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7) should be substituted with a spherical angle symbol : For example, the top left pixel gets a coordinate of HT ht for a pinhole camera model with a field of view of HT ht and HT ht horizontally and vertically, respectively. 8) should be substituted with HT ht : We use an absolute positional encoding, i.e. HT ht Graph where the positional encoding HT ht and the subimage feature vector HT ht are superimposed. [Extracted from the article]

We present a new and efficient solution for the forward world to image projection of a pinhole camera with distortions placed behind a planar refractive slab. Firstly, we introduce a novel way to compute the projection by reducing the problem to finding a real quantity called a slab shift. We characterize a physically meaningful slab shift as the unique solution of a fixed point equation on the one hand and as a specific uniquely defined root of a quartic polynomial in the unknown slab shift on the other. In the latter case we obtain a closed-form formula, which provides the unique physically meaningful projection. Secondly, we develop an approximation of the projection through the slab that reaches single-precision floating point accuracy for practically relevant problem instances with considerably lower computational costs compared to the exact solution. We demonstrate the accuracy and the efficiency of our method with realistic synthetic experiments. We demonstrate with real experiments that our method enables efficient camera calibration behind the windshield for automotive industry applications. [ABSTRACT FROM AUTHOR]

Central catadioptric cameras with a single effective viewpoint contain both mirrors and pinhole cameras that increase the imaging field of view. In this study, the common pole–polar properties of central catadioptric sphere or line images are investigated and used for camera calibration. From these properties, the pole and polar with respect to the image of absolute conic and the modified image of absolute conic, respectively, can be recovered according to the generalized eigenvalue decomposition. Moreover, these techniques are valid for paracatadioptric sensors with the degenerate conic dual to the circular points being considered. At least three images of spheres or lines are required to completely calibrate any central catadioptric camera. The intrinsic parameters of the camera, the shape of reflective mirror, and the distortion parameters can be linearly estimated using the algebraic and geometric constraints of the sphere or line images obtained by the central catadioptric camera. The obtained experimental results demonstrate the effectiveness and feasibility of the proposed calibration algorithm. [ABSTRACT FROM AUTHOR]

Multi-view stereo remains a popular choice when recovering 3D geometry, despite performance varying dramatically according to the scene content. Moreover, typical pinhole camera assumptions fail in the presence of shallow depth of field inherent to macro-scale scenes; limiting application to larger scenes with diffuse reflectance. However, the presence of defocus blur can itself be considered a useful reconstruction cue, particularly in the presence of view-dependent materials. With this in mind, we explore the complimentary nature of stereo and defocus cues in the context of multi-view 3D reconstruction; and propose a complete pipeline for scene modelling from a finite aperature camera that encompasses image formation, camera calibration and reconstruction stages. As part of our evaluation, an ablation study reveals how each cue contributes to the higher performance observed over a range of complex materials and geometries. Though of lesser concern with large apertures, the effects of image noise are also considered. By introducing pre-trained deep feature extraction into our cost function, we show a step improvement over per-pixel comparisons; as well as verify the cross-domain applicability of networks using largely in-focus training data applied to defocused images. Finally, we compare to a number of modern multi-view stereo methods, and demonstrate how the use of both cues leads to a significant increase in performance across several synthetic and real datasets. [ABSTRACT FROM AUTHOR]

Wide field-of-view (FOV) cameras, which capture a larger scene area than narrow FOV cameras, are used in many applications including 3D reconstruction, autonomous driving, and video surveillance. However, wide-angle images contain distortions that violate the assumptions underlying pinhole camera models, resulting in object distortion, difficulties in estimating scene distance, area, and direction, and preventing the use of off-the-shelf deep models trained on undistorted images for downstream computer vision tasks. Image rectification, which aims to correct these distortions, can solve these problems. In this paper, we comprehensively survey progress in wide-angle image rectification from transformation models to rectification methods. Specifically, we first present a detailed description and discussion of the camera models used in different approaches. Then, we summarize several distortion models including radial distortion and projection distortion. Next, we review both traditional geometry-based image rectification methods and deep learning-based methods, where the former formulates distortion parameter estimation as an optimization problem and the latter treats it as a regression problem by leveraging the power of deep neural networks. We evaluate the performance of state-of-the-art methods on public datasets and show that although both kinds of methods can achieve good results, these methods only work well for specific camera models and distortion types. We also provide a strong baseline model and carry out an empirical study of different distortion models on synthetic datasets and real-world wide-angle images. Finally, we discuss several potential research directions that are expected to further advance this area in the future. [ABSTRACT FROM AUTHOR]

We present a method for geometric point light source calibration. Unlike prior works that use Lambertian spheres, mirror spheres, or mirror planes, we use a calibration target consisting of a plane and small shadow casters at unknown positions above the plane. We show that shadow observations from a moving calibration target under a fixed light follow the principles of pinhole camera geometry and epipolar geometry, allowing joint recovery of the light position and 3D shadow caster positions, equivalent to how conventional structure from motion jointly recovers camera parameters and 3D feature positions from observed 2D features. Moreover, we devised a unified light model that works with nearby point lights as well as distant light in one common framework. Our evaluation shows that our method yields light estimates that are stable and more accurate than existing techniques while having a much simpler setup and requiring less manual labor. [ABSTRACT FROM AUTHOR]

We present a simple and accurate procedure to calibrate the pinhole parameters of a Time-of-Flight camera: the principal point $$c=(u_0, v_0)$$ , the focal length $$f$$ and, if needed, the aspect ratio $$\tau $$ . Only one image of a flat surface is needed. Using the radial distances as provided by the Time-of-Flight principle, we reconstruct the pixel rows (or pixel columns) as collinear points in 3-space. Motivated by theoretical results, we claim that the correct values for $$u_0$$ , $$v_0$$ and $$f$$ can be found by an incremental procedure. In case of unknown aspect ratio, some (but few) iterations are needed. [ABSTRACT FROM AUTHOR]

We identify and study two types of 'accidental' images that can be formed in scenes. The first is an accidental pinhole camera image. The second class of accidental images are 'inverse' pinhole camera images, formed by subtracting an image with a small occluder present from a reference image without the occluder. Both types of accidental cameras happen in a variety of different situations. For example, an indoor scene illuminated by natural light, a street with a person walking under the shadow of a building, etc. The images produced by accidental cameras are often mistaken for shadows or interreflections. However, accidental images can reveal information about the scene outside the image, the lighting conditions, or the aperture by which light enters the scene. [ABSTRACT FROM AUTHOR]

This article formulates a near-lighting shape-from-shading problem with a pinhole camera (perspective projection) and presents a solution to reconstruct the Lambertian surface of bones using a sequence of overlapped endoscopic images, with partial boundaries in each image. First we extend the shape-from-shading problem to deal with perspective projection and near point light sources that are not co-located with the camera center. Secondly we propose a multi-image framework which can align partial shapes obtained from different images in the world coordinates by tracking the endoscope. An iterative closest point (ICP) algorithm is used to improve the matching and recover complete occluding boundaries of the bone. Finally, a complete and consistent shape is obtained by simultaneously re-growing the surface normals and depths in all views. In order to fulfill our shape-from-shading algorithm, we also calibrate both geometry and photometry for an oblique-viewing endoscope that are not well addressed before in the previous literatures. We demonstrate the accuracy of our technique using simulations and experiments with artificial bones. [ABSTRACT FROM AUTHOR]

Central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint. Lines and spheres in space are all projected into conics in the central catadioptric image planes, and such conics are called line images and sphere images, respectively. We discovered that there exists an imaginary conic in the central catadioptric image planes, defined as the modified image of the absolute conic (MIAC), and by utilizing the MIAC, the novel identical projective geometric properties of line images and sphere images may be exploited: Each line image or each sphere image is double-contact with the MIAC, which is an analogy of the discovery in pinhole camera that the image of the absolute conic (IAC) is double-contact with sphere images. Note that the IAC also exists in the central catadioptric image plane, but it does not have the double-contact properties with line images or sphere images. This is the main reason to propose the MIAC. From these geometric properties with the MIAC, two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework. Note that there are many linear approaches to central catadioptric camera calibration using line images. It seems that to use the properties that line images are tangent to the MIAC only leads to an alternative geometric construction for calibration. However, for sphere images, there are only some nonlinear calibration methods in literature. Therefore, to propose linear methods for sphere images may be the main contribution of this paper. Our new algorithms have been tested in extensive experiments with respect to noise sensitivity. [ABSTRACT FROM AUTHOR]

Rother and Carlsson introduced the Direct Reference Plane method for obtaining a projective reconstruction from a multi-view system, presuming the availability of a planar reference quadrangle in each view. In this method feature points and camera centres are obtained simultaneously by solving a system of homogeneous linear equations. Each feature-camera visibility pair corresponds to two equations in this system. In this paper we derive a count criterion for characterizing sufficient visibility, yielding a system of linearly independent equations that “determines” feature points and camera centres. Finally we discuss some principles to extend the configuration of feature points and camera centres while maintaining sufficient visibility. [ABSTRACT FROM AUTHOR]

We describe a mathematical and algorithmic study of the Lambertian “Shape-From-Shading” problem for orthographic and pinhole cameras. Our approach is based upon the notion of viscosity solutions of Hamilton-Jacobi equations. This approach provides a mathematical framework in which we can show that the problem is well-posed (we prove the existence of a solution and we characterize all the solutions). Our contribution is threefold. First, we model the camera both as orthographic and as perspective (pinhole), whereas most authors assume an orthographic projection (see Horn and Brooks (1989) for a survey of the SFS problem up to 1989 and Zhang et al. (1999), Kozera (1998), Durou et al. (2004) for more recent ones); thus we extend the applicability of shape from shading methods to more realistic acquisition models. In particular it extends the work of Prados et al. (2002a) and Rouy and Tourin (1992). We provide some novel mathematical formulations of this problem yielding new partial differential equations. Results about the existence and uniqueness of their solutions are also obtained. Second, by introducing a “generic” Hamiltonian, we define a general framework allowing to deal with both models (orthographic and perspective), thereby simplifying the formalization of the problem. Thanks to this unification, each algorithm we propose can compute numerical solutions corresponding to all the modeling. Third, our work allows us to come up with two new generic algorithms for computing numerical approximations of the “continuous solution of the “Shape-From-Shading” problem as well as a proof of their convergence toward that solution. Moreover, our two generic algorithms are able to deal with discontinuous images as well as images containing black shadows. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports published within the issue which include accidental pinhole and pinspeck cameras, acquisition of high spatial and spectral resolution, and fast spectral reflectance recovery.