An algorithm for piecewise-constant velocity estimation and application to particle trajectories in microscopy

We describe a new method for the analysis of spatio-temporal trajectories consisting of the automated identification of periods of constant velocity. Our jump-sparse formalism has critical advantages: (1) it is invariant to trajectory translation, rotation or scaling, (2) it does not rely on a sliding time-window of fixed width, (3) it is robust to random-walk processes, (4) it does not require known number of states and their velocity values. We devise fast algorithms for solving the velocity estimation problem using a combination of convex trajectory regularization and graph cuts optimization techniques and show its accuracy for time-lapse microscopy data.

[1]  Antonin Chambolle,et al.  Total Variation Minimization and a Class of Binary MRF Models , 2005, EMMCVPR.

[2]  William J. Godinez,et al.  Objective comparison of particle tracking methods , 2014, Nature Methods.

[3]  N. Monnier.  Bayesian Inference Approaches for Particle Trajectory Analysis in Cell Biology , 2013 .

[4]  Olga Veksler,et al.  Markov random fields with efficient approximations , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[5]  M. Saxton,et al.  Single-particle tracking: models of directed transport. , 1994, Biophysical journal.

[6]  J. Henry,et al.  Analysis of transient behavior in complex trajectories: application to secretory vesicle dynamics. , 2006, Biophysical journal.

[7]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

[8]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..