Chad English

Comparison of linear and nonlinear calibration methods for phase-measuring profilometry

In phase-shifting-based fringe-projection surface-geometry measurement, phase unwrapping techniques produce a continuous phase distribution that contains the height information of the 3-D object surface. Mapping of the phase distribution to the height of the object has often involved complex derivations of the nonlinear relationship. In this paper, the phase-to-height mapping is formulated using both linear and nonlinear equations, the latter through a simple geometrical derivation. Furthermore, the measurement accuracies of the linear and nonlinear calibrations are compared using measurement simulations where noise is included at the calibration stage only, and where noise is introduced at both the calibration and measurement stages. Measurement accuracies for the linear and nonlinear calibration methods are also compared, based on real-system measurements. From the real-system measurements, the accuracy of the linear calibration was similar to the nonlinear calibration method at the lower range of depth. At the higher range of depth, however, the nonlinear calibration method had considerably higher accuracy. It seems that as the object approaches the projector and camera for the higher range of depth, the assumption of linearity based on small divergence of light from the projector becomes less valid.

Two-step triangular-pattern phase-shifting method for three-dimensional object-shape measurement

Existing phase-shifting measurement methods involve processing of three acquired images or computation of functions that require more complex processing than linear functions. This paper presents a novel two-step triangular-pattern phase-shifting method of 3-D object-shape measurement that combines advantages of earlier techniques. The method requires only two image-acquisition steps to capture two images, and involves projecting linear grayscale-intensity triangular patterns that require simpler computation of the intensity ratio than methods that use sinusoidal patterns. A triangular intensity-ratio distribution is computed from two captured phase-shifted triangular-pattern images. An intensity ratio-to-height conversion algorithm, based on traditional phase-to-height conversion in the sinusoidal-pattern phase-shifting method, is used to reconstruct the object 3-D surface geometry. A smaller pitch of the triangular pattern resulted in higher measurement accuracy; however, an optimal pitch was found, below which intensity-ratio unwrapping failure may occur. Measurement error varied cyclically with depth and may partly be due to projector gamma nonlinearity and image defocus. The use of only two linear triangular patterns in the proposed method has the advantage of less processing than current methods that process three images, or methods that process more complex functions than the intensity ratio. This would be useful for high speed or real-time 3-D object-shape measurement.

Multiple-step triangular-pattern phase shifting and the influence of number of steps and pitch on measurement accuracy

We present new extensions of the two-step, triangular-pattern phase-shifting method for different numbers of phase-shifting steps to increase measurement accuracy and to analyze the influence of the number of phase-shifting steps and pitch of the projected triangular intensity-profile pattern on the measurement accuracy. Phase-shifting algorithms to generate the intensity ratio, essential for surface reconstruction, were developed for each measurement method. Experiments determined that higher measurement accuracy can be obtained with a greater number of phase-shifting steps and a lower value of pitch, as long as the pitch is appropriately selected to be divisible by the number of phase-shifting steps and not below an optimal value, where intensity-ratio unwrapping failure would occur.

Field testing of a 3D automatic target recognition and pose estimation algorithm

Neptec Design Group Ltd. has developed a 3D Automatic Target Recognition (ATR) and pose estimation technology demonstrator in partnership with the Canadian DND. The system prototype was deployed for field testing at Defence Research and Development Canada (DRDC)-Valcartier. This paper discusses the performance of the developed algorithm using 3D scans acquired with an imaging LIDAR. 3D models of civilian and military vehicles were built using scans acquired with a triangulation laser scanner. The models were then used to generate a knowledge base for the recognition algorithm. A commercial imaging LIDAR was used to acquire test scans of the target vehicles with varying range, pose and degree of occlusion. Recognition and pose estimation results are presented for at least 4 different poses of each vehicle at each test range. Results obtained with targets partially occluded by an artificial plane, vegetation and military camouflage netting are also presented. Finally, future operational considerations are discussed.

Imaging and tracking elements of the International Space Station using a 3D autosynchronized scanner

The Neptec Design Group has developed a new 3D auto-synchronized laser scanner for space applications, based on a principle from the National Research Council of Canada. In imaging mode, the Laser Camera System (LCS) raster scans objects and computes high-resolution 3D maps of their surface features. In centroid acquisition mode, the LCS determines the position of discrete target points on an object. The LCS was flight-tested on-board the space shuttle Discovery during mission STS-105 in August 2001. When the shuttle was docked on the International Space Station (ISS), the LCS was used to obtain four high-resolution 3D images of several station elements at ranges from 5 m to 40 m. A comparison of images taken during orbital day and night shows that the LCS is immune to the dynamic lighting conditions encountered on orbit. During the mission, the LCS also tracked a series of retro-reflective and Inconel targets affixed to the Multi-Purpose Lab Module (MPLM), when the module was stationary and moving. Analysis shows that the accuracy of the photosolutions derived from LCS centroid data is comparable to that of the Space Vision System (SVS), Neptecs product presently used by NASA for ISS assembly tasks.

Intensity-ratio error compensation for triangular-pattern phase-shifting profilometry

We present an intensity-ratio error-compensation method to decrease the measurement error caused by projector gamma nonlinearity and image defocus in triangular-pattern phase-shifting profilometry. The intensity-ratio measurement error is first determined by simulating the measurement with the triangular-pattern phase-shifting method with ideal and real captured triangular-pattern images based on the ideal and real gamma nonlinearity functions. A lookup table that stores the intensity-ratio measurement error corresponding to the measured intensity ratio is constructed and used for intensity-ratio error compensation. Experiments demonstrated that the intensity-ratio error compensation method significantly reduced the measurement error in the triangular-pattern phase-shifting method by 28.5%.

Real-time full-field 3-D surface-shape measurement using off-the-shelf components and a single processor

Phase-shifting fringe-projection methods have been increasingly used for three-dimensional (3D) object surface modeling to permit full-field measurement. This paper presents a real-time full-field high-resolution 3D surface-shape measurement system implemented with an efficient 3D shape measurement pipeline and triangular-pattern phase-shifting based on off-the-shelf components, software synchronization and a single computer-processor. The system projects computer-generated fringe patterns with a triangular intensity profile onto an object via a Digital Light Processing (DLP) projector. The projected patterns are electronically shifted and a CCD camera synchronized with the DLP projector by software captures the images from another direction. The captured images are processed by a single computer to reconstruct the 3D shape using triangular-pattern phase-shifting algorithms, and the model is displayed in real time. The 3D shape acquisition system achieved a speed of 5.6 fps for an image size of 648times494 pixels using the two-step triangular-pattern phase-shifting method, without any hardware synchronization or dual processing.

Repeated phase-offset measurement for error compensation in two-step triangular phase-shifting profilometry

Two-step triangular phase-shifting is a recently developed method for 3-D shape measurement. In this method, two triangular gray-level-coded patterns, which are phase-shifted by half of the pitch, are needed to reconstruct the 3-D object. The measurement accuracy is limited by gamma non-linearity and defocus of the projector and camera. This paper presents a repeated phase-offset two-step triangular-pattern phase-shifting method used to decrease the measurement error caused by the gamma non-linearity and defocus in the previously developed two-step triangularpattern phase-shifting 3-D object measurement method. Experimental analysis indicated that a sensitivity threshold based on the gamma non-linearity curve should be used as the minimum intensity of the computer-generated pattern input to the projector to reduce measurement error. In the repeated phase-offset method, two-step triangular phaseshifting is repeated with an initial phase offset of one-eighth of the pitch, and the two obtained 3-D object height distributions are averaged to generate the final 3-D object-height distribution. Experimental results demonstrated that the repeated phase-offset measurement method substantially decreased measurement error compared to the two-step triangular phase-shifting method.

Two-step triangular phase-shifting method for 3-D object-shape measurement

Traditional sinusoidal phase-shifting algorithms involve the calculation of an arctangent function to obtain the phase, which results in slow measurement speed. This paper presents a novel high-speed two-step triangular phase-shifting approach for 3-D object measurement. In the proposed method, a triangular gray-level-coded pattern is used for the projection. Only two triangular patterns, which are phase-shifted by 180 degrees or half of the pitch, are needed to reconstruct the 3-D object. A triangular-shape intensity-ratio distribution is obtained by calculation of the two captured triangular patterns. Removing the triangular shape of the intensity ratio over each pattern pitch generates a wrapped intensity-ratio distribution. The unwrapped intensity-ratio distribution is obtained by removing the discontinuity of the wrapped image with a modified unwrapping method commonly used in the sinusoidal phase-shifting method. An intensity ratio-to-height conversion algorithm, which is based on the traditional phase-to-height conversion algorithm in the sinusoidal phase-shifting method, is used to reconstruct the 3-D surface coordinates of the object. Compared with the sinusoidal and trapezoidal phase shifting methods, the processing speed is faster with similar resolution. This method therefore has the potential for real-time 3-D object measurement. This has applications in inspection tasks, mobile-robot navigation and 3-D surface modeling.

The complementary nature of triangulation and ladar technologies

3D ranging and imaging technology is generally divided into time-based (ladar) and position-based (triangulation) approaches. Traditionally ladar has been applied to long range, low precision applications and triangulation has been used for short range, high precision applications. Measurement speed and precision of both technologies have improved such that ladars are viable at shorter ranges and triangulation is viable at longer ranges. These improvements have produced an overlap of technologies for short to mid-range applications. This paper investigates the two sets of technologies to demonstrate their complementary nature particularly with respect to space and terrestrial applications such as vehicle inspection, navigation, collision avoidance, and rendezvous & docking.