Statistical methods for polyhedral shape classification with incomplete data - application to cryo-electron tomographic images

A certain type of bacterial inclusion, known as a bacterial microcompartment, was recently identified and imaged through cryo-electron tomography. A reconstructed 3D object from single-axis limited angle tilt-series cryo-electron tomography contains missing regions and this problem is known as the missing wedge problem. Due to missing regions on the reconstructed images, analyzing their 3D structures is a challenging problem. The existing methods overcome this problem by aligning and averaging several similar shaped objects. These schemes work well if the objects are symmetric and several objects with almost similar shapes and sizes are available. Since the bacterial inclusions studied here are not symmetric, are deformed, and show a wide range of shapes and sizes, the existing approaches are not appropriate. This research develops new statistical methods for analyzing geometric properties, such as volume, symmetry, aspect ratio, polyhedral structures etc., of these bacterial inclusions in presence of missing data. These methods work with deformed and non-symmetric varied shaped objects and do not necessitate multiple objects for handling the missing wedge problem. The developed methods and contributions include: (a) an improved method for manual image segmentation, (b) a new approach to 'complete' the segmented and reconstructed incomplete 3D images, (c) a polyhedral structural distance model to predict the polyhedral shapes of these microstructures, (d) a new shape descriptor for polyhedral shapes, named as polyhedron profile statistic, and (e) the Bayes classifier, linear discriminant analysis and support vector machine based classifiers for supervised incomplete polyhedral shape classification. Finally, the predicted 3D shapes for these bacterial microstructures belong to the Johnson solids family, and these shapes along with their other geometric properties are important for better understanding of their chemical and biological characteristics.

Effect of solder volume on joint shape with variable chip-to-board contact pad ratio

The objective of this paper is to investigate the effect of the pad size ratio between the chip and board end of a solder joint on the shape of that solder joint in combination with the solder volume available. The shape of the solder joint is correlated to its reliability and thus of importance. For low density chip bond pad applications Flip Chip (FC) manufacturing costs can be kept down by using larger size board pads suitable for solder application. By using “Surface Evolver” software package the solder joint shapes associated with different size/shape solder preforms and chip/board pad ratios are predicted. In this case a so called Flip-Chip Over Hole (FCOH) assembly format has been used. Assembly trials involved the deposition of lead-free 99.3Sn0.7Cu solder on the board side, followed by reflow, an underfill process and back die encapsulation. During the assembly work pad off-sets occurred that have been taken into account for the Surface Evolver solder joint shape prediction and accurately matched the real assembly. Overall, good correlation was found between the simulated solder joint shape and the actual fabricated solder joint shapes. Solder preforms were found to exhibit better control over the solder volume. Reflow simulation of commercially available solder preform volumes suggests that for a fixed stand-off height and chip-board pad ratio, the solder volume value and the surface tension determines the shape of the joint.