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 For non-Lambertian surfaces, the brightness constancy assumption is no longer valid.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

Epälambertilaiset pinnat ja niiden haasteet konenäössä

This thesis regards non-Lambertian surfaces and their challenges, solutions and study in computer vision. The physical theory for understanding the phenomenon is built first, using the Lambertian reflectance model, which defines Lambertian surfaces as ideally diffuse surfaces, whose luminance is isotropic and the luminous intensity obeys Lambert's cosine law. From these two assumptions, non-Lambertian surfaces violate at least the cosine law and are consequently specularly reflecting surfaces, whose perceived brightness is dependent from the viewpoint. Thus non-Lambertian surfaces violate also brightness and colour constancies, which assume that the brightness and colour of same real-world points stays constant across images. These assumptions are used, for example, in tracking and feature matching and thus non-Lambertian surfaces pose complications for object reconstruction and navigation among other tasks in the field of computer vision. After formulating the theoretical foundation of necessary physics and a more general reflectance model called the bi-directional reflectance distribution function, a comprehensive literature review into significant studies regarding non-Lambertian surfaces is conducted. The primary topics of the survey include photometric stereo and navigation systems, while considering other potential fields, such as fusion methods and illumination invariance. The goal of the survey is to formulate a detailed and in-depth answer to what methods can be used to solve the challenges posed by non-Lambertian surfaces, what are these methods' strengths and weaknesses, what are the used datasets and what remains to be answered by further research. After the survey, a dataset is collected and presented, and an outline of another dataset to be published in an upcoming paper is presented. Then a general discussion about the survey and the study is undertaken and conclusions along with proposed future steps are introduced

A single-lobe photometric stereo approach for heterogeneous material

Shape from shading with multiple light sources is an active research area, and a diverse range of approaches have been proposed in recent decades. However, devising a robust reconstruction technique still remains a challenging goal, as the image acquisition process is highly nonlinear. Recent Photometric Stereo variants rely on simplifying assumptions in order to make the problem solvable: light propagation is still commonly assumed to be uniform, and the Bidirectional Reflectance Distribution Function is assumed to be diffuse, with limited interest for specular materials. In this work, we introduce a well-posed formulation based on partial differential equations (PDEs) for a unified reflectance function that can model both diffuse and specular reflections. We base our derivation on ratio of images, which makes the model independent from photometric invariants and yields a well-posed differential problem based on a system of quasi-linear PDEs with discontinuous coefficients. In addition, we directly solve a differential problem for the unknown depth, thus avoiding the intermediate step of approximating the normal field. A variational approach is presented ensuring robustness to noise and outliers (such as black shadows), and this is confirmed with a wide range of experiments on both synthetic and real data, where we compare favorably to the state of the art.Roberto Mecca is a Marie Curie fellow of the “Istituto Nazionale di Alta Matematica” (Italy) for a project shared with University of Cambridge, Department of Engineering and the Department of Mathematics, University of Bologna

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

Light Fields Reconstructing Geometry and Reflectance Properties

Computer vision plays an important role in the progress of automation and digitalization of our society. One of the key challenges is the creation of accurate 3D representations of our environment. The rich information in light fields can enable highly accurate depth estimates, but requires the development of new algorithms. Especially specular reflections pose a challenge for many reconstruction algorithms. This is due to the violation of the brightness consistency assumption, which only holds for Lambertian surfaces. Most surfaces are to some extent specular and an appropriate handling is central to avoid erroneous depth maps. In this thesis we explore the potential of using specular highlights to determine the orientation of surfaces. To this end, we examine epipolar images in light field set ups. In light field data, reflectance properties can be characterized by intensity variations in the epipolar plane space. This space is analysed and compared to the expected reflectance, which is modelled using the render equation with different bidirectional reflection distribution functions. This approach allows us to infer highly accurate surface normals and depth estimates. Furthermore, it reveals material properties encoded in the reflectance by inspecting the intensity profile. Our results demonstrate the potential to increase the accuracy of the depth maps. Multiple cameras in a light field set up let us retrieve additional material properties encoded in the reflectance