Using geometric algebra to create differentiable models for optimizing camera-based optical metrology systems

In the design process of camera-based optical metrology systems numerous intricate and seemingly distinct optimization tasks emerge.A frequently occurring but crucial task in design or calibration is to optimize the spatial degrees of freedom of system components. Of course, modelling the poses of rigid bodies is long solved using rotation matrices and translation vectors, but when it comes to optimizing, this choice of model gets quite tedious to handle. Useful concepts such as homogeneous coordinates or (dual) quaternions have been introduced to overcome this, which however – lacking a unified framework – can quickly become difficult to maintain. As an alternative, in this contribution it is shown how the unifying methods of geometric algebra can be used as an advantage for gradient-based optimization of camera-based optical metrology and imaging systems – and how this can be done in a generalized way for seemingly different objectives with respect to system design and calibration

Efficient generic calibration method for general cameras with single centre of projection

Generic camera calibration is a non-parametric calibration technique that is applicable to any type of vision sensor. However, the standard generic calibration method was developed with the goal of generality and it is therefore sub-optimal for the common case of cameras with a single centre of projection (e.g. pinhole, fisheye, hyperboloidal catadioptric). This paper proposes novel improvements to the standard generic calibration method for central cameras that reduce its complexity, and improve its accuracy and robustness. Improvements are achieved by taking advantage of the geometric constraints resulting from a single centre of projection. Input data for the algorithm is acquired using active grids, the performance of which is characterised. A new linear estimation stage to the generic algorithm is proposed incorporating classical pinhole calibration techniques, and it is shown to be significantly more accurate than the linear estimation stage of the standard method. A linear method for pose estimation is also proposed and evaluated against the existing polynomial method. Distortion correction and motion reconstruction experiments are conducted with real data for a hyperboloidal catadioptric sensor for both the standard and proposed methods. Results show the accuracy and robustness of the proposed method to be superior to those of the standard method

Relating vanishing points to catadioptric camera calibration

This paper presents the analysis and derivation of the geometric relation between vanishing points and camera parameters of central catadioptric camera systems. These vanishing points correspond to the three mutually orthogonal directions of 3D real world coordinate system (i.e. X, Y and Z axes). Compared to vanishing points (VPs) in the perspective projection, the advantages of VPs under central catadioptric projection are that there are normally two vanishing points for each set of parallel lines, since lines are projected to conics in the catadioptric image plane. Also, their vanishing points are usually located inside the image frame. We show that knowledge of the VPs corresponding to XYZ axes from a single image can lead to simple derivation of both intrinsic and extrinsic parameters of the central catadioptric system. This derived novel theory is demonstrated and tested on both synthetic and real data with respect to noise sensitivity

The Double Sphere Camera Model

Vision-based motion estimation and 3D reconstruction, which have numerous applications (e.g., autonomous driving, navigation systems for airborne devices and augmented reality) are receiving significant research attention. To increase the accuracy and robustness, several researchers have recently demonstrated the benefit of using large field-of-view cameras for such applications. In this paper, we provide an extensive review of existing models for large field-of-view cameras. For each model we provide projection and unprojection functions and the subspace of points that result in valid projection. Then, we propose the Double Sphere camera model that well fits with large field-of-view lenses, is computationally inexpensive and has a closed-form inverse. We evaluate the model using a calibration dataset with several different lenses and compare the models using the metrics that are relevant for Visual Odometry, i.e., reprojection error, as well as computation time for projection and unprojection functions and their Jacobians. We also provide qualitative results and discuss the performance of all models

Cognitive visual tracking and camera control

Cognitive visual tracking is the process of observing and understanding the behaviour of a moving person. This paper presents an efficient solution to extract, in real-time, high-level information from an observed scene, and generate the most appropriate commands for a set of pan-tilt-zoom (PTZ) cameras in a surveillance scenario. Such a high-level feedback control loop, which is the main novelty of our work, will serve to reduce uncertainties in the observed scene and to maximize the amount of information extracted from it. It is implemented with a distributed camera system using SQL tables as virtual communication channels, and Situation Graph Trees for knowledge representation, inference and high-level camera control. A set of experiments in a surveillance scenario show the effectiveness of our approach and its potential for real applications of cognitive vision

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