This paper deals with the figure field, which is defined as the negative of the gradient vector field of the linear scale-space image. The scale-space hierarchy is obtained from the connectivity of stationary points determined by figure-field fluxes and trajectories of the stationary points in the scale space. A point at infinity plays an important role in this theory. The figure-field fluxes a...

Sampling the stationary points of a complicated potential energy landscape is a challenging problem. Here, we introduce a sampling method based on relaxation from stationary points of the highest index of the Hessian matrix. We illustrate how this approach can find all the stationary points for potentials or Hamiltonians bounded from above, which includes a large class of important spin models,...

Motivated by the emerging role of interpolating machines in signal processing and machine learning, this work considers computational aspects over-parametrized matrix factorization. In context, optimization landscape may contain spurious stationary points (SSPs). SSPs are full-rank matrices. Because these SSPs, it is impossible to hope for any global guarantees context. For example, when initia...