27,311 research outputs found
A Hilbert Scheme in Computer Vision
Multiview geometry is the study of two-dimensional images of
three-dimensional scenes, a foundational subject in computer vision. We
determine a universal Groebner basis for the multiview ideal of n generic
cameras. As the cameras move, the multiview varieties vary in a family of
dimension 11n-15. This family is the distinguished component of a multigraded
Hilbert scheme with a unique Borel-fixed point. We present a combinatorial
study of ideals lying on that Hilbert scheme.Comment: 26 page
Point triangulation through polyhedron collapse using the l∞ norm
Multi-camera triangulation of feature points based on a minimisation of the overall l(2) reprojection error can get stuck in suboptimal local minima or require slow global optimisation. For this reason, researchers have proposed optimising the l(infinity) norm of the l(2) single view reprojection errors, which avoids the problem of local minima entirely. In this paper we present a novel method for l(infinity) triangulation that minimizes the l(infinity) norm of the l(infinity) reprojection errors: this apparently small difference leads to a much faster but equally accurate solution which is related to the MLE under the assumption of uniform noise. The proposed method adopts a new optimisation strategy based on solving simple quadratic equations. This stands in contrast with the fastest existing methods, which solve a sequence of more complex auxiliary Linear Programming or Second Order Cone Problems. The proposed algorithm performs well: for triangulation, it achieves the same accuracy as existing techniques while executing faster and being straightforward to implement
An Immersive Telepresence System using RGB-D Sensors and Head Mounted Display
We present a tele-immersive system that enables people to interact with each
other in a virtual world using body gestures in addition to verbal
communication. Beyond the obvious applications, including general online
conversations and gaming, we hypothesize that our proposed system would be
particularly beneficial to education by offering rich visual contents and
interactivity. One distinct feature is the integration of egocentric pose
recognition that allows participants to use their gestures to demonstrate and
manipulate virtual objects simultaneously. This functionality enables the
instructor to ef- fectively and efficiently explain and illustrate complex
concepts or sophisticated problems in an intuitive manner. The highly
interactive and flexible environment can capture and sustain more student
attention than the traditional classroom setting and, thus, delivers a
compelling experience to the students. Our main focus here is to investigate
possible solutions for the system design and implementation and devise
strategies for fast, efficient computation suitable for visual data processing
and network transmission. We describe the technique and experiments in details
and provide quantitative performance results, demonstrating our system can be
run comfortably and reliably for different application scenarios. Our
preliminary results are promising and demonstrate the potential for more
compelling directions in cyberlearning.Comment: IEEE International Symposium on Multimedia 201
Optical techniques for 3D surface reconstruction in computer-assisted laparoscopic surgery
One of the main challenges for computer-assisted surgery (CAS) is to determine the intra-opera- tive morphology and motion of soft-tissues. This information is prerequisite to the registration of multi-modal patient-specific data for enhancing the surgeon’s navigation capabilites by observ- ing beyond exposed tissue surfaces and for providing intelligent control of robotic-assisted in- struments. In minimally invasive surgery (MIS), optical techniques are an increasingly attractive approach for in vivo 3D reconstruction of the soft-tissue surface geometry. This paper reviews the state-of-the-art methods for optical intra-operative 3D reconstruction in laparoscopic surgery and discusses the technical challenges and future perspectives towards clinical translation. With the recent paradigm shift of surgical practice towards MIS and new developments in 3D opti- cal imaging, this is a timely discussion about technologies that could facilitate complex CAS procedures in dynamic and deformable anatomical regions
Disparity map generation based on trapezoidal camera architecture for multiview video
Visual content acquisition is a strategic functional block of any visual system. Despite its wide possibilities,
the arrangement of cameras for the acquisition of good quality visual content for use in multi-view video
remains a huge challenge. This paper presents the mathematical description of trapezoidal camera
architecture and relationships which facilitate the determination of camera position for visual content
acquisition in multi-view video, and depth map generation. The strong point of Trapezoidal Camera
Architecture is that it allows for adaptive camera topology by which points within the scene, especially the
occluded ones can be optically and geometrically viewed from several different viewpoints either on the
edge of the trapezoid or inside it. The concept of maximum independent set, trapezoid characteristics, and
the fact that the positions of cameras (with the exception of few) differ in their vertical coordinate
description could very well be used to address the issue of occlusion which continues to be a major
problem in computer vision with regards to the generation of depth map
Trifocal Relative Pose from Lines at Points and its Efficient Solution
We present a new minimal problem for relative pose estimation mixing point
features with lines incident at points observed in three views and its
efficient homotopy continuation solver. We demonstrate the generality of the
approach by analyzing and solving an additional problem with mixed point and
line correspondences in three views. The minimal problems include
correspondences of (i) three points and one line and (ii) three points and two
lines through two of the points which is reported and analyzed here for the
first time. These are difficult to solve, as they have 216 and - as shown here
- 312 solutions, but cover important practical situations when line and point
features appear together, e.g., in urban scenes or when observing curves. We
demonstrate that even such difficult problems can be solved robustly using a
suitable homotopy continuation technique and we provide an implementation
optimized for minimal problems that can be integrated into engineering
applications. Our simulated and real experiments demonstrate our solvers in the
camera geometry computation task in structure from motion. We show that new
solvers allow for reconstructing challenging scenes where the standard two-view
initialization of structure from motion fails.Comment: This material is based upon work supported by the National Science
Foundation under Grant No. DMS-1439786 while most authors were in residence
at Brown University's Institute for Computational and Experimental Research
in Mathematics -- ICERM, in Providence, R
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