Geometric And Radiometric Estimation In A Structured-Light 3D Scanner
Dhillon, Daljit Singh J S
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Measuring 3D surface geometry with precision and accuracy is an important part of many engineering and scientific tasks. 3D Scanning techniques measure surface geometry by estimating the locations of sampled surface points. In recent years, Structured-Light 3D scanners have gained significant popularity owing to their ability to produce highly accurate scans in real-time at a low cost. In this thesis we describe an approach for Structured-Light 3D scanning using a digital camera and a digital projector. We utilise the projective geometric relationships between the projector and the camera to carry out both an implicit calibration of the system and to solve for 3D structure. Our approach to geometric calibration is flexible, reliable and amenable to robust estimation. In addition, we model and account for the radiometric non-linearities in the projector such as gamma distortion. Finally, we apply a post-processing step to efficiently smooth out high-frequency surface noise while retaining the structural details. Consequently, the proposed work reduces the computational load and set-up time of a Structured-Light 3D scanner; thereby speeding up the whole scanning process while retaining the ability to generate highly accurate results. We demonstrate the accuracy of our scanning results on real-world objects of varying degrees of surface complexity. Introduction The projective geometry for a pair of pin-hole viewing devices is completely defined by their intrinsic calibration and their relative motion or extrinsic calibration in the form of matrices. For a Euclidean reconstruction, the geometry elements represented by the calibration matrices must be parameterised and estimated in some form. The use of a projector as the ‘second viewing’ device has led to numerous approaches to model and estimate its intrinsic parameters and relative motion with respect to the camera's 3D co-ordinate system. Proposed thesis work assimilates the benefits of projective geometry constructs such as Homography and the invariance of the cross-ratios to simplify the system calibration and the 3D estimation processes by an implicit modeling of the projector's intrinsic parameters and its relative motion. Though linear modeling of the projective geometry between a camera-projector view-pair captures the most essential aspects of the underlying geometry, it does not accommodate system non-linearities due to radiometric distortions of a projector device. We propose an approach that uses parametric splines to model the systematic errors introduced by radiometric non-linearities and thus correct for them. For 3D surfaces reconstructed as point-clouds, noise manifests itself as some high-frequency variations for the resulting mesh. Various pre and/or post processing techniques are proposed in the literature to model and minimize the effects of noise. We use simple bilateral filtering of the depth-map for the reconstructed surface to smoothen the surface while retaining its structural details. Modeling Projective Relations In our approach for calibrating the projective-geometric structure of a projector-camera view-pair, the frame of reference for measurements is attached to the camera. The camera is calibrated using a commonly used method. To calibrate the scanner system, one common approach is to project sinusoidal patterns onto the reference planes to generate reference phase maps. By relating the phase-information between the projector and image pixels, a dense mapping is obtained. However, this is an over-parameterisation of the calibration information. Since the reference object is a plane, we can use the projective relationships induced by a plane to implicitly calibrate the projector geometry. For the estimation of the three-dimensional structure of the imaged object, we utilise the invariance of cross-ratios along with the calibration information of two reference planes. Our formulation is also extensible to utilise more than two reference plane to compute more than one estimate of the location of an unknown surface point. Such estimates are amenable to statistical analysis which allows us to derive both the shape of an object and associate reliability scores to each estimated point location. Radiometric Correction Structured-light based 3D scanners commonly employ phase-shifted sinusoidal patterns to solve for the correspondence problem. For scanners using projective geometry between a camera and a projector, the projector's radiometric non-linearities introduce systematic errors in establishing correspondences. Such errors manifest as visual artifacts which become pronounced when fewer phase-shifted sinusoidal patterns are used. While these artifacts can be avoided by using a large number of phase-shifts, doing so also increases the acquisition time. We propose to model and rectify such systematic errors using parametric representations. Consequently, while some existing methods retain the complete reference phase maps to account for such distortions, our approach describes the deviations using a few model parameters. The proposed approach can be used to reduce the number of phase-shifted sinusoidal patterns required for codification while suppressing systematic artifacts. Additionally, our method avoids the 1D search steps that are needed when a complete reference phase map is used, thus reducing the computational load for 3D estimation. The effectiveness of our method is demonstrated with reconstruction of some geometric surfaces and a cultural figurine. Filtering Noise For a structured-light 3D scanner, various sources of noise in the environment and the devices lead to inaccuracies in estimating the codewords (phase map) for an unknown surface, during reconstruction. We examine the effects of such noise factors on our proposed methods for geometric and radiometric estimation. We present a quantitative evaluation for our proposed method by scanning the objects of known geometric properties or measures and then computing the deviations from the expected results. In addition, we evaluate the errors introduced due to inaccuracies in system calibration by computing the variance statistics from multiple estimates for the reconstructed 3D points, where each estimate is computed using a different pair of reference planes. Finally, we discuss the efficacy of certain filtering techniques in reducing the high-frequency surface noise when applied to: (a) the images of the unknown surface at a pre-processing stage, or (b) the respective phase (or depth) map at a post-processing stage. Conclusion In this thesis, we motivate the need for a procedurally simple and computationally less demanding approach for projector calibration. We present a method that uses homographies induced by a pair of reference planes to calibrate a structured-light scanner. By using the projective invariance of the cross-ratio, we solved for the 3D geometry of a scanned surface. We demonstrate the fact that 3D geometric information can be derived using our approach with accuracy on the order of 0.1 mm. Proposed method reduces the image acquisition time for calibration and the computational needs for 3D estimation. We demonstrate an approach to effectively model radiometric distortions for the projector using cubic splines. Our approach is shown to give significant improvement over the use of complete reference phase maps and its performance is comparable to that of a sate-of-the-art method, both quantitatively as well as qualitatively. In contrast with that method, proposed method is computationally less expensive, procedurally simpler and exhibits consistent performance even at relatively higher levels of noise in phase estimation. Finally, we use a simple bilateral filtering on the depth-map for the region-of-interest. Bilateral filtering provides the best trade-off between surface smoothing and the preservation of its structural details. Our filtering approach avoids computationally expensive surface normal estimation algorithms completely while improving surface fidelity.