Computational Imaging for Shape Understanding

Geometry is the essential property of real-world scenes. Understanding the shape of the object is critical to many computer vision applications. In this dissertation, we explore using computational imaging approaches to recover the geometry of real-world scenes. Computational imaging is an emerging technique that uses the co-designs of image hardware and computational software to expand the capacity of traditional cameras. To tackle face recognition in the uncontrolled environment, we study 2D color image and 3D shape to deal with body movement and self-occlusion. Especially, we use multiple RGB-D cameras to fuse the varying pose and register the front face in a unified coordinate system. The deep color feature and geodesic distance feature have been used to complete face recognition. To handle the underwater image application, we study the angular-spatial encoding and polarization state encoding of light rays using computational imaging devices. Specifically, we use the light field camera to tackle the challenging problem of underwater 3D reconstruction. We leverage the angular sampling of the light field for robust depth estimation. We also develop a fast ray marching algorithm to improve the efficiency of the algorithm. To deal with arbitrary reflectance, we investigate polarimetric imaging and develop polarimetric Helmholtz stereopsis that uses reciprocal polarimetric image pairs for high-fidelity 3D surface reconstruction. We formulate new reciprocity and diffuse/specular polarimetric constraints to recover surface depths and normals using an optimization framework. To recover the 3D shape in the unknown and uncontrolled natural illumination, we use two circularly polarized spotlights to boost the polarization cues corrupted by the environment lighting, as well as to provide photometric cues. To mitigate the effect of uncontrolled environment light in photometric constraints, we estimate a lighting proxy map and iteratively refine the normal and lighting estimation. Through expensive experiments on the simulated and real images, we demonstrate that our proposed computational imaging methods outperform traditional imaging approaches

Colour Helmholtz Stereopsis for Reconstruction of Complex Dynamic Scenes

Helmholtz Stereopsis (HS) is a powerful technique for reconstruction of scenes with arbitrary reflectance properties. However, previous formulations have been limited to static objects due to the requirement to sequentially capture reciprocal image pairs (i.e. two images with the camera and light source positions mutually interchanged). In this paper, we propose colour HS-a novel variant of the technique based on wavelength multiplexing. To address the new set of challenges introduced by multispectral data acquisition, the proposed novel pipeline for colour HS uniquely combines a tailored photometric calibration for multiple camera/light source pairs, a novel procedure for surface chromaticity calibration and the state-of-the-art Bayesian HS suitable for reconstruction from a minimal number of reciprocal pairs. Experimental results including quantitative and qualitative evaluation demonstrate that the method is suitable for flexible (single-shot) reconstruction of static scenes and reconstruction of dynamic scenes with complex surface reflectance properties

A Bayesian Framework for Enhanced Geometric Reconstruction of Complex Objects by Helmholtz Stereopsis

Helmholtz stereopsis is an advanced 3D reconstruction technique for objects with arbitrary reflectance properties that uniquely characterises surface points by both depth and normal. Traditionally, in Helmholtz stereopsis consistency of depth and normal estimates is assumed rather than explicitly enforced. Furthermore, conventional Helmholtz stereopsis performs maximum likelihood depth estimation without neighbourhood consideration. In this paper, we demonstrate that reconstruction accuracy of Helmholtz stereopsis can be greatly enhanced by formulating depth estimation as a Bayesian maximum a posteriori probability problem. In reformulating the problem we introduce neighbourhood support by formulating and comparing three priors: a depth-based, a normal-based and a novel depth-normal consistency enforcing one. Relative performance evaluation of the three priors against standard maximum likelihood Helmholtz stereopsis is performed on both real and synthetic data to facilitate both qualitative and quantitative assessment of reconstruction accuracy. Observed superior performance of our depth-normal consistency prior indicates a previously unexplored advantage in joint optimisation of depth and normal estimates

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

Material Recognition Meets 3D Reconstruction : Novel Tools for Efficient, Automatic Acquisition Systems

For decades, the accurate acquisition of geometry and reflectance properties has represented one of the major objectives in computer vision and computer graphics with many applications in industry, entertainment and cultural heritage. Reproducing even the finest details of surface geometry and surface reflectance has become a ubiquitous prerequisite in visual prototyping, advertisement or digital preservation of objects. However, today's acquisition methods are typically designed for only a rather small range of material types. Furthermore, there is still a lack of accurate reconstruction methods for objects with a more complex surface reflectance behavior beyond diffuse reflectance. In addition to accurate acquisition techniques, the demand for creating large quantities of digital contents also pushes the focus towards fully automatic and highly efficient solutions that allow for masses of objects to be acquired as fast as possible. This thesis is dedicated to the investigation of basic components that allow an efficient, automatic acquisition process. We argue that such an efficient, automatic acquisition can be realized when material recognition "meets" 3D reconstruction and we will demonstrate that reliably recognizing the materials of the considered object allows a more efficient geometry acquisition. Therefore, the main objectives of this thesis are given by the development of novel, robust geometry acquisition techniques for surface materials beyond diffuse surface reflectance, and the development of novel, robust techniques for material recognition. In the context of 3D geometry acquisition, we introduce an improvement of structured light systems, which are capable of robustly acquiring objects ranging from diffuse surface reflectance to even specular surface reflectance with a sufficient diffuse component. We demonstrate that the resolution of the reconstruction can be increased significantly for multi-camera, multi-projector structured light systems by using overlappings of patterns that have been projected under different projector poses. As the reconstructions obtained by applying such triangulation-based techniques still contain high-frequency noise due to inaccurately localized correspondences established for images acquired under different viewpoints, we furthermore introduce a novel geometry acquisition technique that complements the structured light system with additional photometric normals and results in significantly more accurate reconstructions. In addition, we also present a novel method to acquire the 3D shape of mirroring objects with complex surface geometry. The aforementioned investigations on 3D reconstruction are accompanied by the development of novel tools for reliable material recognition which can be used in an initial step to recognize the present surface materials and, hence, to efficiently select the subsequently applied appropriate acquisition techniques based on these classified materials. In the scope of this thesis, we therefore focus on material recognition for scenarios with controlled illumination as given in lab environments as well as scenarios with natural illumination that are given in photographs of typical daily life scenes. Finally, based on the techniques developed in this thesis, we provide novel concepts towards efficient, automatic acquisition systems

Contributions to image-based object reconstruction : geometric and photometric aspects

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

NOVEL DENSE STEREO ALGORITHMS FOR HIGH-QUALITY DEPTH ESTIMATION FROM IMAGES

This dissertation addresses the problem of inferring scene depth information from a collection of calibrated images taken from different viewpoints via stereo matching. Although it has been heavily investigated for decades, depth from stereo remains a long-standing challenge and popular research topic for several reasons. First of all, in order to be of practical use for many real-time applications such as autonomous driving, accurate depth estimation in real-time is of great importance and one of the core challenges in stereo. Second, for applications such as 3D reconstruction and view synthesis, high-quality depth estimation is crucial to achieve photo realistic results. However, due to the matching ambiguities, accurate dense depth estimates are difficult to achieve. Last but not least, most stereo algorithms rely on identification of corresponding points among images and only work effectively when scenes are Lambertian. For non-Lambertian surfaces, the brightness constancy assumption is no longer valid. This dissertation contributes three novel stereo algorithms that are motivated by the specific requirements and limitations imposed by different applications. In addressing high speed depth estimation from images, we present a stereo algorithm that achieves high quality results while maintaining real-time performance. We introduce an adaptive aggregation step in a dynamic-programming framework. Matching costs are aggregated in the vertical direction using a computationally expensive weighting scheme based on color and distance proximity. We utilize the vector processing capability and parallelism in commodity graphics hardware to speed up this process over two orders of magnitude. In addressing high accuracy depth estimation, we present a stereo model that makes use of constraints from points with known depths - the Ground Control Points (GCPs) as referred to in stereo literature. Our formulation explicitly models the influences of GCPs in a Markov Random Field. A novel regularization prior is naturally integrated into a global inference framework in a principled way using the Bayes rule. Our probabilistic framework allows GCPs to be obtained from various modalities and provides a natural way to integrate information from various sensors. In addressing non-Lambertian reflectance, we introduce a new invariant for stereo correspondence which allows completely arbitrary scene reflectance (bidirectional reflectance distribution functions - BRDFs). This invariant can be used to formulate a rank constraint on stereo matching when the scene is observed by several lighting configurations in which only the lighting intensity varies

High-order regularized regression in Electrical Impedance Tomography

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, that maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit unction which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy, hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem

Reconstruction of the interface between two layered media using far field measurements

International audienceWe consider an inverse transmission scattering problem. This problem consists in determining an interface between two-layered media by far-field measurements. We prove that the interface is uniquely determined by the measurements of the far field pattern associated to incoming plane waves at a fixed frequency. For the reconstruction of the interface we solve a non linear integral equation using a truncated Newton-CG algorithm