Moments for Real-Time Geometric Surface Inspection

Taweepol Suesut

Research output: ThesisDoctoral Thesis


This thesis develops a real-time implementation of a geometric surface inspection system based on light-sectioning. The real-time implementation of hardware such as image sensor, camera interface and hardware processor is considered. A measurement rate of 540 sections per second is achieved with a standard low cost CMOS camera. It is proposed to implement the computation of the individual sections in an FPGA with embedded Power-PC. The FPGA supports giga-bit Ethernet transport of the images from the camera and T-base 100 ethernet to the host computer. Moment-based surface modelling is employed to separate deviations in the local relief from a smooth approximation of the surface. Tensor polynomial approximation on an invariant Cartesian grid generated from a new unitary polynomial basis is used to generate the smooth model for the surface. The methods are demonstrated via automatic inspection in the electrolytic production of copper plates. An analysis and implementation of this approach enables the modeling of the global surface geometry in real-time: simulations show that it is approximately 80 times faster than fitting tensor spline surfaces. The new unitary polynomial basis used for surface modelling is proposed to generate the discrete polynomial moments. Mathematical proofs and numerical testing related to the new polynomial basis are presented. Furthermore, it is proven that the errors in the computation of moments are almost exclusively associated with the application of the recurrence relationship, and it is illustrated that QR decomposition can be used to eliminate the systematic propagation of errors. Fourier analysis is applied to the polynomial bases to determine the spectral distribution of the numerical error. Using the new unitary basis, the discrete polynomial moment provides almost perfect numerical behavior, enabling the modelling of larger images with higher degree polynomials. A new concept of combining periodic with polynomial moments is proposed. The new method of modelling and analyzing 3D surface data acquired using a laser- scanning instrument is presented. The advantage of the new method is that it is able to eliminate some of the problem associated with the Gibbs phenomena. The method is also applied to real-time modelling of 3D surface encountered to separate the global geometry from periodic undulations and local anomalies. The steel blocks with periodic and non smooth surface are presented to demonstrate the system concept. These steel blocks contain the stamped number, which should be read automatically, a complicated task
Translated title of the contributionMomentenberechnung für Geometrische Oberflächeninspektion in Echtzeit
Original languageEnglish
  • O'Leary, Paul, Assessor A (internal)
  • Lee, Peter, Assessor B (external)
Publication statusPublished - 2008

Bibliographical note

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  • Geometric surface inspection FPGA 2D tenssor polynomials

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