Thesis (M.S.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (ℓ. 67-71)

Recent advances in 4D data acquisition systems in the field of Computer Vision have opened up many exciting new possibilities for the interpretation of complex moving surfaces. However, a fundamental problem is that this has also led to a huge increase in the volume of data to be handled. Attempting to make sense of this wealth of information is then a core issue to be addressed if such data can be applied to more complex tasks. Similar problems have been historically encountered in the analysis of 3D static surfaces, leading to the extraction of higher-level features based on analysis of the differential geometry. Our central hypothesis is that there exists a compact set of similarly useful descriptors for the analysis of dynamic 4D surfaces. The primary advantages in considering localised changes are that they provide a naturally useful set of invariant characteristics. We seek a constrained set of terms - a vocabulary - for describing all types of deformation. By using this, we show how to describe what the surface is doing more effectively; and thereby enable better characterisation, and consequently more effective visualisation and comparison. This thesis investigates this claim. We adopt a bottom-up approach of the problem, in which we acquire raw data from a newly constructed commercial 4D data capture system developed by our industrial partners. A crucial first step resolves the temporal non-linear registration between instances of the captured surface. We employ a combined optical/range flow to guide a conformation over a sequence. By extending the use of aligned colour information alongside the depth data we improve this estimation in the case of local surface motion ambiguities. By employing a KLT/thin-plate-spline method we also seek to preserve global deformation for regions with no estimate. We then extend aspects of differential geometry theory for existing static surface analysis to the temporal domain. Our initial formulation considers the possible intrinsic transitions from the set of shapes defined by the variations in the magnitudes of the principal curvatures. This gives rise to a total of 15 basic types of deformation. The change in the combined magnitudes also gives an indication of the extent of change. We then extend this to surface characteristics associated with expanding, rotating and shearing; to derive a full set of differential features. Our experimental results include qualitative assessment of deformations for short episodic registered sequences of both synthetic and real data. The higher-level distinctions extracted are furthermore a useful first step for parsimonious feature extraction, which we then proceed to demonstrate can be used as a basis for further analysis. We ultimately evaluate this approach by considering shape transition features occurring within the human face, and the applicability for identification and expression analysis tasks.

Bézier curves and surfaces are used to great success in computer-aided design and finite element modelling, among other things, due to their tendency of being mathematically convenient to use. This thesis explores the different properties that make Bézier surfaces the strong tool that it is. This requires a closer look at Bernstein polynomials and the de Castiljau algorithm. To illustrate some of these properties, the strain energy of a Bézier surface is calculated. This demands an understanding of what a surface is, which is why this thesis also covers some elementary theory regarding parametrized curves and surface geometry, including the first and second fundamental forms.

La rétrodiffusion associée aux effets de géométrie de surface à des angles d’incidence élevés (62°—76°) et pour quatres angles azimutaux (Q0, 3Q0, 60° et 90°) a été étudiée pour des champs de maïs du Québec (Canada) à l’aide de 3 images du ROS-C du Centre canadien de télédétection. Selon les conditions de drainage des champs, le couvert végétal apporte une plus ou moins grande contribution à la rétrodiffusion. L’effet de géométrie de surface est nettement plus prononcé (amplitude 3,2 dB) pour les champs de maïs sans drainage souterrain que ceux ayant un drainage souterrain (1,5 dB). Le contraste entre ces deux types de champ est rattaché aux différences de pente du couvert végétal ainsi qu’aux variations de biomasse.

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Tracking of human motion and object identification and recognition are important in many applications including motion capture for human-machine interaction systems. This research is part of a global project to enable a service robot to recognize new objects and perform different object-related tasks based on task guidance and demonstration provided by a general user. This research consists of the calibration and testing of two vision systems which are part of a robot-vision system. First, real-time tracking of a human hand is achieved using images acquired from three calibrated synchronized cameras. Hand pose is determined from the positions of physical markers and input to the robot system in real-time. Second, a multi-line laser camera range sensor is designed, calibrated, and mounted on a robot end-effector to provide three-dimensional (3D) geometry information about objects in the robot environment. The laser-camera sensor includes two cameras to provide stereo vision. For the 3D hand tracking, a novel score-based hand tracking scheme is presented employing dynamic multi-threshold marker detection, a stereo camera-pair utilization scheme, marker matching and labeling using epipolar geometry and hand pose axis analysis, to enable real-time hand tracking under occlusion and non-uniform lighting environments. For surface-geometry measurement using the multi-line laser range sensor, two different approaches are analyzed for two-dimensional (2D) to 3D coordinate mapping, using Bezier surface fitting and neural networks, respectively. The neural-network approach was found to be a more viable approach for surface-geometry measurement worth future exploration for its lower magnitude of 3D reconstruction error and consistency over different regions of the object space.

Tracking of human motion and object identification and recognition are important in many applications including motion capture for human-machine interaction systems. This research is part of a global project to enable a service robot to recognize new objects and perform different object-related tasks based on task guidance and demonstration provided by a general user. This research consists of the calibration and testing of two vision systems which are part of a robot-vision system. First, real-time tracking of a human hand is achieved using images acquired from three calibrated synchronized cameras. Hand pose is determined from the positions of physical markers and input to the robot system in real-time. Second, a multi-line laser camera range sensor is designed, calibrated, and mounted on a robot end-effector to provide three-dimensional (3D) geometry information about objects in the robot environment. The laser-camera sensor includes two cameras to provide stereo vision. For the 3D hand tracking, a novel score-based hand tracking scheme is presented employing dynamic multi-threshold marker detection, a stereo camera-pair utilization scheme, marker matching and labeling using epipolar geometry and hand pose axis analysis, to enable real-time hand tracking under occlusion and non-uniform lighting environments. For surface-geometry measurement using the multi-line laser range sensor, two different approaches are analyzed for two-dimensional (2D) to 3D coordinate mapping, using Bezier surface fitting and neural networks, respectively. The neural-network approach was found to be a more viable approach for surface-geometry measurement worth future exploration for its lower magnitude of 3D reconstruction error and consistency over different regions of the object space.

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.

Voiced communication plays a fundamental role in society. Voice research seeks to improve understanding of the fundamental physics governing voice production, with the eventual goal of improving methods to diagnose and treat voice disorders. For this thesis, three different aspects of voice production research were studied. First, porcine vocal fold medial surface geometry was determined, and the three-dimensional geometric distortion induced by freezing the larynx, especially in the region of the vocal folds, was quantified. It was found that porcine vocal folds are qualitatively geometrically similar to canine and human vocal folds, as well as commonly used models, and that freezing of tissue in the larynx causes distortion of around 5%. Second, a setup of multiple high-resolution cameras and a stereo-endoscopy system simultaneously recorded positions on the superior surface of synthetic, self-oscillating vocal fold models to estimate the error in the measurement of the three-dimensional location by the stereo-endoscopy system. The error was found to be low in the transverse plane, whereas the error was relatively large in the inferior-superior direction, suggesting that the stereo-endoscope is applicable for in vivo measurements of absolute distances of the glottis in the transverse plane such as glottal length, width, and area. Third, a function for strain-varying Poisson's ratio for silicone was developed from experimental data. It is anticipated that the findings herein can aid voice researchers as they study voice production, leading to improved voice care.