Month: February 2021

Mirror Surface Reconstruction

Posted on by kai.han

This project addresses the problem of mirror surface reconstruction, and proposes a solution based on observing the reflections of a moving reference plane on the mirror surface. Unlike previous approaches which require tedious calibration, our method can recover the camera intrinsics, the poses of the reference plane, as well as the mirror surface from the observed reflections of the reference plane under at least three unknown distinct poses. We first show that the 3D poses of the reference plane can be estimated from the reflection correspondences established between the images and the reference plane. We then form a bunch of 3D lines from the reflection correspondences, and derive an analytical solution to recover the line projection matrix. We transform the line projection matrix to its equivalent camera projection matrix, and propose a cross-ratio based formulation to optimize the camera projection matrix by minimizing reprojection errors. The mirror surface is then reconstructed based on the optimized cross-ratio constraint. Experimental results on both synthetic and real data are presented, which demonstrate the feasibility and accuracy of our method.

Publications

[1] Kai Han, Miaomiao Liu, Dirk Schnieders, Kwan-Yee K. Wong
Fixed Viewpoint Mirror Surface Reconstruction under an Uncalibrated Camera
IEEE Transactions on Image Processing (TIP), 2021.

[2] Kai Han, Kwan-Yee K. Wong, Dirk Schnieders, Miaomiao Liu
Mirror Surface Reconstruction Under an Uncalibrated Camera
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016.

Further information

Papers and code available here.

Cauchy Proximal Splitting (CPS)

Posted on by o.karakus

In this project, we develop a proximal splitting methodology with a non-convex penalty function based on the heavy-tailed Cauchy distribution. We first suggest a closed-form expression for calculating the proximal operator of the Cauchy prior, which then makes it applicable in generic proximal splitting algorithms. We further derive the condition required for guaranteed convergence to the global minimum in optimisation problems involving the Cauchy based penalty function. Setting the system parameters by satisfying the proposed condition ensures convergence even though the overall cost function is non-convex when minimisation is performed via a proximal splitting algorithm.

The proposed proximal splitting method based on Cauchy regularisation is evaluated by solving generic signal processing examples,
** 1D signal denoising in the frequency domain,
** Two image reconstruction tasks including de-blurring and denoising,
** Error recovery in a multiple-antenna communication system.

We experimentally verify the proposed convergence conditions for various cases, and show the effectiveness of the proposed Cauchy based non-convex penalty function over state-of-the-art penalty functions such as L1 and total variation (TV) norms.

Further information

[1] O. Karakuş, P. Mayo and A. Achim, “Convergence Guarantees for Non-Convex Optimisation With Cauchy-Based Penalties,” in IEEE Transactions on Signal Processing, vol. 68, pp. 6159-6170, 2020, doi: 10.1109/TSP.2020.3032231.

Code

O Karakus, A Achim. (2020): Cauchy Proximal Splitting (CPS).
https://doi.org/10.5523/bris.15y437loa26cr2nx8gnn3l4hzi

Contact

Oktay Karakuş, Perla Mayo, Alin Achim

Funding

This work was supported
** in part by the UK Engineering and Physical Sciences Research Council (EPSRC) under grant EP/R009260/1 (AssenSAR),
** in part by a CONACyT PhD studentship under grant 461322 to Mayo,
** in part by a Leverhulme Trust Research Fellowship to Achim (INFHER).