Discriminative Optimization

This work was developed in the context of Jayakorn Vongkulbshisal’s Dual PhD (IST/CMU) co-advised by Prof. Fernando De la Torre (CMU) and Prof. João Costeira (IST) and sponsored by the Carnegie Mellon Portugal Program. References and publications below

Brief Description

Many computer vision problems are formulated as the optimization of a cost function. This approach faces two main challenges: (i) designing a cost function with a local optimum at an acceptable solution, and (ii) developing an efficient numerical method to search for one (or multiple) of these local optima. While designing such functions is feasible in the noiseless case, the stability and location of local optima are mostly unknown under noise, occlusion, or missing data. In practice, this can result in undesirable local optima or not having a local optimum in the expected place. On the other hand, numerical optimization algorithms in high-dimensional spaces are typically local and often rely on expensive first or second order information to guide the search. To overcome these limitations, this paper proposes Discriminative Optimization (DO), a method that learns search directions from data without the need of a cost function. Specifically, DO explicitly learns a sequence of updates in the search space that leads to stationary points that correspond to desired solutions. We provide a formal analysis of DO and illustrate its benefits in the problem of 3D point cloud registration, camera pose estimation, and image denoising. We show that DO performed comparably or outperformed state-of-the-art algorithms in terms of accuracy, robustness to perturbations, and computational efficiency.

Video with explanation and experiments


 

Applications:  3D shape (point cloud) registration

DO estimates the rigid transformation between a pre-defined model 3D shape and a 3D point cloud from an RGBD camera like the kinect, stereo or lidar. DO is extremely robust and is able to track the objects even if they are severely occluded.


Applications: Homography estimation


 

Applications: Image Denoising


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References:

J. Vongkulbhisal, F. De la Torre, and J. P. Costeira. “Discriminative Optimization: Theory and Applications to Computer Vision Problems,” arXiv preprint arXiv: 1707.04318, 2017.  Accepted IEEE-Transactions on Pattern Analysis and Machine Intelligence (PAMI), 2018
[link]

J. Vongkulbhisal, F. De la Torre, and J. P. Costeira. “Discriminative Optimization: Theory and Applications to Point Cloud Registration,” CVPR, 2017.
[pdf]

Jayakorn Vongkulbhisal, Discriminative Optimization: Theory and Applications to Computer Vision,  PhD in   Electrical and Computer Engineering, Carnegie Mellon University and Instituto Superior Técnico ( Download ) 

See also  http://humansensing.cs.cmu.edu/DO