Tracking Tubular Shaped Objects CISMM: Computer Integrated Systems for Microscopy and Manipulation Collaborators: Bob Goldstein, Erin McCarthy, Michael Stadermann, Sreeja Asokan Project Lead: Russell M. Taylor II Investigators: Yonatan Fridman, Stephen Pizer October D Applications of Cores 3D Applications of Cores Nanotube Conductivity Figure 1: AFM image of a multi-wall carbon nanotube. Figure 2: Corresponding image showing conduc- tivity at all locations. Figure 3: Original AFM image (in grayscale) with computed core and two user-defined dots. Figure 4: Conductivity values plotted along the length of the computed core/backbone. Maximum, average, and minimum values are taken over the nanotube’s cross-sections. : Compute the core of the nanotube and plot conductivity data from corresponding locations in the conductivity image. Allow Solution: Compute the core of the nanotube and plot conductivity data from corresponding locations in the conductivity image. Allow Actin Under DEP Force Figure 5: Actin filaments (white) between parallel electrodes (black) when a DEP force is on (left) and off (right). Solution: Compute the cores of the filaments and plot histograms of the core tangent directions at all core sample points. Figure 6: Orientations of actin filaments wher a DEP force is on (left) and off (right). The left histogram shows alignment at an orientation of about two radians, which is perpendicular to the electrodes. Microtubule Behavior During Asymmetric Cell DivisionProblem: During asymmetric cell division the mitotic spindle positions itself asymmetrically, and microtubules have an effect on this positioning. During asymmetric cell division the mitotic spindle positions itself asymmetrically, and microtubules have an effect on this positioning. The problem is to determine the role of the microtubules on asymmetric spindle positioning by analyzing the stability of the microtubules at the cell cortex. The problem is to determine the role of the microtubules on asymmetric spindle positioning by analyzing the stability of the microtubules at the cell cortex. Solution: Movies are taken of microtubules in a cortical plane (Fig. 7). Microtubules appear as small dots of Movies are taken of microtubules in a cortical plane (Fig. 7). Microtubules appear as small dots of Problem: Understand how conductivity changes with location along a nanotube and with orientation of the nanotube. the user to click on points of interest in the plot, then mark corresponding locations on the core. Problem: Quantify how responsive actin filaments are to a dielectrophoresis (DEP) force by determining how well they align when placed in a force field. Figure 7: Imaging of microtubules in a cortical plane during cell division. Figure 8: Converting a set of movie frames into a single 3D image. fluorescence in these movies, and the residence time of a microtubule at the cortex can be determined by computing the number of movie frames during which it’s visible in the plane of focus. Given a set of movie frames with dots that persist through multiple frames, microtubule stabilities are computed automatically using 3D cores: Given a set of movie frames with dots that persist through multiple frames, microtubule stabilities are computed automatically using 3D cores: By stacking the frames we can create a 3D image in which each persisting dot appears as a tube (Fig. 8). By stacking the frames we can create a 3D image in which each persisting dot appears as a tube (Fig. 8). We track the tubes in the 3D image using cores and see how long (spatially) each tube is – this tells us how long (temporally) each dot persists (Fig. 9). We track the tubes in the 3D image using cores and see how long (spatially) each tube is – this tells us how long (temporally) each dot persists (Fig. 9). Figure 9: The image from Fig. 7 with microtubule dots in the anterior region automatically located and circled. Colors indicate individual microtubule stability. 1.Aylward, SR, E Bullitt (2002). Initialization, noise, singularities, and scale in height ridge traversal for tubular object centerline extraction. IEEE Transactions on Medical Imaging, 21: Aylward, SR, SM Pizer, E Bullitt, D Eberly (1996). Intensity ridge and widths for tubular object segmentation and description. IEEE Workshop on Mathematical Methods in Biomedical Image Analysis, 56: Pizer, SM, D Eberly, BS Morse, DS Fritsch (1998). Zoom-invariant vision of figural shape: The mathematics of cores. Computer Vision and Image Understanding, 69: This work is built upon other work done in MIDAG, including that of Aylward, Bullitt, Eberly, Fritsch, Furst, Morse, and Pizer. Specifically, Aylward and Bullitt [1], [2] use a multi-scale image intensity ridge traversal method in which they separately search for position and width information, and define orientation implicitly. Also see [3] for more information on the mathematics of cores.