Rotation Recovery from Spherical Images without Correspondences

This paper addresses the problem of rotation estimation directly from images defined on the sphere and without correspondence. The method is particularly useful for the alignment of large rotations and has potential impact on 3D shape alignment. The foundation of the method lies in the fact that the spherical harmonic coefficients undergo a unitary mapping when the original image is rotated. The correlation between two images is a function of rotations and we show that it has an SO(3)-Fourier transform equal to the pointwise product of spherical harmonic coefficients of the original images. The resolution of the rotation space depends on the bandwidth we choose for the harmonic expansion and the rotation estimate is found through a direct search in this 3D discretized space. A refinement of the rotation estimate can be obtained from the conservation of harmonic coefficients in the rotational shift theorem. A novel decoupling of the shift theorem with respect to the Euler angles is presented and exploited in an iterative scheme to refine the initial rotation estimates. Experiments show the suitability of the method for large rotations and the dependence of the method on bandwidth and the choice of the spherical harmonic coefficients

Spherical Regression: Learning Viewpoints, Surface Normals and 3D Rotations on n-Spheres

Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation function. Regular regression lacks such a closed geometry, leading to unstable training and convergence to suboptimal local minima. Starting from this insight we revisit regression in convolutional neural networks. We observe many continuous output problems in computer vision are naturally contained in closed geometrical manifolds, like the Euler angles in viewpoint estimation or the normals in surface normal estimation. A natural framework for posing such continuous output problems are $n$-spheres, which are naturally closed geometric manifolds defined in the $\mathbb{R}^{(n+1)}$ space. By introducing a spherical exponential mapping on $n$-spheres at the regression output, we obtain well-behaved gradients, leading to stable training. We show how our spherical regression can be utilized for several computer vision challenges, specifically viewpoint estimation, surface normal estimation and 3D rotation estimation. For all these problems our experiments demonstrate the benefit of spherical regression. All paper resources are available at https://github.com/leoshine/Spherical_Regression.Comment: CVPR 2019 camera read

Active Estimation of Distance in a Robotic Vision System that Replicates Human Eye Movement

Many visual cues, both binocular and monocular, provide 3D information. When an agent moves with respect to a scene, an important cue is the different motion of objects located at various distances. While a motion parallax is evident for large translations of the agent, in most head/eye systems a small parallax occurs also during rotations of the cameras. A similar parallax is present also in the human eye. During a relocation of gaze, the shift in the retinal projection of an object depends not only on the amplitude of the movement, but also on the distance of the object with respect to the observer. This study proposes a method for estimating distance on the basis of the parallax that emerges from rotations of a camera. A pan/tilt system specifically designed to reproduce the oculomotor parallax present in the human eye was used to replicate the oculomotor strategy by which humans scan visual scenes. We show that the oculomotor parallax provides accurate estimation of distance during sequences of eye movements. In a system that actively scans a visual scene, challenging tasks such as image segmentation and figure/ground segregation greatly benefit from this cue.National Science Foundation (BIC-0432104, CCF-0130851

Long-term experiments with an adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In this work, we introduce a method to update the reference views in a hybrid metric-topological map so that a mobile robot can continue to localize itself in a changing environment. The updating mechanism, based on the multi-store model of human memory, incorporates a spherical metric representation of the observed visual features for each node in the map, which enables the robot to estimate its heading and navigate using multi-view geometry, as well as representing the local 3D geometry of the environment. A series of experiments demonstrate the persistence performance of the proposed system in real changing environments, including analysis of the long-term stability

An adaptive spherical view representation for navigation in changing environments

Real-world environments such as houses and offices change over time, meaning that a mobile robot’s map will become out of date. In previous work we introduced a method to update the reference views in a topological map so that a mobile robot could continue to localize itself in a changing environment using omni-directional vision. In this work we extend this longterm updating mechanism to incorporate a spherical metric representation of the observed visual features for each node in the topological map. Using multi-view geometry we are then able to estimate the heading of the robot, in order to enable navigation between the nodes of the map, and to simultaneously adapt the spherical view representation in response to environmental changes. The results demonstrate the persistent performance of the proposed system in a long-term experiment