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We present a new, robust algorithm for tracking fluorescent particles in dynamic image sequences obtained by brightfield or confocal microscopy. Specifically, we consider the problem of extracting the movement of chromosomal telomeres within the nucleus of a budding yeast cell. Our method has three components. The first is an alignment module that compensates for the movement of the biological structure under investigation. In our application, the images are aligned to the center of gravity of the nucleus which is detected by thresholding and fitted with an ellipse. The second step is a Mexican-hat filtering which we show to be optimally tailored to the detection of a Gaussian-like spot in fractal noise. The final component is a tracking algorithm that uses dynamic programming to extract the optimal (x, y, t) trajectory of a particle. We have implemented the method as a Java Plugin for the public-domain ImageJ software. We have applied it to real data and have obtained results that are as good—if not better—as manual tracings. Our new algorithm reduces the analysis time of a 300 image sequence from 10 minutes, when it is done manually, to just a few seconds and offers the benefit of reproducibility.