Leonid Pogorelyuk

Leonid Pogorelyuk, Clarence W. Rowley · princeton

In this paper, a new algorithm for extracting features from sequences of multidimensional observations is presented. The independently developed Dynamic Mode Decomposition and Matrix Pencil methods provide a least-squares model-based approach for estimating complex frequencies present in signals as well as their corresponding amplitudes. Unlike other feature extraction methods such as Fourier Transform or Autoregression which have to be computed for each sequence individually, the least-squares approach considers the whole dataset at once. It invokes order reduction methods to extract a small number of features best describing all given data, and indicate which frequencies correspond to which sequences. As an illustrative example, the new method is applied to regions of different grain orientation in a Transmission Electron Microscopy image.

Leonid Pogorelyuk, Niels Bracher, Aaron Verkleeren et al.

We pilot a family of stable contrastive losses for learning pixel-level representations that jointly capture semantic and geometric information. Our approach maps each pixel of an image to an overcomplete descriptor that is both view-invariant and semantically meaningful. It enables precise point-correspondence across images without requiring momentum-based teacher-student training. Two experiments in synthetic 2D and 3D environments demonstrate the properties of our loss and the resulting overcomplete representations.