Using the MAT to identify protrusions. (A) MAT (green) of a rectangle (red). The black circles demonstrate that each point of MAT is the center of a circle that touches the boundary at two or more points. (B, left) A tilted rectangle on a discrete grid becomes pixelated, creating perturbations along the boundary resulting in a complex MAT. Typically, to reduce large effects of small boundary perturbations, pruning algorithms are used to remove unnecessary lines, leaving only the simple skeleton. (C) Cell with many protrusions presents a highly complex shape. Bar, 20 µm. (D) MAT of the boundary of the cell in C. In this case, the complexity of the MAT properly represents the complexity of cell shape. (E) Boundary profile of cell in C using the distance measured along the paths of the tree graph in D. Red dots at local maxima correspond to tips of cell protrusions.