996, Han and Jang, 1990, Li and Chen, 1999, Lim et al., 1995, Park and Han, 1998). Different numeric curvature estimation approaches have been discussed in literature. Rosenfeld and Johnson (1973) initially defined curvature as a K-cosine function, where K denotes a region of support on the boundary. Sohn, Alexander, Kim, and Snyder (1994) expressed curvature with a formula involving its first- and second-order directional derivatives. Tsai and Chen (1994) computed directly the curvature by measuring the first- and second-order derivatives of the continuous functions. Later, Tsai, Hou, and Su (1999) employed the eigenvalue of covariance matrices to measure the curvature and detect the sharp corners in a contour. Tien, Yeh, and Hsieh (2004) applied K-curvature to represent the boundary of microdrills in order to detect the defects. Sun (2009) adopted K-cosine to detect cornors of 2D digital objects in order to conduct industrial inspection.

This study proposes a position, orientation, and scale-invariant 2D object recognition method which adopted a so-called KRA invariant feature extractor and used grey relational analysis to recognize objects. The KRA feature extractor proceeds in three phrases: firstly, uses K-curvature to convert boundary coordinate information into boundary curvature information; secondly, re-samples the sequence of K-curvature into scaling-free boundary features; and finally transforms the sequence as autocorrelation coefficients, to derive invariant property. Grey relational analysis (GRA) method is then used to classify 2D objects.