Accurately detecting subcellular particles in fluorescence microscopy is of primary interest for further quantitative analysis such as counting, tracking, or classification. Our primary goal is to segment vesicles likely to share nearly the same size in fluorescence microscopy images. Our method termed adaptive thresholding of Laplacian of Gaussian (LoG) images with autoselected scale (ATLAS) automatically selects the optimal scale corresponding to the most frequent spot size in the image. Four criteria are proposed and compared to determine the optimal scale in a scale-space framework. Then, the segmentation stage amounts to thresholding the LoG of the intensity image. In contrast to other methods, the threshold is locally adapted given a probability of false alarm (PFA) specified by the user for the whole set of images to be processed. The local threshold is automatically derived from the PFA value and local image statistics estimated in a window whose size is not a critical parameter. We also propose a new data set for benchmarking, consisting of six collections of one hundred images each, which exploits backgrounds extracted from real microscopy images. We have carried out an extensive comparative evaluation on several data sets with ground-truth, which demonstrates that ATLAS outperforms existing methods. ATLAS does not need any fine parameter tuning and requires very low computation time. Convincing results are also reported on real total internal reflection fluorescence microscopy images.