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.

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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.

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