  Automated particle locating algorithms have revolutionized microscopy image
analysis, enabling researchers to rapidly locate many particles to within a few
pixels in a microscope image. The vast majority of these algorithms operate
through heuristic approaches inspired by computer vision, such as identifying
particles with a blob detection. While rapid, these algorithms are plagued by
biases [4, 15, 24], and many researchers still frequently ignore or understate
these biases. In this paper, we examine sources of biases in particle
localization. Rather than exhaustively examine all possible sources of bias, we
illustrate their scale, the large number of sources, and the difficulty of
correcting the biases with a heuristic method. We do this by generating a
series of simple images, introducing sources of bias one at a time. Using these
images, we examine the performance of two heuristic algorithms throughout the
process: a centroid algorithm and a Gaussian fitting algorithm. We contrast the
two heuristic methods with a new approach based on reconstructing an image with
a generative model to fit the data (Parameter Extraction from Reconstructing
Images, or PERI). While the heuristic approaches produce considerable biases
even on unrealistically simple images, the reconstruction-based approach
accurately measures particle positions even in complex, highly realistic
images. We close by reiterating the fundamental reason that a
reconstruction-based approach accurately extracts particle positions -- any
imperfections in the fit both demonstrate which sources of systematic error are
still present and provide a roadmap to incorporating them.
