Reconstruction of Linearly Parameterized Models from Single Images with a Camera of Unknown Focal Length

This paper deals with the problem of recovering the dimensions of an object and its pose from a single image acquired with a camera of unknown focal length. It is assumed that the object in question can be modeled as a polyhedron where the coordinates of the vertices can be expressed as a linear function of a dimension vector, λ. The reconstruction program takes as input, a set of correspondences between features in the model and features in the image. From this information, the program determines an appropriate projection model for the camera (scaled orthographic or perspective), the dimensions of the object, its pose relative to the camera and, in the case of perspective projection, the focal length of the camera. This paper describes how the reconstruction problem can be framed as an optimization over a compact set with low dimension - no more than four. This optimization problem can be solved efficiently by coupling standard nonlinear optimization techniques with a multistart method which generates multiple starting points for the optimizer by sampling the parameter space uniformly. The result is an efficient, reliable solution system that does not require initial estimates for any of the parameters being estimated

Radially-Distorted Conjugate Translations

This paper introduces the first minimal solvers that jointly solve for affine-rectification and radial lens distortion from coplanar repeated patterns. Even with imagery from moderately distorted lenses, plane rectification using the pinhole camera model is inaccurate or invalid. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle imagery, which is now common from consumer cameras. The solvers are derived from constraints induced by the conjugate translations of an imaged scene plane, which are integrated with the division model for radial lens distortion. The hidden-variable trick with ideal saturation is used to reformulate the constraints so that the solvers generated by the Grobner-basis method are stable, small and fast. Rectification and lens distortion are recovered from either one conjugately translated affine-covariant feature or two independently translated similarity-covariant features. The proposed solvers are used in a \RANSAC-based estimator, which gives accurate rectifications after few iterations. The proposed solvers are evaluated against the state-of-the-art and demonstrate significantly better rectifications on noisy measurements. Qualitative results on diverse imagery demonstrate high-accuracy undistortions and rectifications. The source code is publicly available at https://github.com/prittjam/repeats

Reconstructing the primordial power spectrum from the CMB

We propose a straightforward and model independent methodology for characterizing the sensitivity of CMB and other experiments to wiggles, irregularities, and features in the primordial power spectrum. Assuming that the primordial cosmological perturbations are adiabatic, we present a function space generalization of the usual Fisher matrix formalism, applied to a CMB experiment resembling Planck with and without ancillary data. This work is closely related to other work on recovering the inflationary potential and exploring specific models of non-minimal, or perhaps baroque, primordial power spectra. The approach adopted here, however, most directly expresses what the data is really telling us. We explore in detail the structure of the available information and quantify exactly what features can be reconstructed and at what statistical significance.Comment: 43 pages Revtex, 23 figure