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

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

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

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

Procedural function-based modelling of volumetric microstructures

We propose a new approach to modelling heterogeneous objects containing internal volumetric structures with size of details orders of magnitude smaller than the overall size of the object. The proposed function-based procedural representation provides compact, precise, and arbitrarily parameterised models of coherent microstructures, which can undergo blending, deformations, and other geometric operations, and can be directly rendered and fabricated without generating any auxiliary representations (such as polygonal meshes and voxel arrays). In particular, modelling of regular lattices and cellular microstructures as well as irregular porous media is discussed and illustrated. We also present a method to estimate parameters of the given model by fitting it to microstructure data obtained with magnetic resonance imaging and other measurements of natural and artificial objects. Examples of rendering and digital fabrication of microstructure models are presented

Computer Assisted Relief Generation - a Survey

In this paper we present an overview of the achievements accomplished to date in the field of computer aided relief generation. We delineate the problem, classify the different solutions, analyze similarities, investigate the evelopment and review the approaches according to their particular relative strengths and weaknesses. In consequence this survey is likewise addressed to researchers and artists through providing valuable insights into the theory behind the different concepts in this field and augmenting the options available among the methods presented with regard to practical application

Stereoscopic Sketchpad: 3D Digital Ink

--Context-- This project looked at the development of a stereoscopic 3D environment in which a user is able to draw freely in all three dimensions. The main focus was on the storage and manipulation of the ‘digital ink’ with which the user draws. For a drawing and sketching package to be effective it must not only have an easy to use user interface, it must be able to handle all input data quickly and efficiently so that the user is able to focus fully on their drawing. --Background-- When it comes to sketching in three dimensions the majority of applications currently available rely on vector based drawing methods. This is primarily because the applications are designed to take a users two dimensional input and transform this into a three dimensional model. Having the sketch represented as vectors makes it simpler for the program to act upon its geometry and thus convert it to a model. There are a number of methods to achieve this aim including Gesture Based Modelling, Reconstruction and Blobby Inflation. Other vector based applications focus on the creation of curves allowing the user to draw within or on existing 3D models. They also allow the user to create wire frame type models. These stroke based applications bring the user closer to traditional sketching rather than the more structured modelling methods detailed. While at present the field is inundated with vector based applications mainly focused upon sketch-based modelling there are significantly less voxel based applications. The majority of these applications focus on the deformation and sculpting of voxmaps, almost the opposite of drawing and sketching, and the creation of three dimensional voxmaps from standard two dimensional pixmaps. How to actually sketch freely within a scene represented by a voxmap has rarely been explored. This comes as a surprise when so many of the standard 2D drawing programs in use today are pixel based. --Method-- As part of this project a simple three dimensional drawing program was designed and implemented using C and C++. This tool is known as Sketch3D and was created using a Model View Controller (MVC) architecture. Due to the modular nature of Sketch3Ds system architecture it is possible to plug a range of different data structures into the program to represent the ink in a variety of ways. A series of data structures have been implemented and were tested for efficiency. These structures were a simple list, a 3D array, and an octree. They have been tested for: the time it takes to insert or remove points from the structure; how easy it is to manipulate points once they are stored; and also how the number of points stored effects the draw and rendering times. One of the key issues brought up by this project was devising a means by which a user is able to draw in three dimensions while using only two dimensional input devices. The method settled upon and implemented involves using the mouse or a digital pen to sketch as one would in a standard 2D drawing package but also linking the up and down keyboard keys to the current depth. This allows the user to move in and out of the scene as they draw. A couple of user interface tools were also developed to assist the user. A 3D cursor was implemented and also a toggle, which when on, highlights all of the points intersecting the depth plane on which the cursor currently resides. These tools allow the user to see exactly where they are drawing in relation to previously drawn lines. --Results-- The tests conducted on the data structures clearly revealed that the octree was the most effective data structure. While not the most efficient in every area, it manages to avoid the major pitfalls of the other structures. The list was extremely quick to render and draw to the screen but suffered severely when it comes to finding and manipulating points already stored. In contrast the three dimensional array was able to erase or manipulate points effectively while the draw time rendered the structure effectively useless, taking huge amounts of time to draw each frame. The focus of this research was on how a 3D sketching package would go about storing and accessing the digital ink. This is just a basis for further research in this area and many issues touched upon in this paper will require a more in depth analysis. The primary area of this future research would be the creation of an effective user interface and the introduction of regular sketching package features such as the saving and loading of images

A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces

We present a new high-order, local meshfree method for numerically solving reaction diffusion equations on smooth surfaces of codimension 1 embedded in ℝd. The novelty of the method is in the approximation of the Laplace-Beltrami operator for a given surface using Hermite radial basis function (RBF) interpolation over local node sets on the surface. This leads to compact (or implicit) RBF generated finite difference (RBF-FD) formulas for the Laplace-Beltrami operator, which gives rise to sparse differentiation matrices. The method only requires a set of (scattered) nodes on the surface and an approximation to the surface normal vectors at these nodes. Additionally, the method is based on Cartesian coordinates and thus does not suffer from any coordinate singularities. We also present an algorithm for selecting the nodes used to construct the compact RBF-FD formulas that can guarantee the resulting differentiation matrices have desirable stability properties. The improved accuracy and computational cost that can be achieved with this method over the standard (explicit) RBF-FD method are demonstrated with a series of numerical examples. We also illustrate the flexibility and general applicability of the method by solving two different reaction-diffusion equations on surfaces that are defined implicitly and only by point clouds

A Concept For Surface Reconstruction From Digitised Data

Reverse engineering and in particular the reconstruction of surfaces from digitized data is an important task in industry. With the development of new digitizing technologies such as laser or photogrammetry, real objects can be measured or digitized quickly and cost effectively. The result of the digitizing process is a set of discrete 3D sample points. These sample points have to be converted into a mathematical, continuous surface description, which can be further processed in different computer applications. The main goal of this work is to develop a concept for such a computer aided surface generation tool, that supports the new scanning technologies and meets the requirements in industry towards such a product. Therefore first, the requirements to be met by a surface reconstruction tool are determined. This marketing study has been done by analysing different departments of several companies. As a result, a catalogue of requirements is developed. The number of tasks and applications shows the importance of a fast and precise computer aided reconstruction tool in industry. The main result from the analysis is, that many important applications such as stereolithographie, copy milling etc. are based on triangular meshes or they are able to handle these polygonal surfaces. Secondly the digitizer, currently available on the market and used in industry are analysed. Any scanning system has its strength and weaknesses. A typical problem in digitizing is, that some areas of a model cannot be digitized due to occlusion or obstruction. The systems are also different in terms of accuracy, flexibility etc. The analysis of the systems leads to a second catalogue of requirements and tasks, which have to be solved in order to provide a complete and effective software tool. The analysis also shows, that the reconstruction problem cannot be solved fully automatically due to many limitations of the scanning technologies. Based on the two requirements, a concept for a software tool in order to process digitized data is developed and presented. The concept is restricted to the generation of polygonal surfaces. It combines automatic processes, such as the generation of triangular meshes from digitized data, as well as user interactive tools such as the reconstruction of sharp corners or the compensation of the scanning probe radius in tactile measured data. The most difficult problem in this reconstruction process is the automatic generation of a surface from discrete measured sample points. Hence, an algorithm for generating triangular meshes from digitized data has been developed. The algorithm is based on the principle of multiple view combination. The proposed approach is able to handle large numbers of data points (examples with up to 20 million data points were processed). Two pre-processing algorithm for triangle decimation and surface smoothing are also presented and part of the mesh generation process. Several practical examples, which show the effectiveness, robustness and reliability of the algorithm are presented

Ubiquitous volume rendering in the web platform

176 p.The main thesis hypothesis is that ubiquitous volume rendering can be achieved using WebGL. The thesis enumerates the challenges that should be met to achieve that goal. The results allow web content developers the integration of interactive volume rendering within standard HTML5 web pages. Content developers only need to declare the X3D nodes that provide the rendering characteristics they desire. In contrast to the systems that provide specific GPU programs, the presented architecture creates automatically the GPU code required by the WebGL graphics pipeline. This code is generated directly from the X3D nodes declared in the virtual scene. Therefore, content developers do not need to know about the GPU.The thesis extends previous research on web compatible volume data structures for WebGL, ray-casting hybrid surface and volumetric rendering, progressive volume rendering and some specific problems related to the visualization of medical datasets. Finally, the thesis contributes to the X3D standard with some proposals to extend and improve the volume rendering component. The proposals are in an advance stage towards their acceptance by the Web3D Consortium