Landmark-Based Registration of Curves via the Continuous Wavelet Transform

This paper is concerned with the problem of the alignment of multiple sets of curves. We analyze two real examples arising from the biomedical area for which we need to test whether there are any statistically significant differences between two subsets of subjects. To synchronize a set of curves, we propose a new nonparametric landmark-based registration method based on the alignment of the structural intensity of the zero-crossings of a wavelet transform. The structural intensity is a multiscale technique recently proposed by Bigot (2003, 2005) which highlights the main features of a signal observed with noise. We conduct a simulation study to compare our landmark-based registration approach with some existing methods for curve alignment. For the two real examples, we compare the registered curves with FANOVA techniques, and a detailed analysis of the warping functions is provided

Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference

Pose-Timeline for Propagating Motion Edits

Motion editing often requires repetitive operations for modifying similar action units to give a similar effector impression. This paper proposes a system for efficiently and flexibly editing the sequence of iterative actionsby a few intuitive operations. Our system visualizes a motion sequence on a summary timeline with editablepose-icons, and drag-and-drop operations on the timeline enable intuitive controls of temporal properties of themotion such as timing, duration, and coordination. This graphical interface is also suited to transfer kinematicaland temporal features between two motions through simple interactions with a quick preview of the resultingposes. Our method also integrates the concept of edit propagation by which the manual modification of one actionunit is automatically transferred to the other units that are robustly detected by similarity search technique. Wedemonstrate the efficiency of our pose-timeline interface with a propagation mechanism for the timing adjustmentof mutual actions and for motion synchronization with a music sequence

A multiresolution approach to time warping achieved by a Bayesian prior-posterior transfer fitting strategy.

The procedure known as warping aims at reducing phase variability in a sample of functional curve observations, by applying a smooth bijection to the argument of each of the functions. We propose a natural representation of warping functions in terms of a new type of elementary function named `warping component functions' which are combined into the warping function by composition. A sequential Bayesian estimation strategy is introduced, which fits a series of models and transfers the posterior of the previous fit into the prior of the next fit. Model selection is based on a warping analogue to wavelet thresholding, combined with Bayesian inference.Bayesian inference; Functional data analysis; Markov chain Monte Carlo sampling; Time warping; Warping components; Warping function;

Distribution on Warp Maps for Alignment of Open and Closed Curves

Alignment of curve data is an integral part of their statistical analysis, and can be achieved using model- or optimization-based approaches. The parameter space is usually the set of monotone, continuous warp maps of a domain. Infinite-dimensional nature of the parameter space encourages sampling based approaches, which require a distribution on the set of warp maps. Moreover, the distribution should also enable sampling in the presence of important landmark information on the curves which constrain the warp maps. For alignment of closed and open curves in $\mathbb{R}^d, d=1,2,3$, possibly with landmark information, we provide a constructive, point-process based definition of a distribution on the set of warp maps of $[0,1]$ and the unit circle $\mathbb{S}^1$ that is (1) simple to sample from, and (2) possesses the desiderata for decomposition of the alignment problem with landmark constraints into multiple unconstrained ones. For warp maps on $[0,1]$, the distribution is related to the Dirichlet process. We demonstrate its utility by using it as a prior distribution on warp maps in a Bayesian model for alignment of two univariate curves, and as a proposal distribution in a stochastic algorithm that optimizes a suitable alignment functional for higher-dimensional curves. Several examples from simulated and real datasets are provided