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

The Spatio-Temporal Poisson Point Process: A Simple Model for the Alignment of Event Camera Data

Event cameras, inspired by biological vision systems, provide a natural and data efficient representation of visual information. Visual information is acquired in the form of events that are triggered by local brightness changes. Each pixel location of the camera's sensor records events asynchronously and independently with very high temporal resolution. However, because most brightness changes are triggered by relative motion of the camera and the scene, the events recorded at a single sensor location seldom correspond to the same world point. To extract meaningful information from event cameras, it is helpful to register events that were triggered by the same underlying world point. In this work we propose a new model of event data that captures its natural spatio-temporal structure. We start by developing a model for aligned event data. That is, we develop a model for the data as though it has been perfectly registered already. In particular, we model the aligned data as a spatio-temporal Poisson point process. Based on this model, we develop a maximum likelihood approach to registering events that are not yet aligned. That is, we find transformations of the observed events that make them as likely as possible under our model. In particular we extract the camera rotation that leads to the best event alignment. We show new state of the art accuracy for rotational velocity estimation on the DAVIS 240C dataset. In addition, our method is also faster and has lower computational complexity than several competing methods

NONPARAMETRIC CURVE ALIGNMENT

Congealing is a flexible nonparametric data-driven framework for the joint alignment of data. It has been successfully applied to the joint alignment of binary images of digits, binary images of object silhouettes, grayscale MRI images, color images of cars and faces, and 3D brain volumes. This research enhances congealing to practically and effectively apply it to curve data. We develop a parameterized set of nonlinear transformations that allow us to apply congealing to this type of data. We present positive results on aligning synthetic and real curve data sets and conclude with a discussion on extending this work to simultaneous alignment and clustering