Effective computational tools for shape analysis are needed in many areas of science and engineering. We address this and propose a new fast iterative algorithm to compute the elastic geodesic distance between shapes of closed planar curves. The original algorithm for this has cubic time complexity with respect to the number of nodes per curve. Hence it is not suitable for large shape data sets. We aim for large-scale shape analysis and thus propose an iterative algorithm based on the original one but with quadratic time complexity. In practice, we observe subquadratic, almost linear running times, and that our algorithm scales very well with large numbers of nodes. The key to our algorithm is the decoupling of the optimization for the starting point and rotation from that of the reparametrization, and the development of fast dynamic programming and iterative nonlinear constrained optimization algorithms that work in tandem to compute optimal reparametrizations fast.

Image cytometry has emerged as a valuable in vitro screening tool and advances in automated microscopy have made it possible to readily analyze large cellular populations of image data. The purpose of this paper is to illustrate the viability of using cell shape to test equality of cell populations based on image data. Shape space theory is reviewed, from which differences between shapes can be quantified in terms of geodesic distance. Several multivariate nonparametric statistical hypothesis tests are adapted to test equality of cell populations. It is illustrated that geodesic distance can be a better feature than cell spread area and roundness in distinguishing between cell populations. Tests based on geodesic distance are able to detect natural perturbations of cells, whereas Kolmogorov-Smirnov tests based on area and roundness are not.

Cell segmentation is a critical step in the analysis pipeline for most imaging cytometry experiments and evaluating the performance of segmentation algorithms is important for aiding the selection of segmentation algorithms. Four popular algorithms are evaluated based on their cell segmentation performance. Because segmentation involves the classification of pixels belonging to regions within the cell or belonging to background, these algorithms are evaluated based on their total misclassification error. Misclassification error is particularly relevant in the analysis of quantitative descriptors of cell morphology involving pixel counts, such as projected area, aspect ratio and diameter. Since the cumulative distribution function captures completely the stochastic properties of a population of misclassification errors it is used to compare segmentation performance.