Robust Spatial Autoregressive Modeling for Hardwood Log Inspection

Zhu, Delong; Beex, A.A.

doi:10.1006/jvci.1994.1004

Cited by 17 publications

(7 citation statements)

References 9 publications

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“…If we let denote the asymptotic functional form of , (16) reduces to (19) The asymptotic influence function of the estimator at is defined as the Gâteaux derivative [16] given by (20) It is the directional derivative of in the direction of at . To derive it, let us first substitute (18) into (19) to get (21) Differentiating with respect to , it follows: (22) Evaluating (22) at , assuming Fisher consistency given by , and interchanging differentiation and integration in the first term of the summation, we get (23) Applying the chain rule to the kernel of the first integral and using the sifting property of the Dirac measure, we obtain (24) Solving for , we get (25) Deriving given by (17) with respect to while assuming that and are independent of over the neighborhood where the derivative is applied, it follows: (26) where is the Hessian matrix of , which is equal to . Applying the chain rule to the derivative of with respect to and using the fact that , we obtain (27) where .…”

Section: Influence Function Of the Gm-estimatormentioning

confidence: 99%

“…In signal processing, the M-estimators introduced by Huber in 1964 [16] and the least median of squares (LMS) estimator proposed by Rousseeuw and Leroy [18] have received a great deal of attention [20], [21]. In particular, the use of M-estimators has been advocated for a broad range of applications such as spectrum estimation [22], multiuser detection in wireless communications [23], image filtering [24], and image modeling for log defect recognition [25] and classification [26].…”

Section: Introductionmentioning

confidence: 99%

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A Robust GM-Estimator for the Automated Detection of External Defects on Barked Hardwood Logs and Stems

Thomas

Mili

2007

IEEE Trans. Signal Process.

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The ability to detect defects on hardwood trees and logs holds great promise for the hardwood forest products industry. At every stage of wood processing, there is a potential for improving value and recovery with knowledge of the location, size, shape, and type of log defects. This paper deals with a new method that processes hardwood laser-scanned surface data for defect detection. The detection method is based on robust circle fitting applied to scanned cross-section data sets recorded along the log length. It can be observed that these data sets have missing data and include large outliers induced by loose bark that dangles from the log trunk. Because of that and because of the nonlinearity of the circle model, which presents both additive and nonadditive errors, we initiated a new robust Generalized M-estimator for which the residuals are standardized via scale estimates calculated by means of projection statistics and incorporated in the Huber objective function, yielding a bounded influence method. Our projection statistics are based on the 2-D radial vectors instead of the row vectors of the Jacobian matrix as advocated in the literature dealing with linear regression. These radial distances allow us to develop algorithms aimed at pinpointing large surface rises and depressions from the contour image levels, and thereby, locating severe external defects having at least a height of 0.5 in and a diameter of 5 in.

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Section: Influence Function Of the Gm-estimatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Robust GM-Estimator for the Automated Detection of External Defects on Barked Hardwood Logs and Stems

Thomas

Mili

2007

IEEE Trans. Signal Process.

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“…Textile, paper, glass, wood, metal, food, and industrial parts on a conveyor belt can all be cited under this heading. Computer tomography images were employed to detect internal defects in hardwood logs [2]. Multi-thresholding, morphological processing, and focus of attention mechanisms were used for the segmentation and recognition of the defects [3].…”

Section: Introductionmentioning

confidence: 99%

On-Line Defect Detection in Web Offset Printing

Shankar¹,

Ravi²,

Zhong

2003

The Fourth International Conference on Control and Automation 2003 ICCA Final Program and Book of Abstracts ICCA-03

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This paper presents a detailed description of a vision system developed to detect and locate the nonuniformities that appear on the web offset printing machine. Specifically, the system is capable of monitoring the high-speed web offset printing in a real time environment and alerting the operator of any events (e.g., structural faults, color variations, missing characters, ink splashes, streaks, etc.) that disrupt the uniformities in the web offset printing. Such events are thought to affect crucial printing properties, resulting in non-uniformities in printing and impacting its quality and printability. This paper describes the vision system in terms of its hardware modules, as well as the image processing algorithms that it utilizes to scan the color images and locate areas of defect from the printing web. Basically, the system utilizes high-speed image scanning algorithms to detect edges and boundaries using linear and non-linear filters of dynamic size, threshold and transformation for further analysis. In addition to being tested in a laboratory environment, a prototype of this system was constructed and deployed to a web printing system, where its performance was evaluated under realistic conditions. The system was installed on a Flexo gravure-print-press machine for testing, and it was found that the vision system was able to successfully monitor and detect nonuniformities.

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“…Textile, paper, glass, wood, metal, food, and industrial parts on a conveyor belt can all be cited under this heading. Computer tomography images were employed to detect internal defects in hardwood logs [15]. Multi-thresholding, morphological processing, and focus of attention mechanisms were used for the segmentation and recognition of the defects [16].…”

Section: Introductionmentioning

confidence: 99%

<title>Facet model and mathematical morphology for surface characterization</title>

et al. 1999

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This paper describes an algorithm for the automatic segmentation and representation of surface structures and non-uniformities in an industrial setting. The automatic image processing and analysis algorithm is developed as part of a complete on-line web characterization system of a papermaking process at the wet end. The goal is to: (1) link certain types of structures on the surface of the web to known machine parameter values, and (2) find the connection between detected structures at the beginning of the line and defects seen on the final product. Images of the pulp mixture (slurry), carried by a fast moving table, are obtained using a stroboscopic light and a CCD camera. This characterization algorithm succeeded where conventional contrast and edge detection techniques failed due to a poorly controlled environment. The images obtained have poor contrast and contain noise caused by a variety of sources.After a number of enhancement steps, conventional segmentation methods still failed to detect any structures and are consequently discarded. Techniques tried include the Canny edge detector, the Sobel, Roberts, and Prewitt's filters, as well as zero crossings. The facet model algorithm, is then applied to the images with various parameter settings and is found to be successful in detecting the various topographic characteristics of the surface of the slurry. Pertinent topographic elements are retained and a filtered image computed. Carefully tailored morphological operators are then applied to detect and segment regions of interest. Those regions are then selected according to their size, elongation, and orientation. Their bounding rectangles are computed and represented. Also addressed in this paper are aspects of the real time implementation of this algorithm for on-line use. The algorithm is tested on over 500 images of slurry and is found to segment and characterize nonuniformities on all 500 images.

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Robust Spatial Autoregressive Modeling for Hardwood Log Inspection

Cited by 17 publications

References 9 publications

A Robust GM-Estimator for the Automated Detection of External Defects on Barked Hardwood Logs and Stems

A Robust GM-Estimator for the Automated Detection of External Defects on Barked Hardwood Logs and Stems

On-Line Defect Detection in Web Offset Printing

<title>Facet model and mathematical morphology for surface characterization</title>

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