In optical 3-D measurements, two steps are generally required to obtain the whole-body 3-D shapes of objects: measuring the 3-D shape from different views, and afterwards connecting them together. The multiview overlapping scanning connection technique in a cylindrical coordinate system is an effective method for measuring a surface with a rotation axis, e.g., a 360-deg shape. However, there are great difficulties in measuring a more complex surface, such as those with concavities or composed of several discontinuous patches, because a complex surface generally cannot be explicitly represented in cylindrical coordinates. To solve these problems, a novel multiview connection method based on virtual cylinders for measurement of 3-D surfaces is proposed. In a Cartesian coordinate system, the virtual cylinders are determined by least-squares fitting to the local overlapping surface patches. The error movements are obtained from a linear equation system based on the virtual cylinders. The connection of adjacent views is then performed by coordinate transformation in 3-D space. Both computer simulation and experimental results are presented to verify the effectiveness of the suggested method.
A frequency encoding approach for fringe projection profilometry is proposed. First, a series of fringe patterns are generated in computer where the pixels are encoded with the temporal frequencies. Second, the patterns are cast on the object surface by an LCD projector and then the distorted patterns are captured by a CCD camera. Third, a least squares algorithm based on a linear prediction is deduced to estimate the frequencies, and then the depth map is further reconstructed by using the mapping relationship between the temporal frequency and the depth of the object surface. Experimental results are presented to demonstrate the validity of this technique.
A novel calibration method for fringe projection 3-D measurement system is presented. To get the data serving the calibration, a calibration gauge with white-black checker pattern is transferred to different positions with known depths. At each position, the phase values in the black squares are regarded as invalid data for their lower modulation, and the phase distribution of the whole calibration gauge is obtained by the least-square fitting to the phases in the white squares according to the theoretical distribution function. The phase-to-depth and pixel to lateral coordinate mapping relationship are simultaneously calibrated. The validityof the proposed method is demonstrated by experimental results.
This paper presents a novel calibration approach for determining the mapping relationship between the depth map and the phase difference in fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and hence perfectly describes the mapping between the depth map and the phase-difference distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions. A least-squares estimation algorithm with linear computation is deduced to retrieve the related parameters and to reconstruct the mapping function. Both computer simulation and experiment are carried out to demonstrate the validity of this technique.
This paper presents a novel least squares calibration approach for fringe projection profilometry. This approach is based on a simple nonlinear function, which is deduced by analyzing the geometry of measurement system and perfectly describes the mapping relationship between the depth map and phase distribution. The calibration is implemented by translating a target plane to a sequence of given positions with known depths, and measuring its phase distributions. Based on least squares estimation, an algorithm with linear computation is deduced to retrieve the related parameters, by which the burden of computational complexity is effectively alleviated. In experiment, a plaster statue is measured to demonstrate the validity of the principle.
In optical three-dimensional measurement, fringe projection technique has found more and more applications. However, in 3D measurement of complex objects, due to the inherent limitation of triangulation, occultation is unavoidable. Meanwhile, the surface of the measured object usually contains discontinuities or the object profile is often sharply steep. Another problem is that for the measurement of a surface with complex reflectivity or quasi-specular, the resulting phase values are unreliable. Therefore, there must be some invalid areas caused by shadow, phase errors or discontinuities, etc. in just a single-view. For compensating the lacked 3-D coordinates of the points in the areas, the multi-frequency fringe projection method is used and temporal phase unwrapping is applied. Invalid areas are marked and further cancelled according to the modulation and phase fitting reliability. To obtain the whole 3D world coordinates of the measured object, a novel connection method based on the principle of the virtual cylinder is presented to accurately integrate the 3D coordinates of every single-view into a global coordinate system. The connection method derives from a technique named Multi-view (aperture) Overlap-scanning Technique (MAOST) based on overlapping areas. The measurement results of an automobile headlamp reflector are experimentally presented to demonstrate the validity.
In this paper, the multi-aperture overlap-scanning technique (MAOST) and its recent developments are presented. In the first instance, MAOST is used in interferometry, and the principle of MAOST for interferometry is that, a tested large-scale plane is covered by an array of interferometric subapertures, and the relationship between each couple of adjacent subapertures is determined from their overlapping areas by a least squares method, and then the profile of tested plane is obtained by connecting all the subapertures together. Recently, to meet the requirements of advanced manufacturing, the idea of MAOST has been extended to precision three-dimensional (3-D) measurement. In practice, a whole-body 3-D shape is acquired by two steps: first measuring the 3-D shape from different views and afterwards connecting all the views together. In order to accurately determine the position and orientation of every single-view in a common coordinate system, an iterative algorithm based on MAOST concept is utilized.