Cells use a variety of methods to migrate. One of these, referred to as amoeboid motion, involves alternating cycles of morphological expansion and retraction . Employed by numerous mammalian cell lines including neutrophils and lymphocytes , , it is also seen in the metastatic migration of some tumor cells . Amoeboid motility is best understood in the social amoeba Dictyostelium discoideum. It is a complex cellular process driven by highly-organized cytoskeletal dynamics containing numerous molecular species and regulated by an intricate signaling network. An important aspect of studying is to understand how the roles played by these molecules and signaling pathways are integrated. And a widely used approach is to characterize phenotype-specific morphological dynamics among various types of cells. Traditionally, amoeboid motility has been characterized by a number of different parameters . Some, such as velocity, directional persistence, and chemotactic index, are determined by the position of the cell's centroid as it migrates in response to external chemical cues, a process known as chemotaxis. Characterizations which address cellular morphology are based on cell shape parameters such as perimeter, area, roundness, and body orientation. Though these parameters can be used to identify some differences between strains of chemotactic cells, they primarily provide global information about chemotaxis and chemoattractant-induced cell shape changes, hence are insufficient to distinguish cell strains based on local morphological information, such as pseudopodial protrusions, that typify amoeboid motility. When the activities of pseudopodia are described in some studies, the protrusions have been identified and outlined manually , . In addition to being highly time consuming, these manual methods have the drawback that they are based on subjective judgements. Thus, an efficient and systematic approach is necessary for cell shape characterization. Here, we develop a series of automated methods to characterize amoeboid locomotion based on the skeleton of a planar shape . Skeletonization, also known as the medial axis transform, is a technique in morphological image processing used to reduce a binary shape into a series of connected lines - the skeleton - which roughly maintain the form of the shape. Though it has long been used to analyze static shapes in cell biology -, skeletonization has not been used to track dynamic shape information during amoeboid motility. To achieve this, three imaging techniques were used to acquire movies of motile Dictyostelium cells during chemotaxis: fluorescent, phase-contrast, and differential interference contrast (DIC). Accordingly, three different image segmentation approaches were designed to generate binary images from these movies, where the white regions represented cell area and the black ones were background. Next, to remove high-frequency spatial fluctuations resulted from image noise, quadratic B-spline curves were fitted to cell boundaries based on the shape-space model and recursive least-square estimation . Skeletonization was then used to extract the skeleton of each cell shape in the movies. Because the original skeletons were sensitive to small boundary variations, branch pruning was used following to eliminate the spurious ones based on the length of a branch and the local curvature of the corresponding boundary curve. Finally, these pruned skeletons were combined with the shape difference, which was defined as either "positive flow" or "negative flow" of a cell during motility, to locate pseudopodia protrusions and retractions (Fig. 1) and compute their angles and lengths. Our methods are capable of capturing the stochastic features of pseudopodial protrusions and retractions for various phenotypes. For example, we can quantify a cell's protrusion efficiency when moving toward the chemoattractant by looking at the angle distribution of protrusions along the membrane , . This has been shown to provide more information compared to chemotactic index, a widely used quantity to characterize chemotaxis efficiency. Moreover, our methods are able to describe the temporal dynamics of individual pseudopodia by obtaining the time series of protrusion and retraction angles, and modeling it using a second-order autoregressive process . Analysis based on these dynamics can provide various quantities to characterize pseudopodial activities among different phenotypes, such as lifetimes, splitting rates, and state persistences. Furthermore, our results can be coupled with the measurements of different cellular component distributions along the cell body, thus facilitate the understanding of the relation between cellular polarization and motility.