3 research outputs found
Overviews of Optimization Techniques for Geometric Estimation
We summarize techniques for optimal geometric estimation from noisy observations for computer
vision applications. We first discuss the interpretation of optimality and point out that geometric
estimation is different from the standard statistical estimation. We also describe our noise
modeling and a theoretical accuracy limit called the KCR lower bound. Then, we formulate estimation
techniques based on minimization of a given cost function: least squares (LS), maximum
likelihood (ML), which includes reprojection error minimization as a special case, and Sampson
error minimization. We describe bundle adjustment and the FNS scheme for numerically solving
them and the hyperaccurate correction that improves the accuracy of ML. Next, we formulate
estimation techniques not based on minimization of any cost function: iterative reweight, renormalization,
and hyper-renormalization. Finally, we show numerical examples to demonstrate that
hyper-renormalization has higher accuracy than ML, which has widely been regarded as the most
accurate method of all. We conclude that hyper-renormalization is robust to noise and currently is
the best method
Oblique circle method for measuring the curvature and twist of mitotic spindle microtubule bundles
The highly ordered spatial organization of microtubule bundles in the mitotic spindle is crucial for its proper functioning. The recent discovery of twisted shapes of microtubule bundles and spindle chirality suggests that the bundles extend along curved paths in three dimensions, rather than being confined to a plane. This, in turn, implies that rotational forces, i.e., torques, exist in the spindle in addition to the widely studied linear forces. However, studies of spindle architecture and forces are impeded by a lack of a robust method for the geometric quantification of microtubule bundles in the spindle. In this work, we describe a simple method for measuring and evaluating the shapes of microtubule bundles by characterizing them in terms of their curvature and twist. By using confocal microscopy, we obtain three-dimensional images of spindles, which allows us to trace the entire microtubule bundle. For each traced bundle, we first fit a plane and then fit a circle lying in that plane. With this robust method, we extract the curvature and twist, which represent the geometric information characteristic for each bundle. As the bundle shapes reflect the forces within them, this method is valuable for the understanding of forces that act on chromosomes during mitosis