Motion from Fixation

We study the problem of estimating rigid motion from a sequence of monocular perspective images obtained by navigating around an object while fixating a particular feature point. The motivation comes from the mechanics of the buman eye, which either pursuits smoothly some fixation point in the scene, or "saccades" between different fixation points. In particular, we are interested in understanding whether fixation helps the process of estimating motion in the sense that it makes it more robust, better conditioned or simpler to solve. We cast the problem in the framework of "dynamic epipolar geometry", and propose an implicit dynamical model for recursively estimating motion from fixation. This allows us to compare directly the quality of the estimates of motion obtained by imposing the fixation constraint, or by assuming a general rigid motion, simply by changing the geometry of the parameter space while maintaining the same structure of the recursive estimator. We also present a closed-form static solution from two views, and a recursive estimator of the absolute attitude between the viewer and the scene. One important issue is how do the estimates degrade in presence of disturbances in the tracking procedure. We describe a simple fixation control that converges exponentially, which is complemented by a image shift-registration for achieving sub-pixel accuracy, and assess how small deviations from perfect tracking affect the estimates of motion

A closed-form solution to estimate uncertainty in non-rigid structure from motion

Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or base-trajectory methods. Despite the efficiency in deformable shape reconstruction, it remains unclear how to assess the uncertainty of the recovered shape from the SDP process. In this paper, we present a statistical inference on the element-wise uncertainty quantification of the estimated deforming 3D shape points in the case of the exact low-rank SDP problem. A closed-form uncertainty quantification method is proposed and tested. Moreover, we extend the exact low-rank uncertainty quantification to the approximate low-rank scenario with a numerical optimal rank selection method, which enables solving practical application in SDP based NRSfM scenario. The proposed method provides an independent module to the SDP method and only requires the statistic information of the input 2D tracked points. Extensive experiments prove that the output 3D points have identical normal distribution to the 2D trackings, the proposed method and quantify the uncertainty accurately, and supports that it has desirable effects on routinely SDP low-rank based NRSfM solver.Comment: 9 pages, 2 figure

Motion from "X" by Compensating "Y"

This paper analyzes the geometry of the visual motion estimation problem in relation to transformations of the input (images) that stabilize particular output functions such as the motion of a point, a line and a plane in the image. By casting the problem within the popular "epipolar geometry", we provide a common framework for including constraints such as point, line of plane fixation by just considering "slices" of the parameter manifold. The models we provide can be used for estimating motion from a batch using the preferred optimization techniques, or for defining dynamic filters that estimate motion from a causal sequence. We discuss methods for performing the necessary compensation by either controlling the support of the camera or by pre-processing the images. The compensation algorithms may be used also for recursively fitting a plane in 3-D both from point-features or directly from brightness. Conversely, they may be used for estimating motion relative to the plane independent of its parameters

A factorization approach to inertial affine structure from motion

We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives

A factorization approach to inertial affine structure from motion

We consider the problem of reconstructing a 3-D scene from a moving camera with high frame rate using the affine projection model. This problem is traditionally known as Affine Structure from Motion (Affine SfM), and can be solved using an elegant low-rank factorization formulation. In this paper, we assume that an accelerometer and gyro are rigidly mounted with the camera, so that synchronized linear acceleration and angular velocity measurements are available together with the image measurements. We extend the standard Affine SfM algorithm to integrate these measurements through the use of image derivatives