A variational level set method is developed for the supervised classification problem. Nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin-based loss and a geometric regularization term new to machine learning: the surface area of the decision boundary. This geometric level set classifier is analyzed i...

We define the robustness of a level set homology class of a function f : X → R as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theoretic framework, we compute the robustness for each class, using a connection to extended persistent homology. The special case X = R 3 has ramifications in medical imaging and scientific visualization.

This paper is concerned with the simulation of the Partial Diierential Equation (PDE) driven evolution of a closed surface by means of an implicit representation. In most applications, the natural choice for the implicit representation is the signed distance function to the closed surface. Osher and Sethian propose to evolve the distance function with a Hamilton-Jacobi equation. Unfortunately t...

This paper discusses a universal approach to the construction of confidence regions for level sets {h(x) ≥ 0} ⊂ Rd of a function h of interest. The proposed construction is based on a plug-in estimate of the level sets using an appropriate estimate �hn of h. The approach provides finite sample upper and lower confidence limits. This leads to generic conditions under which the constructed confid...

A new data structure is presented for geometrically modeling multiobjects. The model can exhibit elastic and fluid-like behavior to enable interpretability between tasks that require both deformable registration and active contour segmentation. The data structure consists of a label mask, distance field, and springls (a constellation of disconnected triangles). The representation has sub-voxel ...

α-amylase has been studied extensively from various sides. this enzyme is used in many industries .many applications of this enzyme have encouraged us for greater attempts on the study of α-amylase and to search for more effective processes. in this investigation, the structure of nanotube - catalytic site of bacillus subtilis α- amylase was optimized by hyperchem 7.0 and then it was investigat...

We present results from direct measurements of the $^{27}{\rm Al}(\alpha,n)$ thick target yield laboratory incident energies $E_{\alpha}\approx$ 3$-$5~MeV, performed with $^{3}$HeBF$_{3}$ Giant Barrel (HeBGB) neutron detector at Edwards Accelerator Laboratory. Our have a small energy cadence in order to address discrepancies and sparseness thick-target data sets existing for this region. find g...