Recovering facial shape using a statistical model of surface normal direction

In this paper, we show how a statistical model of facial shape can be embedded within a shape-from-shading algorithm. We describe how facial shape can be captured using a statistical model of variations in surface normal direction. To construct this model, we make use of the azimuthal equidistant projection to map the distribution of surface normals from the polar representation on a unit sphere to Cartesian points on a local tangent plane. The distribution of surface normal directions is captured using the covariance matrix for the projected point positions. The eigenvectors of the covariance matrix define the modes of shape-variation in the fields of transformed surface normals. We show how this model can be trained using surface normal data acquired from range images and how to fit the model to intensity images of faces using constraints on the surface normal direction provided by Lambert's law. We demonstrate that the combination of a global statistical constraint and local irradiance constraint yields an efficient and accurate approach to facial shape recovery and is capable of recovering fine local surface details. We assess the accuracy of the technique on a variety of images with ground truth and real-world images

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

A rigorous and realistic Shape From Shading method and some of its applications

This article proposes a rigorous and realistic solution of the Lambertian Shape From Shading (SFS) problem. The power of our approach is threefolds. First, our work is based on a rigorous mathematical method: we define a new notion of weak solutions (in the viscosity sense) which does not necessarily requires boundary data (contrary to the work of [rouy-tourin:92,prados-faugeras-etal:02,prados-faugeras:03,camilli-falcone:96,falcone-sagona-etal:01]) and which allows to define a solution as soon as the image is (Lipschitz) continuous (contrary to the work of [oliensis:91,dupuis-oliensis:94]). We prove the existence and uniqueness of this (new) solution and we approximate it by using a provably convergent algorithm. Second, it improves the applicability of the SFS to real images: we complete the realistic work of [prados-faugeras:03,tankus-sochen-etal:03], by modeling the problem with a pinhole camera and with a single point light source located at the optical center. This new modelization appears very relevant for applications. Moreover, our algorithm can deal with images containing discontinuities and black shadows. It is very robust to pixel noise and to errors on parameters. It is also generic: i.e. we propose a unique algorithm which can compute numerical solutions of the various perspective and orthographic SFS models. Finally, our algorithm seems to be the most efficient iterative algorithm of the SFS literature. Third, we propose three applications (in three different areas) based on our SFS method

Single-picture reconstruction and rendering of trees for plausible vegetation synthesis

State-of-the-art approaches for tree reconstruction either put limiting constraints on the input side (requiring multiple photographs, a scanned point cloud or intensive user input) or provide a representation only suitable for front views of the tree. In this paper we present a complete pipeline for synthesizing and rendering detailed trees from a single photograph with minimal user effort. Since the overall shape and appearance of each tree is recovered from a single photograph of the tree crown, artists can benefit from georeferenced images to populate landscapes with native tree species. A key element of our approach is a compact representation of dense tree crowns through a radial distance map. Our first contribution is an automatic algorithm for generating such representations from a single exemplar image of a tree. We create a rough estimate of the crown shape by solving a thin-plate energy minimization problem, and then add detail through a simplified shape-from-shading approach. The use of seamless texture synthesis results in an image-based representation that can be rendered from arbitrary view directions at different levels of detail. Distant trees benefit from an output-sensitive algorithm inspired on relief mapping. For close-up trees we use a billboard cloud where leaflets are distributed inside the crown shape through a space colonization algorithm. In both cases our representation ensures efficient preservation of the crown shape. Major benefits of our approach include: it recovers the overall shape from a single tree image, involves no tree modeling knowledge and minimal authoring effort, and the associated image-based representation is easy to compress and thus suitable for network streaming.Peer ReviewedPostprint (author's final draft

Single View Reconstruction for Human Face and Motion with Priors

Single view reconstruction is fundamentally an under-constrained problem. We aim to develop new approaches to model human face and motion with model priors that restrict the space of possible solutions. First, we develop a novel approach to recover the 3D shape from a single view image under challenging conditions, such as large variations in illumination and pose. The problem is addressed by employing the techniques of non-linear manifold embedding and alignment. Specifically, the local image models for each patch of facial images and the local surface models for each patch of 3D shape are learned using a non-linear dimensionality reduction technique, and the correspondences between these local models are then learned by a manifold alignment method. Local models successfully remove the dependency of large training databases for human face modeling. By combining the local shapes, the global shape of a face can be reconstructed directly from a single linear system of equations via least square. Unfortunately, this learning-based approach cannot be successfully applied to the problem of human motion modeling due to the internal and external variations in single view video-based marker-less motion capture. Therefore, we introduce a new model-based approach for capturing human motion using a stream of depth images from a single depth sensor. While a depth sensor provides metric 3D information, using a single sensor, instead of a camera array, results in a view-dependent and incomplete measurement of object motion. We develop a novel two-stage template fitting algorithm that is invariant to subject size and view-point variations, and robust to occlusions. Starting from a known pose, our algorithm first estimates a body configuration through temporal registration, which is used to search the template motion database for a best match. The best match body configuration as well as its corresponding surface mesh model are deformed to fit the input depth map, filling in the part that is occluded from the input and compensating for differences in pose and body-size between the input image and the template. Our approach does not require any makers, user-interaction, or appearance-based tracking. Experiments show that our approaches can achieve good modeling results for human face and motion, and are capable of dealing with variety of challenges in single view reconstruction, e.g., occlusion

3D reconstruction for plastic surgery simulation based on statistical shape models

This thesis has been accomplished in Crisalix in collaboration with the Universitat Pompeu Fabra within the program of Doctorats Industrials. Crisalix has the mission of enhancing the communication between professionals of plastic surgery and patients by providing a solution to the most common question during the surgery planning process of ``How will I look after the surgery?''. The solution proposed by Crisalix is based in 3D imaging technology. This technology generates the 3D reconstruction that accurately represents the area of the patient that is going to be operated. This is followed by the possibility of creating multiple simulations of the plastic procedure, which results in the representation of the possible outcomes of the surgery. This thesis presents a framework capable to reconstruct 3D shapes of faces and breasts of plastic surgery patients from 2D images and 3D scans. The 3D reconstruction of an object is a challenging problem with many inherent ambiguities. Statistical model based methods are a powerful approach to overcome some of these ambiguities. We follow the intuition of maximizing the use of available prior information by introducing it into statistical model based methods to enhance their properties. First, we explore Active Shape Models (ASM) which are a well known method to perform 2D shapes alignment. However, it is challenging to maintain prior information (e.g. small set of given landmarks) unchanged once the statistical model constraints are applied. We propose a new weighted regularized projection into the parameter space which allows us to obtain shapes that at the same time fulfill the imposed shape constraints and are plausible according to the statistical model. Second, we extend this methodology to be applied to 3D Morphable Models (3DMM), which are a widespread method to perform 3D reconstruction. However, existing methods present some limitations. Some of them are based in non-linear optimizations computationally expensive that can get stuck in local minima. Another limitation is that not all the methods provide enough resolution to represent accurately the anatomy details needed for this application. Given the medical use of the application, the accuracy and robustness of the method, are important factors to take into consideration. We show how 3DMM initialization and 3DMM fitting can be improved using our weighted regularized projection. Finally, we present a framework capable to reconstruct 3D shapes of plastic surgery patients from two possible inputs: 2D images and 3D scans. Our method is used in different stages of the 3D reconstruction pipeline: shape alignment; 3DMM initialization and 3DMM fitting. The developed methods have been integrated in the production environment of Crisalix, proving their validity.Aquesta tesi ha estat realitzada a Crisalix amb la col·laboració de la Universitat Pompeu Fabra sota el pla de Doctorats Industrials. Crisalix té com a objectiu la millora de la comunicació entre els professionals de la cirurgia plàstica i els pacients, proporcionant una solució a la pregunta que sorgeix més freqüentment durant el procés de planificació d'una operació quirúrgica ``Com em veuré després de la cirurgia?''. La solució proposada per Crisalix està basada en la tecnologia d'imatge 3D. Aquesta tecnologia genera la reconstrucció 3D de la zona del pacient operada, seguit de la possibilitat de crear múltiples simulacions obtenint la representació dels possibles resultats de la cirurgia. Aquesta tesi presenta un sistema capaç de reconstruir cares i pits de pacients de cirurgia plàstica a partir de fotos 2D i escanegis. La reconstrucció en 3D d'un objecte és un problema complicat degut a la presència d'ambigüitats. Els mètodes basats en models estadístics son adequats per mitigar-les. En aquest treball, hem seguit la intuïció de maximitzar l'ús d'informació prèvia, introduint-la al model estadístic per millorar les seves propietats. En primer lloc, explorem els Active Shape Models (ASM) que són un conegut mètode fet servir per alinear contorns d'objectes 2D. No obstant, un cop aplicades les correccions de forma del model estadístic, es difícil de mantenir informació de la que es disposava a priori (per exemple, un petit conjunt de punts donat) inalterada. Proposem una nova projecció ponderada amb un terme de regularització, que permet obtenir formes que compleixen les restriccions de forma imposades i alhora són plausibles en concordança amb el model estadístic. En segon lloc, ampliem la metodologia per aplicar-la als anomenats 3D Morphable Models (3DMM) que són un mètode extensivament utilitzat per fer reconstrucció 3D. No obstant, els mètodes de 3DMM existents presenten algunes limitacions. Alguns estan basats en optimitzacions no lineals, computacionalment costoses i que poden quedar atrapades en mínims locals. Una altra limitació, és que no tots el mètodes proporcionen la resolució adequada per representar amb precisió els detalls de l'anatomia. Donat l'ús mèdic de l'aplicació, la precisió i la robustesa són factors molt importants a tenir en compte. Mostrem com la inicialització i l'ajustament de 3DMM poden ser millorats fent servir la projecció ponderada amb regularització proposada. Finalment, es presenta un sistema capaç de reconstruir models 3D de pacients de cirurgia plàstica a partir de dos possibles tipus de dades: imatges 2D i escaneigs en 3D. El nostre mètode es fa servir en diverses etapes del procés de reconstrucció: alineament de formes en imatge, la inicialització i l'ajustament de 3DMM. Els mètodes desenvolupats han estat integrats a l'entorn de producció de Crisalix provant la seva validesa

Opt: A Domain Specific Language for Non-linear Least Squares Optimization in Graphics and Imaging

Many graphics and vision problems can be expressed as non-linear least squares optimizations of objective functions over visual data, such as images and meshes. The mathematical descriptions of these functions are extremely concise, but their implementation in real code is tedious, especially when optimized for real-time performance on modern GPUs in interactive applications. In this work, we propose a new language, Opt (available under http://optlang.org), for writing these objective functions over image- or graph-structured unknowns concisely and at a high level. Our compiler automatically transforms these specifications into state-of-the-art GPU solvers based on Gauss-Newton or Levenberg-Marquardt methods. Opt can generate different variations of the solver, so users can easily explore tradeoffs in numerical precision, matrix-free methods, and solver approaches. In our results, we implement a variety of real-world graphics and vision applications. Their energy functions are expressible in tens of lines of code, and produce highly-optimized GPU solver implementations. These solver have performance competitive with the best published hand-tuned, application-specific GPU solvers, and orders of magnitude beyond a general-purpose auto-generated solver