Implicit feedback is a key source of information for many recommendation and personalization approaches. However, using it typically requires multiple episodes of interaction and roundtrips to a recommendation engine. This adds latency and neglects the opportunity of immediate personalization for a user while the user is navigating recommendations.

The Mumford-Shah functional has had a major impact on a variety of image analysis problems, including image segmentation and filtering, and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the Mumford-Shah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by evolving via gradient descent, which is known for its overdependence on initialization and the tendency to produce undesirable local minima. In order to reduce these problems, we reformulate the corresponding Mumford-Shah functional on an arbitrary graph and apply the techniques of combinatorial optimization to produce a fast, low-energy solution. In contrast to traditional optimization methods, use of these combinatorial techniques necessitates consideration of the reconstructed image outside of its usual boundary, requiring additionally the inclusion of regularization for generating these values. The energy of the solution provided by this graph formulation is compared with the energy of the solution computed via traditional gradient descent-based narrow-band level set methods. This comparison demonstrates that our graph formulation and optimization produces lower energy solutions than the traditional gradient descent based contour evolution methods in significantly less time. Finally, we demonstrate the usefulness of the graph formulation to apply the Mumford-Shah functional to new applications such as point clustering and filtering of nonuniformly sampled images.

In supplement to an earlier paper, we present an altered cost functional for the computation of an edge-preserving optical flow that is invariant to rotation. In addition, we explain how the solutions to the resulting non-linear partial differential equations may be computed more efficiently with non-linear multigrid techniques. We prove the rotational invariance of this functional and report computation times on a real image sequence.

Convolutive blind source separation and adaptive beamforming have a similar goal-extracting a source of interest (or multiple sources) while reducing undesired interferences. A benefit of source separation is that it overcomes the conventional cross-talk or leakage problem of adaptive beamforming. Beamforming on the other hand exploits geometric information which is often readily available but not utilized in blind algorithms. We propose to join these benefits by combining cross-power minimization of second-order source separation with geometric linear constraints used in adaptive beamforming. We find that the geometric constraints resolve some of the ambiguities inherent in the independence criterion such as frequency permutations and degrees of freedom provided by additional sensors. We demonstrate the new method in performance comparisons for actual room recordings of two and three simultaneous acoustic sources.