Placing a micro lens array in front of an image sensor transforms a normal camera into a single lens 3D camera, which also allows the user to change the focus and the point of view after a picture has been taken. While the concept of such plenoptic cameras is known since 1908, only recently the increased computing power of low-cost hardware and the advances in micro lens array production, have made the application of plenoptic cameras feasible. This text presents a detailed analysis of plenoptic cameras as well as introducing a new type of plenoptic camera with an extended depth of field and a maximal effective resolution of up to a quarter of the sensor resolution.

Abstract. Plenoptic cameras provide a robust way to capture 3D information with a single shot. This is accomplished by encoding the direction of the incoming rays with a microlens array (MLA) in front of the camera sensor. In the focused plenoptic camera, a MLA acts like multiple small cameras that capture the virtual scene on the focus plane of a main lens from slightly different angles, which enables algorithmic depth reconstruction. This virtual depth is measured on the camera side, and independent of the main lens used. The connection between actual lateral distances and virtual depth, however, does depend on the main lens parameters, and needs to be carefully calibrated. In this paper, we propose an approach to calibrate focused plenoptic cameras, which allows a metric analysis of a given scene. To achieve this, we minimize an energy model based upon the thin lens equation. The model allows to estimate intrinsic and extrinsic parameters and corrects for radial lateral as well as radial depth distortion.

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In this article we discuss the 2D-3D pose estimation problem of 3D free-form contours. In our scenario we observe objects of any 3D shape in an image of a calibrated camera. Pose estimation means to estimate the relative position and orientation (containing a rotation R and translation T ) of the 3D object to the reference camera system. The fusion of modeling free-form contours within the pose estimation problem is achieved by using the conformal geometric algebra. The conformal geometric algebra is a geometric algebra which models entities as stereographically projected entities in a homogeneous model. This leads to a linear description of kinematics on the one hand and projective geometry on the other hand. To model free-form contours in the conformal framework we use twists to model cycloidal curves as twist-depending functions and interpret n-times nested twist generated curves as functions generated by 3D Fourier descriptors. This means, we use the twist concept to apply a spectral domain representation of 3D contours within the pose estimation problem. We will show that twist representations of objects can be numerically efficient and easily be applied to the pose estimation problem. The pose problem itself is formalized as implicit problem and we gain constraint equations, which have to be fulfilled with respect to the unknown rigid body motion. Several experiments visualize the robustness and real-time performance of our algorithms.

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