In this paper, we introduce a novel method for depth acquisition based on refraction of light. A scene is captured directly by a camera and by placing a transparent medium between the scene and the camera. A depth map of the scene is then recovered from the displacements of scene points in the images. Unlike other existing depth from refraction methods, our method does not require prior knowledge of the pose and refractive index of the transparent medium, but instead can recover them directly from the input images. By analyzing the displacements of corresponding scene points in the images, we derive closed form solutions for recovering the pose of the transparent medium and develop an iterative method for estimating the refractive index of the medium. Experimental results on both synthetic and real-world data are presented, which demonstrate the effectiveness of the proposed method.

In this paper, we introduce a novel method for depth acquisition based on refraction of light. A scene is captured twice by a fixed perspective camera, with the first image captured directly by the camera and the second by placing a transparent medium between the scene and the camera. A depth map of the scene is then recovered from the displacements of scene points in the images. Unlike other existing depth from refraction methods, our method does not require the knowledge of the pose and refractive index of the transparent medium, but can recover them directly from the input images. We hence call our method self-calibrating depth from refraction. Experimental results on both synthetic and real-world data are presented, which demonstrate the effectiveness of the proposed method.

This paper addresses the problem of estimating the poses of a reference plane in specular shape recovery. Unlike existing methods which require an extra mirror or an extra reference plane and camera, our proposed method recovers the poses of the reference plane directly from its reflections on the specular surface. By establishing reflection correspondences on the reference plane in three distinct poses, our method estimates the poses of the reference plane in two steps. First, by applying a colinearity constraint to the reflection correspondences, a simple closed-form solution is derived for recovering the poses of the reference plane relative to its initial pose. Second, by applying a ray incidence constraint to the incident rays formed by the reflection correspondences and the visual rays cast from the image, a closed-form solution is derived for recovering the poses of the reference plane relative to the camera. The shape of the specular surface then follows. Experimental results on both synthetic and real data are presented, which demonstrate the feasibility and accuracy of our proposed method.

This paper introduces a novel method for 3D reconstruction from spherical mirrors in a single view. Traditional reconstruction algorithms either assume both intrinsic and extrinsic parameters of the cameras being known precisely and rely on multiple view information to recover 3D objects, or use reflections of the 3D objects on spherical mirrors with known radii in a single calibrated view. It will be shown in this paper that 3D objects can be recovered up to a scale using an unknown spherical mirror in a single view. Experimental results on both synthetic and real data show the practicality of the proposed reconstruction method.

This paper proposes a stratified approach for camera calibration using spheres. Previous works have exploited epipolar tangents to locate frontier points on spheres for estimating the epipolar geometry. It is shown in this paper that other than the frontier points, two additional point features can be obtained by considering the bitangent envelopes of a pair of spheres. A simple method for locating the images of such point features and the sphere centers is presented. An algorithm for recovering the fundamental matrix in a plane plus parallax representation using these recovered image points and the epipolar tangents from three spheres is developed. A new formulation of the absolute dual quadric as a cone tangent to a dual sphere with the plane at infinity being its vertex is derived. This allows the recovery of the absolute dual quadric, which is used to upgrade the weak calibration to a full calibration. Experimental results on both synthetic and real data are presented, which demonstrate the feasibility and the high precision achieved by our proposed algorithm.