Inspection and measurement of three-dimensional objects are widely needed in industries for quality monitoring and control, inspection, and reverse engineering. A number of visual or optical methods have been developed for that purpose using laser structured light, moire, stereo vision, confocal microscope and so on. However, those conventional methods have inherent two shortcomings. One is the occlusion problem, and therefore, only a part of surface geometry can be measured. The other one is that measuring condition is unreliable according to the surface reflection properties of the object. X-ray imaging method, on the other hand, has inherent merits over the conventional optical methods : Firstly, both the surface and the inner structure of an object can be achieved, secondly the surface reflection property of an object does not affect the characteristics of its x-ray images. Due to these advantages, x-ray imaging technologies are used in a number of industrial applications instead of conventional optical or visual systems.
There are several 3D imaging methods, such as computed tomography, digital tomosynthesis(DT), x-ray stereo, and algebraic reconstruction methods. In tomography method, a number of images projected from all and uniformly sampled directions by fan-beam x-ray are required to achieve a cross-section of an object, which makes a strict restriction in industrial applications. Although the accuracy is not sufficient, DT method makes a cross-sectional image in a very short time with a smaller number of oblique projection images, and thus can be used in industrial inspection. Algebraic method is available to reconstruct 3D object in a limited imaging conditions, insufficient image number and view angle, however the conventional method requires a huge computation time and memory.
In this research, a new 3D x-ray imaging system is proposed and realized with a series of three dimensional measurement and reconstruction imaging technologies. The research scope in this thesis includes both the system technologies with calibration, and x-ray 3D imaging algorithms for measurement and reconstruction of an object from x-ray images.
The system proposed here is a real-time digital imaging system from which eight images projected from different views are obtained within 0.5 seconds without mechanical movement of the target object or x-ray source and image sensor. It is composed of a scanned beam x-ray source, an image intensifier, a rotating prism and a CCD camera. Image distortion caused by the image intensifier and the optical components in the system is corrected by a series of image correction methods with a neural network feature extraction method. X-ray source coordinates calibration method is also proposed here, where the scanned x-ray positions are analyzed through a set of x-ray pattern images.
There are two approaches available to measure or reconstruct 3D structure of an object from these x-ray images. The first one is geometric approach, where the image features such as edges and corner points are used. Once the features are detected, 3D structure of an object can be understood from stereo copic method. However, it is not easy to detect these features through conventional image processing algorithms, since the intensity variation in x-ray images is closely dependent on the view direction or the object pose. Therefore, the object pose information is prerequisite for reliable feature detection in x-ray images. For this purpose, we propose a pose estimation method based on a principal axes analysis from its x-ray images. Here, the 3D inertia matrix and the centroid of an object is obtained from three x-ray images projected from different views, and then the rotational and translation parameters are determined from principal axes analysis. Once the object pose is determined, the image features are estimated through mathematical imaging model, and the feature locations in x-ray images are detected by image correlation technique. Then, the 3D shape of the object is reconstructed by stereo method. Here, 3D measurement is made in a recursive manner that a given primitive model of an object is revised so that the features are matched in x-ray images.
The second one is the photometric approach, where the intensity information in x-ray images is used. Since image intensity represents the medium density or intersection length along the ray, 3D volume of an object can be inferred based on the intensity by a reconstruction algorithm such as algebraic reconstruction technique(ART). In this research, an efficient and fast computing 3D volume reconstruction method called uniform and simultaneous algebraic reconstruction technique(USART). Since voxel based ray sampling scheme is utilized here, all voxels within the reconstruction region are equally weighted and updated evenly, and thus advanced performances in convergence and stability could be achieved. For fast implementation of USART, spherical voxel elements are employed here in computation instead of cubic voxels. By utilizing sphere elements, the reconstruction equation is simplified and required computation time and memory is also reduced.
The proposed 3D x-ray imaging technologies are implemented into the developed x-ray system with calibrations. A series of experiments are performed to show the validity of the proposed methods : 3D structure of mechanical parts and PCB solder joints are measured or reconstructed. 3D Reconstruction results on various defects of BGA solder joints show the usability of the 3D x-ray imaging methods.
