Biomedical subjects

Marc Niethammer

Publications and source records attributed to Marc Niethammer.

3 recordsLinked to original sources

PubMed2006

On the detection of simple points in higher dimensions using cubical homology.

Simple point detection is an important task for several problems in discrete geometry, such as topology preserving thinning in image processing to compute discrete skeletons. In this paper, the approach to simple point detection is based on techniques from cubical homology, a framework ideally suited for problems in image processing. A (d-dimensional) unitary cube (for a d-dimensional digital image) is associated with every discrete picture element, instead of a point in epsilon(d) (the d-dimensional Euclidean space) as has been done previously. A simple point in this setting then refers to the removal of a unitary cube without changing the topology of the cubical complex induced by the digital image. The main result is a characterization of a simple point p (i.e., simple unitary cube) in terms of the homology groups of the (3d - 1) neighborhood of p for arbitrary, finite dimensions

Algorithms↗

PubMed2006

Model-based analysis of dispersion curves using chirplets.

Time-frequency representations, like the spectrogram or the scalogram, are widely used to characterize dispersive waves. The resulting energy distributions, however, suffer from the uncertainty principle, which complicates the allocation of energy to individual propagation modes (especially when the dispersion curves of these modes are close to each other in the time-frequency domain). This research applies the chirplet as a tool to analyze dispersive wave signals based on a dispersion model. The chirplet transform, a generalization of both the wavelet and the short-time Fourier transform, enables the extraction of components of a signal with a particular instantaneous frequency and group delay. An adaptive algorithm identifies frequency regions for which quantitative statements can be made about an individual mode's energy, and employs chirplets (locally adapted to a dispersion curve model) to extract the (proportional) energy distribution of that single mode from a multimode dispersive wave signal. The effectiveness of this algorithm is demonstrated on a multimode synthetic Lamb wave signal for which the ground-truth energy distribution is known for each mode. Finally, the robustness of this algorithm is demonstrated on real, experimentally measured Lamb wave signals by an adaption of a correlation technique developed in previous research.

Journal Article↗

PubMed2003

Localization of notches with Lamb waves.

A time-frequency representation (TFR) is used to analyze the interaction of a multimode and dispersive Lamb wave with a notch, and then serves as the basis for a correlation technique to locate the notch. The experimental procedure uses a laser source and a dual-probe laser interferometer to generate and detect Lamb waves in a notched plate. The high fidelity, broad-bandwidth, point-like and noncontact nature of laser ultrasonics are critical to the success of this study, making it possible to experimentally measure transient Lamb waves without any frequency biases. A specific TFR, the reassigned spectrogram, is used to resolve the dispersion curves of the individual modes of the plate, and then the slowness-frequency representation (SFR) of the plate is calculated from this reassigned spectrogram. By considering the notch to be an additional (second) source, the reflected and transmitted contributions of each Lamb mode are automatically identified using the SFRs. These results are then used to develop a quantitative understanding of the interaction of an incident Lamb wave with a notch, helping to identify mode conversion. Finally, two complementary, automated localization techniques are developed based on this understanding of scattering of Lamb waves.

Models, Theoretical↗