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...nly the combination of all three pairings is sufficient to constrain translation to within measurement errors. The rotation is initialised with the result of an SVD analysis of the paired directions (=-=[10]-=-, page 431) plus a large variance. The translation is also initialised with a large variance but with an arbitrary mean (the zero vector). In Figure 2 we show the relative position of the model and da...

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...ems) is the basic estimation tool we are using. Here we merely give a brief description of its function; more details, in particular, the Kalman filter equations, can be readily found elsewhere, e.g. =-=[11, 1, 2]-=-. Knowledge at time step k about a parameter vector or state, x, is represented by the estimated mean vector,sx k , and variance matrix, X k , of an assumed Gaussian probability distribution. Observat...

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... foundation of the approach is based on representing the uncertainty by a variance matrix. This by itself is not new and a number of vision, robotics and tracking projects have followed this approach =-=[18, 12, 20, 2]-=-. That work has used the variance representation to encode fully constrained but statistically erroneous poses. The advantage of the statistical approach is that there are well-known and understood st...

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...to represent the open degrees-of-freedom (i.e. lack of knowledge) by one or more very large eigenvalues in the variance matrix. Unlike the interval bounding method on parameter space (see for example =-=[4]-=-, [8]), the covariance (off diagonal) terms in the variance matrix represent correlations between the components of the parameter and allow degrees of freedom in any direction in the parameter space, ...

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... foundation of the approach is based on representing the uncertainty by a variance matrix. This by itself is not new and a number of vision, robotics and tracking projects have followed this approach =-=[18, 12, 20, 2]-=-. That work has used the variance representation to encode fully constrained but statistically erroneous poses. The advantage of the statistical approach is that there are well-known and understood st...

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...ems) is the basic estimation tool we are using. Here we merely give a brief description of its function; more details, in particular, the Kalman filter equations, can be readily found elsewhere, e.g. =-=[11, 1, 2]-=-. Knowledge at time step k about a parameter vector or state, x, is represented by the estimated mean vector,sx k , and variance matrix, X k , of an assumed Gaussian probability distribution. Observat...

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...for 2D-to-2D and 3D-to-2D problems. The examples shown in the paper are based on a surface-patch matching system where the 2 data surface patches are extracted from range data (by some adaptations of =-=[3]-=-) and the model surfaces are specialised instances of quadratic surfaces [7]. The foundation of the approach is based on representing the uncertainty by a variance matrix. This by itself is not new an...

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...[16], were used to represent the bounds on the parameters. There are also links with early research into pose constraints from object relationships as specified in a robot programming language (RAPT) =-=[17]-=- though that work modeled relationships as exact and not uncertain. 2 The Statistical Framework 2.1 Kalman Filtering The Kalman filter (and its extension for non-linear problems) is the basic estimati...

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... foundation of the approach is based on representing the uncertainty by a variance matrix. This by itself is not new and a number of vision, robotics and tracking projects have followed this approach =-=[18, 12, 20, 2]-=-. That work has used the variance representation to encode fully constrained but statistically erroneous poses. The advantage of the statistical approach is that there are well-known and understood st...

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...present the open degrees-of-freedom (i.e. lack of knowledge) by one or more very large eigenvalues in the variance matrix. Unlike the interval bounding method on parameter space (see for example [4], =-=[8]-=-), the covariance (off diagonal) terms in the variance matrix represent correlations between the components of the parameter and allow degrees of freedom in any direction in the parameter space, not j...

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...r Missing Features Once a few model features are recognised and a complete pose is estimated, the pose estimate can be used to predict the image position of additional, unmatched model features (e.g. =-=[5, 8, 9]-=-). Direct image verification can then occur. In the context of our approach to representing degrees of freedom, it is possible to make such predictions even if only partial pose estimates are known. F...

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...el subcomponent hierarchy is used, it is also possible to use partially or fully constrained subcomponent positions to estimate the pose of the full object [8]. This allows a "hierarchical synthe=-=sis" [19]-=-, bottom-up recognition of the object from previously recognised subcomponents. Abstractly, the pose estimation process requires three support functions [15]: 1) inversion of the transform between the...

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...r Missing Features Once a few model features are recognised and a complete pose is estimated, the pose estimate can be used to predict the image position of additional, unmatched model features (e.g. =-=[5, 8, 9]-=-). Direct image verification can then occur. In the context of our approach to representing degrees of freedom, it is possible to make such predictions even if only partial pose estimates are known. F...

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...d on a surface-patch matching system where the 2 data surface patches are extracted from range data (by some adaptations of [3]) and the model surfaces are specialised instances of quadratic surfaces =-=[7]-=-. The foundation of the approach is based on representing the uncertainty by a variance matrix. This by itself is not new and a number of vision, robotics and tracking projects have followed this appr...

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... foundation of the approach is based on representing the uncertainty by a variance matrix. This by itself is not new and a number of vision, robotics and tracking projects have followed this approach =-=[18, 12, 20, 2]-=-. That work has used the variance representation to encode fully constrained but statistically erroneous poses. The advantage of the statistical approach is that there are well-known and understood st...

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...8]. This allows a "hierarchical synthesis" [19], bottom-up recognition of the object from previously recognised subcomponents. Abstractly, the pose estimation process requires three support =-=functions [15]-=-: 1) inversion of the transform between the subcomponent and object frames, 2) composition of the subcomponent pose estimate with the inverted transform to obtain a pose estimate for the parent, and 3...

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...RIA [20] and Oxford University [12]. The approach to partial evidence representation is similar to that of [4] and [8] except that there intervals, which are known to be inferior to variance matrices =-=[16]-=-, were used to represent the bounds on the parameters. There are also links with early research into pose constraints from object relationships as specified in a robot programming language (RAPT) [17]...

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...t equation in Appendix A). In other circumstances, at least the first two pairs of matched directions must be processed together by concatenating the observation vectors and the measurement functions =-=[13]-=-. Also, a good prior estimate of the rotation helps to minimise the number of iterations in the IEKF and for this we used a method based on singular value decomposition (see [10], page 431). One other...