We present a strategy to determine shrinked rotation-symmetric aspheres. First, we approximate nonlinearly a
conic based on a direct least squares start-solution with quadratic constraint to a set of datapoints. Afterwards,
we smooth aspheres polynomially.
The requirements of optical surfaces are increasing with respect to their functionality and accuracy of form. Furthermore, it is a goal for the optical industry to unify the lens process from development to production. In our phase of design we have an arbitrary set of 3D-points of a free formed surface. With approximation through NURBS, we get a continuous description of this surface. To the generated NURB-Spline, we have developed a CNC-program for the UPM-3000 machine, which drives the cutter along the level curve. Therefore, we triangulate the NURBS-surface. By the desired accuracy and the generated triangles, we determine levels of the surface. Thus, we refine the given triangulation. Hence we have a triangular decomposition for each level, which will be driven along by the cutter. The described method will be compared to the common raster-fly-cut-method for accuracy and cutting time.
The LINOS Photonics company has developed a new tactile sensor to measure aspheric surfaces. The sensing device drives along spherical coordinates and the measuring data of a level curve is obtained by the rotation of the lens. The complete asphere of the lens is reconstructed by a number of such level curves. All data is given in a spherical coordinate system. The company provides a software to determine the error between the actual surface and a reference asphere with respect to a cartesian coordinate system. But the algorithm depends on the strong assumption that the peak of the reconstructed asphere is equal to the rotational point of the measuring instrument. Our algorithm expands the existing method. We minimize the distance of the reference asphere to the measuring points in a cartesian coordinate system. To do this, we calculate the optimal rotation and translation of the reference asphere
to the measured points. This defines a non-linear optimization problem, which is solved with algorithm of Levenberg and Marquardt. Furthermore, we are able to calculate the Jacobi matrix with
respect to the rotation center. The output of the proposed algorithms contains the maximal deviation for each measuring point in z-direction and the variance of the error. Additionally, we determine a pseudo tangential deviation between the reference and the actual geometry by a secant method. Altogether the new algorithm enables us to deliver comparable results for the asphere measuring problem.
Visual features of lumber can be used to assure its quality in stiffness and strength. Specifically, the average annual ring distance of the planks and the position of the center of the annual rings of the front side supply a close relation to some quality parameters of planks. Unfortunately, it turns out to be difficult to detect the average annual ring width by simple image vision methods due to distortions in the front side image of a plank caused by the cutting process. In this paper we propose two integrating methods which are capable of being used in an industrial application. One is based on quantizations of color images, the other on local Fourier transformations to detect the main wave in an image.
A valuable visual indicator to grade the stiffness and strength of planks can be obtained by analyzing the structure of the grain on it. To integrate an analyzing image vision module in an industrial selection process a real-time system is needed to build. Two main objectives must be reached: First a stable edge detector should extract the grain edges. Second these grain edges have to be tracked to achieve a complete grain representation. This representation can be used to analyze the regularity of the grain. Since the visual nature of grain varies a lot even on a single plank we present an edge detector which is adaptive and a grain tracking algorithm capable of closing gaps between pixels. Both steps work in real-time (i.e. 5 frames per second resulting in 1 meter per second).
Method for 3D reconstruction of known rigid objects from a single monocular image or a sequence of monocular images is presented. In the first part of the paper, a new computational approach to estimate pose and orientation of well-known objects in a 3D-scene from a single frame is discussed. The underlying theory is described in the context of a prototype matching problem and the existence of optimal solutions is proved. Furthermore, it is straightforward to extend the concept of prototype matching to the case of stereo or pseudo stereo applications and even more general setups. Hence, an improved 3D reconstruction with higher accuracy and increased stability can be achieved, for instance, by moving the camera along a linear sledge. The estimation of the ego-motion of a camera is covered as a special case by the introduced modeling via prototype matching. In the second part, experimental results for natural image sequences are analyzed. The derived accuracy and execution times of the described algorithms are illustrated. The last section deals with implementational details necessary to reduce the execution time under real-time restrictions.
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