Generalized Image Acquisition and Analysis
From Capture to Simulation - Connecting Forward and Inverse Problems in Fluids
We explore the connection between fluid capture, simulation
and proximal methods, a class of algorithms commonly used
for inverse problems in image processing and computer
vision. Our key finding is that the proximal operator
constraining fluid velocities to be divergence-free is
directly equivalent to the pressure-projection methods
commonly used in incompressible flow solvers. This
observation lets us treat the inverse problem of fluid
tracking as a constrained flow problem all while working in
an efficient, modular framework. In addition it lets us
tightly couple fluid simulation into flow tracking,
providing a global prior that significantly increases
tracking accuracy and temporal coherence as compared to
previous techniques. We demonstrate how we can use these
improved results for a variety of applications, such as
re-simulation, detail enhancement, and domain
modification. We furthermore give an outlook of the
applications beyond fluid tracking that our proximal
operator framework could enable by exploring the connection
of deblurring and fluid guiding.
Projects
Discovering the Structure of a Planar Mirror System from Multiple Observations of a Single Point
CVPR 2013
Abstract
We investigate the problem of identifying the position of a
viewer inside a room of planar mirrors with unknown geometry
in conjunction with the room’s shape parameters. We consider
the observations to consist of angularly resolved depth
measurements of a single scene point that is being observed
via many multi-bounce interactions with the specular room
geometry.
Applications of this problem statement include areas such as
calibration, acoustic echo cancelation and time-of-flight
imaging. We theoretically analyze the problem and derive
sufficient conditions for a combination of convex room
geometry, observer, and scene point to be
reconstructable. The resulting constructive algorithm is
exponential in nature and, therefore, not directly
applicable to practical scenarios.
To counter the situation, we propose theoretically devised
geo- metric constraints that enable an efficient pruning of
the solution space and develop a heuristic randomized search
algorithm that uses these constraints to obtain an effective
solution. We demon- strate the effectiveness of our
algorithm on extensive simulations as well as in a
challenging real-world calibration scenario.
Bibtex
@inproceedings{Reshetouski:13,
author = {Ilya Rehsetouski and Alkhazur Manakov and Ayush Bhandari and Ramesh Raskar and Hans-Peter Seidel and Ivo Ihrke},
title = {Discovering the Structure of a Planar Mirror System from Multiple Observations of a Single Point},
booktitle = {Proceedings of CVPR},
year = 2013,
pages = {xx--yy},
}
author = {Ilya Rehsetouski and Alkhazur Manakov and Ayush Bhandari and Ramesh Raskar and Hans-Peter Seidel and Ivo Ihrke},
title = {Discovering the Structure of a Planar Mirror System from Multiple Observations of a Single Point},
booktitle = {Proceedings of CVPR},
year = 2013,
pages = {xx--yy},
}