Catadioptric stereo-vision system using a spherical mirror

Abstract In the computer vision field, the reconstruction of target surfaces is usually achieved by using 3D optical scanners assembled integrating digital cameras and light emitters. However, these solutions are limited by the low field of view, which requires multiple acquisition from different views to reconstruct complex free-form geometries. The combination of mirrors and lenses (catadioptric systems) can be adopted to overcome this issue. In this work, a stereo catadioptric optical scanner has been developed by assembling two digital cameras, a spherical mirror and a multimedia white light projector. The adopted configuration defines a non-single viewpoint system, thus a non-central catadioptric camera model has been developed. An analytical solution to compute the projection of a scene point onto the image plane (forward projection) and vice-versa (backward projection) is presented. The proposed optical setup allows omnidirectional stereo vision thus allowing the reconstruction of target surfaces with a single acquisition. Preliminary results, obtained measuring a hollow specimen, demonstrated the effectiveness of the described approach

Vision-Based Navigation III: Pose and Motion from Omnidirectional Optical Flow and a Digital Terrain Map

An algorithm for pose and motion estimation using corresponding features in omnidirectional images and a digital terrain map is proposed. In previous paper, such algorithm for regular camera was considered. Using a Digital Terrain (or Digital Elevation) Map (DTM/DEM) as a global reference enables recovering the absolute position and orientation of the camera. In order to do this, the DTM is used to formulate a constraint between corresponding features in two consecutive frames. In this paper, these constraints are extended to handle non-central projection, as is the case with many omnidirectional systems. The utilization of omnidirectional data is shown to improve the robustness and accuracy of the navigation algorithm. The feasibility of this algorithm is established through lab experimentation with two kinds of omnidirectional acquisition systems. The first one is polydioptric cameras while the second is catadioptric camera.Comment: 6 pages, 9 figure

Single View 3D Reconstruction under an Uncalibrated Camera and an Unknown Mirror Sphere

In this paper, we develop a novel self-calibration method for single view 3D reconstruction using a mirror sphere. Unlike other mirror sphere based reconstruction methods, our method needs neither the intrinsic parameters of the camera, nor the position and radius of the sphere be known. Based on eigen decomposition of the matrix representing the conic image of the sphere and enforcing a repeated eignvalue constraint, we derive an analytical solution for recovering the focal length of the camera given its principal point. We then introduce a robust algorithm for estimating both the principal point and the focal length of the camera by minimizing the differences between focal lengths estimated from multiple images of the sphere. We also present a novel approach for estimating both the principal point and focal length of the camera in the case of just one single image of the sphere. With the estimated camera intrinsic parameters, the position(s) of the sphere can be readily retrieved from the eigen decomposition(s) and a scaled 3D reconstruction follows. Experimental results on both synthetic and real data are presented, which demonstrate the feasibility and accuracy of our approach. © 2016 IEEE.postprin

A Theory of Catadioptric Image Formation

Conventional video cameras have limited fields of view which make them restrictive for certain applications in computational vision. A catadioptric sensor uses a combination of lenses and mirrors placed in a carefully arranged configuration to capture a much wider field of view. When designing a catadioptric sensor, the shape of the mirror(s) should ideally be selected to ensure that the complete catadioptric system has a single effective viewpoint. The reason a single viewpoint is so desirable is that it is a requirement for the generation of pure perspective images from the sensed image(s). In this paper, we derive and analyze the complete class of single-lens single-mirror catadioptric sensors which satisfy the fixed viewpoint constraint. Some of the solutions turn out to be degenerate with no practical value, while other solutions lead to realizable sensors. We also derive an expression for the spatial resolution of a catadioptric sensor, and include a preliminary analysis of the defocus blur caused by the use of a curved mirror

Design and Analysis of a Single-Camera Omnistereo Sensor for Quadrotor Micro Aerial Vehicles (MAVs)

We describe the design and 3D sensing performance of an omnidirectional stereo (omnistereo) vision system applied to Micro Aerial Vehicles (MAVs). The proposed omnistereo sensor employs a monocular camera that is co-axially aligned with a pair of hyperboloidal mirrors (a vertically-folded catadioptric configuration). We show that this arrangement provides a compact solution for omnidirectional 3D perception while mounted on top of propeller-based MAVs (not capable of large payloads). The theoretical single viewpoint (SVP) constraint helps us derive analytical solutions for the sensor’s projective geometry and generate SVP-compliant panoramic images to compute 3D information from stereo correspondences (in a truly synchronous fashion). We perform an extensive analysis on various system characteristics such as its size, catadioptric spatial resolution, field-of-view. In addition, we pose a probabilistic model for the uncertainty estimation of 3D information from triangulation of back-projected rays. We validate the projection error of the design using both synthetic and real-life images against ground-truth data. Qualitatively, we show 3D point clouds (dense and sparse) resulting out of a single image captured from a real-life experiment. We expect the reproducibility of our sensor as its model parameters can be optimized to satisfy other catadioptric-based omnistereo vision under different circumstances