Three-dimensional modeling of the human jaw/teeth using optics and statistics.

Object modeling is a fundamental problem in engineering, involving talents from computer-aided design, computational geometry, computer vision and advanced manufacturing. The process of object modeling takes three stages: sensing, representation, and analysis. Various sensors may be used to capture information about objects; optical cameras and laser scanners are common with rigid objects, while X-ray, CT and MRI are common with biological organs. These sensors may provide a direct or an indirect inference about the object, requiring a geometric representation in the computer that is suitable for subsequent usage. Geometric representations that are compact, i.e., capture the main features of the objects with a minimal number of data points or vertices, fall into the domain of computational geometry. Once a compact object representation is in the computer, various analysis steps can be conducted, including recognition, coding, transmission, etc. The subject matter of this dissertation is object reconstruction from a sequence of optical images using shape from shading (SFS) and SFS with shape priors. The application domain is dentistry. Most of the SFS approaches focus on the computational part of the SFS problem, i.e. the numerical solution. As a result, the imaging model in most conventional SFS algorithms has been simplified under three simple, but restrictive assumptions: (1) the camera performs an orthographic projection of the scene, (2) the surface has a Lambertian reflectance and (3) the light source is a single point source at infinity. Unfortunately, such assumptions are no longer held in the case of reconstruction of real objects as intra-oral imaging environment for human teeth. In this work, we introduce a more realistic formulation of the SFS problem by considering the image formation components: the camera, the light source, and the surface reflectance. This dissertation proposes a non-Lambertian SFS algorithm under perspective projection which benefits from camera calibration parameters. The attenuation of illumination is taken account due to near-field imaging. The surface reflectance is modeled using the Oren-Nayar-Wolff model which accounts for the retro-reflection case. In this context, a new variational formulation is proposed that relates an evolving surface model with image information, taking into consideration that the image is taken by a perspective camera with known parameters. A new energy functional is formulated to incorporate brightness, smoothness and integrability constraints. In addition, to further improve the accuracy and practicality of the results, 3D shape priors are incorporated in the proposed SFS formulation. This strategy is motivated by the fact that humans rely on strong prior information about the 3D world around us in order to perceive 3D shape information. Such information is statistically extracted from training 3D models of the human teeth. The proposed SFS algorithms have been used in two different frameworks in this dissertation: a) holistic, which stitches a sequence of images in order to cover the entire jaw, and then apply the SFS, and b) piece-wise, which focuses on a specific tooth or a segment of the human jaw, and applies SFS using physical teeth illumination characteristics. To augment the visible portion, and in order to have the entire jaw reconstructed without the use of CT or MRI or even X-rays, prior information were added which gathered from a database of human jaws. This database has been constructed from an adult population with variations in teeth size, degradation and alignments. The database contains both shape and albedo information for the population. Using this database, a novel statistical shape from shading (SSFS) approach has been created. Extending the work on human teeth analysis, Finite Element Analysis (FEA) is adapted for analyzing and calculating stresses and strains of dental structures. Previous Finite Element (FE) studies used approximate 2D models. In this dissertation, an accurate three-dimensional CAD model is proposed. 3D stress and displacements of different teeth type are successfully carried out. A newly developed open-source finite element solver, Finite Elements for Biomechanics (FEBio), has been used. The limitations of the experimental and analytical approaches used for stress and displacement analysis are overcome by using FEA tool benefits such as dealing with complex geometry and complex loading conditions

Passive method for 3D reconstruction of human jaw: theory and application.

Oral dental applications based on visual data pose various challenges. There are problems with lighting (effect of saliva, tooth dis-colorization, gum texture, and other sources of specularity) and motion (even inevitable slight motions of the upper/ lower jaw may lead to errors far beyond the desired tolerance of sub-millimeter accuracy). Nowadays, the dental CAM systems have become more compromised and accurate to obtain the geometric data of the jaw from the active sensor (laser scanner). However, they have not met the expectations and the needs of dental professionals in many ways. The probes in these systems are bulky { even their newer versions - and are hard to maneuver. It requires multiple scans to get full coverage of the oral cavity. In addition, the dominant drawback of these systems is the cost. Stereo-based 3D reconstruction provides the highest accuracy among vision systems of this type. However, the evaluation of it\u27s performance for both accuracy results and the number of 3D points that are reconstructed would be affected by the type of the application and the quality of the data that is been acquired from the object of interest. Therefore, in this study, the stereo-based 3D reconstruction will vi be evaluated for the dental application. The handpiece of sensors holder would reach to areas inside the oral cavity, the gap between the tooth in the upper jaw and the tooth in the lower jaw in these areas would be very small, in such the stereo algorithms would not be able to reconstruct the tooth in that areas because of the distance between the optical sensors and the object of interest \tooth as well as the configuration of optical sensors are contradicted the geometric constraint roles of the stereo-based 3D reconstruction. Therefore, the configuration of the optical sensors as well as the number of sensors in the hand piece of sensors holder will be determined based on the morphological of the teeth surfaces. In addition to the 3D reconstruction, the panoramic view of a complete arch of human teeth will be accomplished as an application of dental imaging. Due to the low rate of features on teeth surfaces, the normal tooth surface is extracted using shape from shading. The extracted surface normals impact many imprecise values because of the oral environment; hence an algorithm is being formulated to rectify these values and generate normal maps. The normal maps reveal the impacted geometric properties of the images inside an area, boundary, and shape. Furthermore, the unrestricted camera movement problem is investigated. The camera may be moved along the jaw curve with different angles and distances due to handshaking. To overcome this problem, each frame is tested after warping it, and only correct frames are used to generate the panoramic view. The proposed approach outperforms comparing to the state-of-art auto stitching method

Phenomenological modeling of image irradiance for non-Lambertian surfaces under natural illumination.

Various vision tasks are usually confronted by appearance variations due to changes of illumination. For instance, in a recognition system, it has been shown that the variability in human face appearance is owed to changes to lighting conditions rather than person\u27s identity. Theoretically, due to the arbitrariness of the lighting function, the space of all possible images of a fixed-pose object under all possible illumination conditions is infinite dimensional. Nonetheless, it has been proven that the set of images of a convex Lambertian surface under distant illumination lies near a low dimensional linear subspace. This result was also extended to include non-Lambertian objects with non-convex geometry. As such, vision applications, concerned with the recovery of illumination, reflectance or surface geometry from images, would benefit from a low-dimensional generative model which captures appearance variations w.r.t. illumination conditions and surface reflectance properties. This enables the formulation of such inverse problems as parameter estimation. Typically, subspace construction boils to performing a dimensionality reduction scheme, e.g. Principal Component Analysis (PCA), on a large set of (real/synthesized) images of object(s) of interest with fixed pose but different illumination conditions. However, this approach has two major problems. First, the acquired/rendered image ensemble should be statistically significant vis-a-vis capturing the full behavior of the sources of variations that is of interest, in particular illumination and reflectance. Second, the curse of dimensionality hinders numerical methods such as Singular Value Decomposition (SVD) which becomes intractable especially with large number of large-sized realizations in the image ensemble. One way to bypass the need of large image ensemble is to construct appearance subspaces using phenomenological models which capture appearance variations through mathematical abstraction of the reflection process. In particular, the harmonic expansion of the image irradiance equation can be used to derive an analytic subspace to represent images under fixed pose but different illumination conditions where the image irradiance equation has been formulated in a convolution framework. Due to their low-frequency nature, irradiance signals can be represented using low-order basis functions, where Spherical Harmonics (SH) has been extensively adopted. Typically, an ideal solution to the image irradiance (appearance) modeling problem should be able to incorporate complex illumination, cast shadows as well as realistic surface reflectance properties, while moving away from the simplifying assumptions of Lambertian reflectance and single-source distant illumination. By handling arbitrary complex illumination and non-Lambertian reflectance, the appearance model proposed in this dissertation moves the state of the art closer to the ideal solution. This work primarily addresses the geometrical compliance of the hemispherical basis for representing surface reflectance while presenting a compact, yet accurate representation for arbitrary materials. To maintain the plausibility of the resulting appearance, the proposed basis is constructed in a manner that satisfies the Helmholtz reciprocity property while avoiding high computational complexity. It is believed that having the illumination and surface reflectance represented in the spherical and hemispherical domains respectively, while complying with the physical properties of the surface reflectance would provide better approximation accuracy of image irradiance when compared to the representation in the spherical domain. Discounting subsurface scattering and surface emittance, this work proposes a surface reflectance basis, based on hemispherical harmonics (HSH), defined on the Cartesian product of the incoming and outgoing local hemispheres (i.e. w.r.t. surface points). This basis obeys physical properties of surface reflectance involving reciprocity and energy conservation. The basis functions are validated using analytical reflectance models as well as scattered reflectance measurements which might violate the Helmholtz reciprocity property (this can be filtered out through the process of projecting them on the subspace spanned by the proposed basis, where the reciprocity property is preserved in the least-squares sense). The image formation process of isotropic surfaces under arbitrary distant illumination is also formulated in the frequency space where the orthogonality relation between illumination and reflectance bases is encoded in what is termed as irradiance harmonics. Such harmonics decouple the effect of illumination and reflectance from the underlying pose and geometry. Further, a bilinear approach to analytically construct irradiance subspace is proposed in order to tackle the inherent problem of small-sample-size and curse of dimensionality. The process of finding the analytic subspace is posed as establishing a relation between its principal components and that of the irradiance harmonics basis functions. It is also shown how to incorporate prior information about natural illumination and real-world surface reflectance characteristics in order to capture the full behavior of complex illumination and non-Lambertian reflectance. The use of the presented theoretical framework to develop practical algorithms for shape recovery is further presented where the hitherto assumed Lambertian assumption is relaxed. With a single image of unknown general illumination, the underlying geometrical structure can be recovered while accounting explicitly for object reflectance characteristics (e.g. human skin types for facial images and teeth reflectance for human jaw reconstruction) as well as complex illumination conditions. Experiments on synthetic and real images illustrate the robustness of the proposed appearance model vis-a-vis illumination variation. Keywords: computer vision, computer graphics, shading, illumination modeling, reflectance representation, image irradiance, frequency space representations, {hemi)spherical harmonics, analytic bilinear PCA, model-based bilinear PCA, 3D shape reconstruction, statistical shape from shading

3D-reconstruction of human jaw from a single image : integration between statistical shape from shading and shape from shading.

Object modeling is a fundamental problem in engineering, involving talents from computer-aided design, computational geometry, computer vision and advanced manufacturing. The process of object modeling takes three stages: sensing, representation, and analysis. Various sensors may be used to capture information about objects; optical cam- eras and laser scanners are common with rigid objects, while X-ray, CT and MRI are common with biological organs. These sensors may provide a direct or indirect inference about the object, requiring a geometric representation in the computer that is suitable for subsequent usage. Geometric representations that are compact, i.e., capture the main features of the objects with minimal number of data points or vertices, fall into the domain of computational geometry. Once a compact object representation is in the computer, various analysis steps can be conducted, including recognition, coding, transmission, etc. The subject matter of this thesis is object reconstruction from a sequence of optical images. An approach to estimate the depth of the visible portion of the human teeth from intraoral cameras has been developed, extending the classical shape from shading (SFS) solution to non-Lambertian surfaces with known object illumination characteristics. To augment the visible portion, and in order to have the entire jaw reconstructed without the use of CT or MRI or even X-rays, additional information will be added to database of human jaws. This database has been constructed from an adult population with variations in teeth size, degradation and alignments. The database contains both shape and albedo information for the population. Using this database, a novel statistical shape from shading (SSFS) approach has been created. To obtain accurate result from shape from shading and statistical shape from shading, final step will be integrated two approaches (SFS,SSFS) by using Iterative Closest Point algorithm (ICP). Keywords: computer vision, shading, 3D shape reconstruction, shape from shading, statistical, shape from shading, Iterative Closest Point

Reflectance Transformation Imaging (RTI) System for Ancient Documentary Artefacts

This tutorial summarises our uses of reflectance transformation imaging in archaeological contexts. It introduces the UK AHRC funded project reflectance Transformation Imaging for Anciant Documentary Artefacts and demonstrates imaging methodologies

Final Report to NSF of the Standards for Facial Animation Workshop

The human face is an important and complex communication channel. It is a very familiar and sensitive object of human perception. The facial animation field has increased greatly in the past few years as fast computer graphics workstations have made the modeling and real-time animation of hundreds of thousands of polygons affordable and almost commonplace. Many applications have been developed such as teleconferencing, surgery, information assistance systems, games, and entertainment. To solve these different problems, different approaches for both animation control and modeling have been developed

{3D} Morphable Face Models -- Past, Present and Future

In this paper, we provide a detailed survey of 3D Morphable Face Models over the 20 years since they were first proposed. The challenges in building and applying these models, namely capture, modeling, image formation, and image analysis, are still active research topics, and we review the state-of-the-art in each of these areas. We also look ahead, identifying unsolved challenges, proposing directions for future research and highlighting the broad range of current and future applications

3D Digital Surveying and Modelling of Cave Geometry: Application to Paleolithic Rock Art

3D digital surveying and modelling of cave geometry represents a relevant approach for research, management and preservation of our cultural and geological legacy. In this paper, a multi-sensor approach based on a terrestrial laser scanner, a high-resolution digital camera and a total station is presented. Two emblematic caves of Paleolithic human occupation and situated in northern Spain, “Las Caldas” and “Peña de Candamo”, have been chosen to put in practise this approach. As a result, an integral and multi-scalable 3D model is generated which may allow other scientists, pre-historians, geologists…, to work on two different levels, integrating different Paleolithic Art datasets: (1) a basic level based on the accurate and metric support provided by the laser scanner; and (2) a advanced level using the range and image-based modelling

3D Face Modelling, Analysis and Synthesis

Human faces have always been of a special interest to researchers in the computer vision and graphics areas. There has been an explosion in the number of studies around accurately modelling, analysing and synthesising realistic faces for various applications. The importance of human faces emerges from the fact that they are invaluable means of effective communication, recognition, behaviour analysis, conveying emotions, etc. Therefore, addressing the automatic visual perception of human faces efficiently could open up many influential applications in various domains, e.g. virtual/augmented reality, computer-aided surgeries, security and surveillance, entertainment, and many more. However, the vast variability associated with the geometry and appearance of human faces captured in unconstrained videos and images renders their automatic analysis and understanding very challenging even today. The primary objective of this thesis is to develop novel methodologies of 3D computer vision for human faces that go beyond the state of the art and achieve unprecedented quality and robustness. In more detail, this thesis advances the state of the art in 3D facial shape reconstruction and tracking, fine-grained 3D facial motion estimation, expression recognition and facial synthesis with the aid of 3D face modelling. We give a special attention to the case where the input comes from monocular imagery data captured under uncontrolled settings, a.k.a. \textit{in-the-wild} data. This kind of data are available in abundance nowadays on the internet. Analysing these data pushes the boundaries of currently available computer vision algorithms and opens up many new crucial applications in the industry. We define the four targeted vision problems (3D facial reconstruction $\&$ tracking, fine-grained 3D facial motion estimation, expression recognition, facial synthesis) in this thesis as the four 3D-based essential systems for the automatic facial behaviour understanding and show how they rely on each other. Finally, to aid the research conducted in this thesis, we collect and annotate a large-scale videos dataset of monocular facial performances. All of our proposed methods demonstarte very promising quantitative and qualitative results when compared to the state-of-the-art methods