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The H matrices can be required by the tracker (e.g., by the EKF) as well as for maximum-likelihood pose estimation. Computing H requires the screen point derivatives from the warp function: for example, given by the respective Lie algebras, in terms of the incremental pose p, as described in Section 2.3. Dropping the object and modality indices, two equivalent forms for the measurement model may be required by a given Bayesian tracker: Explicit form: zk = h ( sk , ek , vk ) Implicit form (likelihood): P ( zk sk ) In the rst form, vk is the measurement noise, with covariance Rk , usually diagonal or block diagonal, that can be provided externally or updated online, depending on the modality. The second form is the likelihood of the observation z given s, and alone can be used for maximum-likelihood parameter estimation, such as LSE optimization for Gaussian models (Section 5.2). Often, in computer vision applications a multihypothesis association is a more realistic and robust model, in the presence of clutter background and missing detections, which implies a non-Gaussian likelihood with multiple modes, such as a Gaussian mixture. Moreover, in analogy with the data fusion terminology [71], Sec. 4.4, we also classify our measurements into three levels (Fig. 3.3):

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Here are some examples of invalid variable names:

=COUNTIF(Data, > &A1)

and P is the state-space dimension of the natural cubic spline for S [Smin, Smax ], Q is the temporal space dimension of the spline, w is a weighting function that re ects the importance of particular prices; that is, at-the-money prices should be weighted

Combining SIP mobility with MIP can, however, give excellent results in some application scenarios by reducing both the delay and the handover time [17], keeping, for example, the handover time at roughly 100 ms in 802.11 wireless networks independent of the delay between the mobile node and the corresponding node on the Internet. Using MIP alone would have increased the handover time in a linear fashion with the delay between the two nodes.

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[56] Thomas M Cover and Joy A Thomas Elements of Information Theory Wiley, New York, 1991 [57] Daniel Cremers, Mika l Rousson, and Rachid Deriche A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape Int J Comput Vision, 72(2):195 215, 2007 [58] James W Davis and Aaron F Bobick The representation and recognition of human movement using temporal templates In 1997 Conference on Computer Vision and Pattern Recognition, San Juan, Puerto Rico, June 17 19, 1997, pp 928 934 IEEE Computer Society, Washington, DC, 1997 [59] A P Dempster, N M Laird, and D B Rubin Maximum likelihood from incomplete data via the EM algorithm J R Statist Soc B, 39(1):1 38, 1977 [60] Tom Drummond and Roberto Cipolla Visual tracking and control using Lie algebras In 1999 Conference on Computer Vision and Pattern Recognition, Los Alamitos, CA, Vol 2, pp 2652 2659.

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IEEE Computer Society, Washington, DC, 1999 [61] Tom Drummond and Roberto Cipolla Real-time visual tracking of complex structures IEEE Trans Pattern Anal Mach Intell, 24(7):932 946, 2002 [62] Richard O Duda and Peter E Hart Use of the Hough transformation to detect lines and curves in pictures Commun ACM, 15(1):11 15, 1972 [63] J Duetscher, A Blake, and I Reid Articulated body motion capture by annealed particle ltering In IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2000, Vol 2, p 2126 [64] Pedro F Felzenszwalb and Daniel P Huttenlocher Distance transforms of sampled functions Technical Report Cornell Computing and Information Science, Icheca, NY, Sept 2004 [65] Martin A Fischler and Robert C Bolles Random sample consensus: a paradigm for model tting with applications to image analysis and automated cartography Commun ACM, 24(6):381 395, 1981 [66] Y Freund and R Schapire A short introduction to boosting J.

interest rate caps can be expressed as European put options on pure discount bonds. Thus, if we know the price of caps, we can nd the implied volatility parameter by using equation (10.75). The optimization, which can be done using a Newton-Raphson type procedure, involves searching over all possible values of the parameter . The value of that minimizes the function is the volatility that best calibrates the model to the market for the choice of function to be minimized. We could use (10.115) to calibrate a Ho and Lee model since only the volatility needs to be determined the volatility is not a function of any other parameters. In contrast to the Ho and Lee model, the Vasicek (and Hull-White extended Vasicek) spot rate volatility equation contains two parameters, a and , so that in order to calibrate the model to market prices we need to nd the best t for both a and simultaneously to market data. If we have M individual European pure discount bond put prices, we can minimize modeli (a, ) marketi marketi i =1

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