What value covariance information in estimating vision parameters?

Abstract

Many parameter estimation methods used in computer vi

Ray Divergence-Based Bundle Adjustment Conditioning for Multi-view Stereo

“…Something very important to note here is that image feature covariances [10,11] are defined completely by the intensity variations in local neighborhoods and thus may look rather random to visual inspection, with no clear pattern as the image is traversed, as seen on the right in Fig. 3.…”

“…For example, two perfect matches could still yield a non-zero ray divergence due to camera inaccuracies. Therefore, using ray divergence or even the values provided by Beder et al's metric [9], though more expensive to compute and not inclusive of radial distortion, provide a stronger constraint towards weighting bundle adjustment than image-based covariances [10,11]. The right side of Fig.…”

“…Their analysis is based on computing a confidence ellipsoid for each computed 3D scene point X, such that its roundness measures the quality of each obtained point. For two views, the covariance matrices of image feature matches x and x" are given by C and C" respectively [10,11]. Then, the covariance matrix C XX of the distribution of the scene point coordinates X is proportional to the upper left 4 × 4 submatrix N −1 1:4,1:4 for the inverse of the 5 × 5 matrix N given by Eq.…”

“…Furthermore, since ray divergence encodes camera inaccuracy information, we show how it can be used in weighted bundle adjustment to improve its convergence properties. It is shown how this scheme outperforms weighting based on more-expensive image feature covariance metrics [10,11] or Beder et al's confidence measure. The entire procedure is first derived for the two-view case, but later shown how this can easily be extended to multiple views.…”

From fns to heiv: a link between two vision parameter estimation methods

“…. , n, Λ xi is a k × k symmetric covariance matrix describing the uncertainty of the data point x i (see [4], [5], [6]). If J AML is minimized over those nonzero parameter vectors for which (2) holds, then the vector at which the minimum of J AML is attained, the constrained minimizer of J AML , defines the approximated maximum likelihood estimate θ AML .…”