| 1. |
- Ask, Erik, et al.
(författare)
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Exploiting p-Fold Symmetries for Faster Polynomial Equation Solving
- 2012
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Ingår i: 21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of. - International Association for Pattern Recognition (IAPR) & IEEE. - 978-4-9906441-1-6 ; s. 3232-3235
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Konferensbidrag (refereegranskat)abstract
- Numerous geometric problems in computer vision in- volve the solution of systems of polynomial equations. This is true for problems with minimal information, but also for finding stationary points for overdetermined problems. The state-of-the-art is based on the use of numerical linear algebra on the large but sparse co- efficient matrix that represents the expanded original equation set. In this paper we present two simplifica- tions that can be used (i) if the zero vector is one of the solutions or (ii) if the equations display certain p- fold symmetries. We evaluate the simplifications on a few example problems and demonstrate that significant speed increases are possible without loosing accuracy.
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| 2. |
- Burgess, Simon, et al.
(författare)
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Node Localization in Unsynchronized Time of Arrival Sensor Networks
- 2012
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Ingår i: 21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of. - International Association for Pattern Recognition (IAPR) & IEEE. - 978-4-9906441-1-6 ; s. 2042-2046
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Konferensbidrag (refereegranskat)abstract
- We present a method for solving the previously unstudied problem of localizing a set of receivers and directions from transmitters placed far from the receivers, measuring unsynchronized time of arrival data. The same problem is present in node localization of microphone and antenna arrays. The solution algorithm using 5 receivers and 9 transmitters is extended to the overdetermined case in a straightforward manner. Degenerate cases are shown to be when i) the measurement matrix has rank 4 or less or ii) the directions from the transmitters to the receivers lie on an intersection between the unit sphere and another quadric surface. In simulated experiments we explore how sensitive the solution is with respect to different degrees of far field approximations of the transmitters and with respect to noise in the data. Using real data we get a reconstruction of the receivers with a relative error of 14%.
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| 3. |
- Burgess, Simon, et al.
(författare)
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Pose Estimation from Minimal Dual-Receiver Configurations
- 2012
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Ingår i: 21st International Conference on Pattern Recognition (ICPR 2012), Proceedings of. - International Association for Pattern Recognition (IAPR) & IEEE. - 978-4-9906441-1-6 ; s. 2553-2556
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Konferensbidrag (refereegranskat)abstract
- Using multiple receivers (microphones or antennas) in a rigid configuration, such as on a smartphone, it is possible to measure time difference of arrival to the receivers. This in turn can be used to determine the direction to the transmissions, if there are at least three receivers. When using two receivers it can be used to determine the angle to the transmissions relative to the line through the two receivers. In this paper we study three minimal problems for pose using such data: (i) determine position and orientation using five transmissions, (ii) determine position and orientation using four transmissions and known ’down’ direction and (iii) determine position using three transmissions and known orientation. Numerically stable solvers are implemented. An experimental validation of the solvers are performed on simulated data
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| 4. |
- Kuang, Yubin, et al.
(författare)
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Numerically Stable Optimization of Polynomial Solvers for Minimal Problems
- 2012
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Ingår i: Lecture Notes in Computer Science (Computer Vision ECCV 2012, 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012, Proceedings, Part III). - Springer, Heidelberg. - 1611-3349 (online) .- 0302-9743 (print). - 3642337112 - 978-3-642-33711-6 (print) - 978-3-642-33712-3 (online) ; 7574, s. 100-113
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Konferensbidrag (refereegranskat)abstract
- Numerous geometric problems in computer vision involve the solu- tion of systems of polynomial equations. This is particularly true for so called minimal problems, but also for finding stationary points for overdetermined prob- lems. The state-of-the-art is based on the use of numerical linear algebra on the large but sparse coefficient matrix that represents the original equations multi- plied with a set of monomials. The key observation in this paper is that the speed and numerical stability of the solver depends heavily on (i) what multiplication monomials are used and (ii) the set of so called permissible monomials from which numerical linear algebra routines choose the basis of a certain quotient ring. In the paper we show that optimizing with respect to these two factors can give both significant improvements to numerical stability as compared to the state of the art, as well as highly compact solvers, while still retaining numerical stabil- ity. The methods are validated on several minimal problems that have previously been shown to be challenging
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| 5. |
- Kuang, Yubin, et al.
(författare)
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Optimizing Visual Vocabularies Using Soft Assignment Entropies
- 2011
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Ingår i: Lecture Notes in Computer Science. - Springer. - 1611-3349 (online) .- 0302-9743 (print). - 978-3-642-19282-1(online) - 978-3-642-19281-4 (print) ; 6495, s. 255-268
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Konferensbidrag (refereegranskat)abstract
- The state of the art for large database object retrieval in images is based on quantizing descriptors of interest points into visual words. High similarity between matching image representations (as bags of words) is based upon the assumption that matched points in the two images end up in similar words in hard assignment or in similar representations in soft assignment techniques. In this paper we study how ground truth correspondences can be used to generate better visual vocabularies. Matching of image patches can be done e.g. using deformable models or from estimating 3D geometry. For optimization of the vocabulary, we propose minimizing the entropies of soft assignment of points. We base our clustering on hierarchical k-splits. The results from our entropy based clustering are compared with hierarchical k-means. The vocabularies have been tested on real data with decreased entropy and increased true positive rate, as well as better retrieval performance.
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| 6. |
- Kuang, Yubin, et al.
(författare)
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Supervised Feature Quantization with Entropy Optimization
- 2011
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Ingår i: Computer Vision Workshops (ICCV Workshops), 2011 IEEE International Conference on. - IEEE. - 978-1-4673-0062-9 (print) ; s. 1386-1393
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Konferensbidrag (refereegranskat)abstract
- Feature quantization is a crucial component for efficient large scale image retrieval and object recognition. By quantizing local features into visual words, one hopes that features that match each other obtain the same word ID. Then, similarities between images can be measured with respect to the corresponding histograms of visual words. Given the appearance variations of local features, traditional quantization methods do not take into account the distribution of matched features. In this paper, we investigate how to encode additional prior information on the feature distribution via entropy optimization by leveraging ground truth correspondence data. We propose a computationally efficient optimization scheme for large scale vocabulary training. The results from our experiments suggest that entropy-optimized vocabulary performs better than unsupervised quantization methods in terms of recall and precision for feature matching. We also demonstrate the advantage of the optimized vocabulary for image retrieval.
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| 7. |
- Kuang, Yubin, et al.
(författare)
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Understanding TOA and TDOA Network Calibration using Far Field Approximation as Initial Estimate
- 2012
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Ingår i: ICPRAM 2012 - Proceedings of the 1st International Conference on Pattern Recognition Applications and Methods, Volume 2. - SciTePress. - 978-9-898425-99-7 ; s. 590-596
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Konferensbidrag (refereegranskat)abstract
- This paper presents a study of the so called far field approximation to the problem of determining both the direction to a number of transmittors and the relative motion of a single antenna using relative distance measurements. The same problem is present in calibration of microphone and wifi-transmittor arrays. In the far field approximation we assume that the relative motion of the antenna is small in comparison to the distances to the base stations. The problem can be solved uniquely with at least three motions of the antenna and at least six real or virtual transmittors. The failure modes of the problem is determined to be (i) when the antenna motion is planar or (ii) when the transmittor directions lie on a cone. We also study to what extent the solution can be obtained in these degenerate configurations. The solution algorithm for the minimal case can be extended to the overdetermined case in a straightforward manner. We also implement and test algorithms for non-linear optimization of the residuals. In experiments we explore how sensitive the calibration is with respect to different degrees of far field approximations of the transmittors and with respect to noise in the data.
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