LQ-bundle adjustment

In this paper we propose a method to solve for an Lq solution of bundle adjustment, a non-linear parameter estimation problem. Given a set of images of a scene, bundle adjustment simultaneously estimates camera parameters and 3D structure of the scene. Generally, a least squares criterion is minimized by using the Levenberg-Marquardt (LM) method, a non-linear least squares optimization method. It is known that the least squares methods are not robust to outliers, even a single outlier can deviate the solution from its true value. Therefore, we propose a method to minimize an Lq cost function, for 1 ≤ q < 2. The Lq cost function minimizes the sum of the q-th power of errors. The proposed method has an advantage of using the Levenberg-Marquardt (LM) method to find a robust solution of the problem. Our experimental results confirm that the proposed method is more robust to outliers than the standard least squares method

Generalized Weiszfeld algorithms for Lq optimization

In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L₂ cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors usually gives more robust results in the presence of outliers for some values of q, for example, q = 1. The Weiszfeld algorithm is a classic algorithm for finding the geometric L1 mean of a set of points in Euclidean space. It is provably optimal and requires neither differentiation, nor line search. The Weiszfeld algorithm has also been generalized to find the L1 mean of a set of points on a Riemannian manifold of non-negative curvature. This paper shows that the Weiszfeld approach may be extended to a wide variety of problems to find an Lq mean for 1 ≤ q <; 2, while maintaining simplicity and provable convergence. We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global Lq optimum) and multiple rotation averaging (for which no such proof exists). Experimental results of Lq optimization for rotations show the improved reliability and robustness compared to L₂ optimization.This research has been funded by National ICT Australia

The inflation bias under Calvo and Rotemberg pricing

New Keynesian analysis relies heavily on two workhorse models of nominal inertia – due to Calvo (1983) and Rotemberg (1982), respectively – to generate a meaningful role for monetary policy. These are often used interchangeably since they imply an isomorphic linearized Phillips curve and, if the steady-state is efficient, the same policy conclusions. In this paper we compute time-consistent optimal monetary policy in the benchmark New Keynesian model containing each form of price stickiness using global solution techniques. We find that, due to an offsetting endogenous impact on average markups, the inflation bias problem under Calvo contracts is often significantly greater than under Rotemberg pricing, despite the fact that the former typically exhibits far greater welfare costs of inflation. The nonlinearities inherent in the New Keynesian model are significant and the form of nominal inertia adopted is not innocuous

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