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SUMMARY A general framework for a novel non-geodesic decomposition of high dimensional spheres or high dimensional shape spaces for planar landmarks is discussed. The decomposition, Principal Nested Spheres, finds a sequence of submanifolds with decreasing intrinsic dimensions, which can be interpreted as an analogue of Principal Component Analysis (PCA).(More)
The statistical analysis of covariance matrix data is considered, and in particular methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean(More)
fMRI studies of brain activity at rest study slow (<0.1 Hz) intrinsic fluctuations in the blood-oxygenation-level-dependent (BOLD) signal that are observed in a temporal scale of several minutes. The origin of these fluctuations is not clear but has previously been associated with slow changes in rhythmic neuronal activity resulting from changes in cortical(More)
This work presents a novel method of mapping the brain's response to single stimuli in space and time without prior knowledge of the paradigm timing: paradigm free mapping (PFM). This method is based on deconvolution of the hemodynamic response from the voxel time series assuming a linear response and using a ridge-regression algorithm. Statistical(More)
The ability to detect single trial responses in functional magnetic resonance imaging (fMRI) studies is essential, particularly if investigating learning or adaptation processes or unpredictable events. We recently introduced paradigm free mapping (PFM), an analysis method that detects single trial blood oxygenation level dependent (BOLD) responses without(More)
A novel backwards viewpoint of Principal Component Analysis is proposed. In a wide variety of cases, that fall into the area of Object Oriented Data Analysis, this viewpoint is seen to provide much more natural and accessable analogs of PCA than the standard forward viewpoint. Examples considered here include principal curves, landmark based shape analysis,(More)
This paper presents a new methodology for improving the tracking of multiple targets in complex scenes. The new method, Motion Parameter Sharing, incorporates social motion information into tracking predictions. This is achieved by allowing a tracker to share motion estimates within groups of targets which have previously been moving in a coordinated(More)