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

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 facial shape estimation from a single image under arbitrary pose and illumination.

Humans have the uncanny ability to perceive the world in three dimensions (3D), otherwise known as depth perception. The amazing thing about this ability to determine distances is that it depends only on a simple two-dimensional (2D) image in the retina. It is an interesting problem to explain and mimic this phenomenon of getting a three-dimensional perception of a scene from a flat 2D image of the retina. The main objective of this dissertation is the computational aspect of this human ability to reconstruct the world in 3D using only 2D images from the retina. Specifically, the goal of this work is to recover 3D facial shape information from a single image of unknown pose and illumination. Prior shape and texture models from real data, which are metric in nature, are incorporated into the 3D shape recovery framework. The output recovered shape, likewise, is metric, unlike previous shape-from-shading (SFS) approaches that only provide relative shape. This work starts first with the simpler case of general illumination and fixed frontal pose. Three optimization approaches were developed to solve this 3D shape recovery problem, starting from a brute-force iterative approach to a computationally efficient regression method (Method II-PCR), where the classical shape-from-shading equation is cast as a regression framework. Results show that the output of the regression-like approach is faster in timing and similar in error metrics when compared to its iterative counterpart. The best of the three algorithms above, Method II-PCR, is compared to its two predecessors, namely: (a) Castelan et al. [1] and (b) Ahmed et al. [2]. Experimental results show that the proposed method (Method II-PCR) is superior in all aspects compared to the previous state-of-the-art. Robust statistics was also incorporated into the shape recovery framework to deal with noise and occlusion. Using multiple-view geometry concepts [3], the fixed frontal pose was relaxed to arbitrary pose. The best of the three algorithms above, Method II-PCR, once again is used as the primary 3D shape recovery method. Results show that the pose-invariant 3D shape recovery version (for input with pose) has similar error values compared to the frontal-pose version (for input with frontal pose), for input images of the same subject. Sensitivity experiments indicate that the proposed method is, indeed, invariant to pose, at least for the pan angle range of (-50° to 50°). The next major part of this work is the development of 3D facial shape recovery methods, given only the input 2D shape information, instead of both texture and 2D shape. The simpler case of output 3D sparse shapes was dealt with, initially. The proposed method, which also use a regression-based optimization approach, was compared with state-of-the art algorithms, showing decent performance. There were five conclusions that drawn from the sparse experiments, namely, the proposed approach: (a) is competitive due to its linear and non-iterative nature, (b) does not need explicit training, as opposed to [4], (c) has comparable results to [4], at a shorter computational time, (d) better in all aspects than Zhang and Samaras [5], and (e) has the limitation, together with [4] and [5], in terms of the need to manually annotate the input 2D feature points. The proposed method was then extended to output 3D dense shapes simply by replacing the sparse model with its dense equivalent, in the regression framework inside the 3D face recovery approach. The numerical values of the mean height and surface orientation error indicate that even if shading information is unavailable, a decent 3D dense reconstruction is still possible

Extracting Depth Information From Photographs of Faces

Recently new methods of recovering the 3D appearance of objects, like stereo- imaging sensors, laser scanners, and range-imaging sensors provide automatic tools for obtaining the 3D appearance of an object but they require the presence of the object. When only photographic images are available, it is still possible to reconstruct the 3D appearance of the object if there is also a model which can be referenced. The human face is very popular with researchers who try to solve the problems including facial recognition, animation, composition, or modelling. However it is rare to find attempts to reconstruct shape from single photographic images of human faces, although there are numerous methods to solve the shape-from-shading (SFS) problem to date. This thesis describes a novel geometrical approach to reconstructing the original face from a very impoverished facial model1 and a single Lambertian image. This thesis also introduces a different approach to the SFS problem in the sense that it uses prior knowledge of the object, the so-called shape-from-prior-knowledge approach, and addresses the question of what degree of impoverishment is sufficient to compromise the reconstruction. Most recovered surfaces using conventional SFS methods suffer from flattening so that we cannot view them in other directions. We believe that this flatness is due to the lack of geometric knowledge of the subject to be recovered. In this thesis, it is also argued that our approach improves upon existing SFS techniques, because a reconstructed face looks correct even when it is turned to a different orientation from the one in the input image

Single View Modeling and View Synthesis

This thesis develops new algorithms to produce 3D content from a single camera. Today, amateurs can use hand-held camcorders to capture and display the 3D world in 2D, using mature technologies. However, there is always a strong desire to record and re-explore the 3D world in 3D. To achieve this goal, current approaches usually make use of a camera array, which suffers from tedious setup and calibration processes, as well as lack of portability, limiting its application to lab experiments. In this thesis, I try to produce the 3D contents using a single camera, making it as simple as shooting pictures. It requires a new front end capturing device rather than a regular camcorder, as well as more sophisticated algorithms. First, in order to capture the highly detailed object surfaces, I designed and developed a depth camera based on a novel technique called light fall-off stereo (LFS). The LFS depth camera outputs color+depth image sequences and achieves 30 fps, which is necessary for capturing dynamic scenes. Based on the output color+depth images, I developed a new approach that builds 3D models of dynamic and deformable objects. While the camera can only capture part of a whole object at any instance, partial surfaces are assembled together to form a complete 3D model by a novel warping algorithm. Inspired by the success of single view 3D modeling, I extended my exploration into 2D-3D video conversion that does not utilize a depth camera. I developed a semi-automatic system that converts monocular videos into stereoscopic videos, via view synthesis. It combines motion analysis with user interaction, aiming to transfer as much depth inferring work from the user to the computer. I developed two new methods that analyze the optical flow in order to provide additional qualitative depth constraints. The automatically extracted depth information is presented in the user interface to assist with user labeling work. In this thesis, I developed new algorithms to produce 3D contents from a single camera. Depending on the input data, my algorithm can build high fidelity 3D models for dynamic and deformable objects if depth maps are provided. Otherwise, it can turn the video clips into stereoscopic video

3D face structure extraction from images at arbitrary poses and under arbitrary illumination conditions

With the advent of 9/11, face detection and recognition is becoming an important tool to be used for securing homeland safety against potential terrorist attacks by tracking and identifying suspects who might be trying to indulge in such activities. It is also a technology that has proven its usefulness for law enforcement agencies by helping identifying or narrowing down a possible suspect from surveillance tape on the crime scene, or quickly by finding a suspect based on description from witnesses.In this thesis we introduce several improvements to morphable model based algorithms and make use of the 3D face structures extracted from multiple images to conduct illumination analysis and face recognition experiments. We present an enhanced Active Appearance Model (AAM), which possesses several sub-models that are independently updated to introduce more model flexibility to achieve better feature localization. Most appearance based models suffer from the unpredictability of facial background, which might result in a bad boundary extraction. To overcome this problem we propose a local projection models that accurately locates face boundary landmarks. We also introduce a novel and unbiased cost function that casts the face alignment as an optimization problem, where shape constraints obtained from direct motion estimation are incorporated to achieve a much higher convergence rate and more accurate alignment. Viewing angles are roughly categorized to four different poses, and the customized view-based AAMs align face images in different specific pose categories. We also attempt at obtaining individual 3D face structures by morphing a 3D generic face model to fit the individual faces. Face contour is dynamically generated so that the morphed face looks realistic. To overcome the correspondence problem between facial feature points on the generic and the individual face, we use an approach based on distance maps. With the extracted 3D face structure we study the illumination effects on the appearance based on the spherical harmonic illumination analysis. By normalizing the illumination conditions on different facial images, we extract a global illumination-invariant texture map, which jointly with the extracted 3D face structure in the form of cubic morphing parameters completely encode an individual face, and allow for the generation of images at arbitrary pose and under arbitrary illumination.Face recognition is conducted based on the face shape matching error, texture error and illumination-normalized texture error. Experiments show that a higher face recognition rate is achieved by compensating for illumination effects. Furthermore, it is observed that the fusion of shape and texture information result in a better performance than using either shape or texture information individually.Ph.D., Electrical Engineering -- Drexel University, 200

Electromagnetic analysis of bidirectional reflectance from roughened surfaces and applications to surface shape recovery

Scattering from randomly rough surfaces is a well-established sub area of electrodynamics. There remains much to be done since each surface and optical processes that may occur in within the scattering medium, and countless other scenarios, is different. There are also illumination models that describe lighting in a scene on the macroscopic scale where geometrical optics can be considered adequate. Of particular interest for us is the intersection of the physical scattering theories and the illumination models. We present two contributions: 1) A minimum of two independent images are needed since any opaque surface can be uniquely specified in terms of its outward-normal vector field. This required the development of a global, nonlinear, alternating optimization scheme to compute parameter estimates. It is shown that high accuracy estimates can be obtained. 2)The smooth emergence of geometrical optics from physical optics using a full wave electromagnetic solution of the 1D scattering problem. It is shown here that the geometrical optics limit is arrived at in a smooth transition from physical optics starting with the electric field integral equation by varying the size of roughness structures on the surface and calculating the scattering cross length . Starting from roughness features smaller than the incident wavelength and also considering the size of the surface fluctuations relative to the size of the surface, the scattered light patterns show expected wave behavior that gradually transitions to geometrical ray optics as the size of surface roughness features increases well beyond the wavelength

Face Recognition Under Varying Illumination

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2006Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2006Bu çalışmada, aydınlanma değişimlerine karşı gürbüz ve yenilikçi bir yüz tanıma sistemi oluşturulması amaçlanmıştır. Eğitim aşamasında her kişi için tek bir yüz görüntüsünün olduğu varsayılmıştır. Aydınlanma değişimlerine karşı Doğrusal Ayrışım Analizi’nin (DAA) Temel Bileşenli Analizi’ne (TBA) karşı daha başarılı olduğu bilindiğinden, sistemin verimliliğini arttırmak üzere DAA kullanmasına karar verilmiştir. Sınıfsal ayrışım yaklaşımlarda görünen “Az Örnek Sayısı” sorununu çözmek üzere “Oran Görüntü” adı verilen başarılı bir yöntem, görüntü sentezlemek için uygulanmıştır. Bu yöntem kullanılarak her giriş görüntüsü için bir görüntü uzayı oluşturulmuştur. Kullanılan yöntem ayrıca, herhangi bir ışıklandırma koşulunda alınmış görüntüyü, önden ışıklandırılmış hale geri çatabilmeye izin vermektedir. YaleB veritabanı üzerinde yapılan deneysel sonuçlar, var olan yöntemlerle karşılaştırıldığında, bu yaklaşımın daha başarılı sonuçlar elde ettiğini göstermektedir.This paper proposes a novel approach for creating a Face Recognition System robust to illumination variation. Is considered the case when only one image per person is available during the training phase. Knowing the superiority of Linear Discriminant Analysis (LDA) over Principal Component Analysis (PCA) in regard to variable illumination, it was decided to use this fact to improve the performance of this system. To solve the Small Sample Size (SSS) problem related with class-based discriminant approaches it was applied an image synthesis method based on a successful technique known as the Quotient Image to create the image space of any input image. Furthermore an iterative algorithm is used for the restoration of frontal illumination of a face illuminated by an arbitrary angle. Experimental results on the YaleB database show that this approach can achieve a top recognition rate compared with existing methods.Yüksek LisansM.Sc

Realistic visualisation of cultural heritage objects

This research investigation used digital photography in a hemispherical dome, enabling a set of 64 photographic images of an object to be captured in perfect pixel register, with each image illuminated from a different direction. This representation turns out to be much richer than a single 2D image, because it contains information at each point about both the 3D shape of the surface (gradient and local curvature) and the directionality of reflectance (gloss and specularity). Thereby it enables not only interactive visualisation through viewer software, giving the illusion of 3D, but also the reconstruction of an actual 3D surface and highly realistic rendering of a wide range of materials. The following seven outcomes of the research are claimed as novel and therefore as representing contributions to knowledge in the field: A method for determining the geometry of an illumination dome; An adaptive method for finding surface normals by bounded regression; Generating 3D surfaces from photometric stereo; Relationship between surface normals and specular angles; Modelling surface specularity by a modified Lorentzian function; Determining the optimal wavelengths of colour laser scanners; Characterising colour devices by synthetic reflectance spectra

Photometric Reconstruction from Images: New Scenarios and Approaches for Uncontrolled Input Data

The changes in surface shading caused by varying illumination constitute an important cue to discern fine details and recognize the shape of textureless objects. Humans perform this task subconsciously, but it is challenging for a computer because several variables are unknown and intermix in the light distribution that actually reaches the eye or camera. In this work, we study algorithms and techniques to automatically recover the surface orientation and reflectance properties from multiple images of a scene. Photometric reconstruction techniques have been investigated for decades but are still restricted to industrial applications and research laboratories. Making these techniques work on more general, uncontrolled input without specialized capture setups has to be the next step but is not yet solved. We explore the current limits of photometric shape recovery in terms of input data and propose ways to overcome some of its restrictions. Many approaches, especially for non-Lambertian surfaces, rely on the illumination and the radiometric response function of the camera to be known. The accuracy such algorithms are able to achieve depends a lot on the quality of an a priori calibration of these parameters. We propose two techniques to estimate the position of a point light source, experimentally compare their performance with the commonly employed method, and draw conclusions which one to use in practice. We also discuss how well an absolute radiometric calibration can be performed on uncontrolled consumer images and show the application of a simple radiometric model to re-create night-time impressions from color images. A focus of this thesis is on Internet images which are an increasingly important source of data for computer vision and graphics applications. Concerning reconstructions in this setting we present novel approaches that are able to recover surface orientation from Internet webcam images. We explore two different strategies to overcome the challenges posed by this kind of input data. One technique exploits orientation consistency and matches appearance profiles on the target with a partial reconstruction of the scene. This avoids an explicit light calibration and works for any reflectance that is observed on the partial reference geometry. The other technique employs an outdoor lighting model and reflectance properties represented as parametric basis materials. It yields a richer scene representation consisting of shape and reflectance. This is very useful for the simulation of new impressions or editing operations, e.g. relighting. The proposed approach is the first that achieves such a reconstruction on webcam data. Both presentations are accompanied by evaluations on synthetic and real-world data showing qualitative and quantitative results. We also present a reconstruction approach for more controlled data in terms of the target scene. It relies on a reference object to relax a constraint common to many photometric stereo approaches: the fixed camera assumption. The proposed technique allows the camera and light source to vary freely in each image. It again avoids a light calibration step and can be applied to non-Lambertian surfaces. In summary, this thesis contributes to the calibration and to the reconstruction aspects of photometric techniques. We overcome challenges in both controlled and uncontrolled settings, with a focus on the latter. All proposed approaches are shown to operate also on non-Lambertian objects