Using the Split Bregman Algorithm to Solve the Self-repelling Snakes Model

Preserving contour topology during image segmentation is useful in many practical scenarios. By keeping the contours isomorphic, it is possible to prevent over-segmentation and under-segmentation, as well as to adhere to given topologies. The Self-repelling Snakes model (SR) is a variational model that preserves contour topology by combining a non-local repulsion term with the geodesic active contour model. The SR is traditionally solved using the additive operator splitting (AOS) scheme. In our paper, we propose an alternative solution to the SR using the Split Bregman method. Our algorithm breaks the problem down into simpler sub-problems to use lower-order evolution equations and a simple projection scheme rather than re-initialization. The sub-problems can be solved via fast Fourier transform or an approximate soft thresholding formula which maintains stability, shortening the convergence time, and reduces the memory requirement. The Split Bregman and AOS algorithms are compared theoretically and experimentally.

Coding strategy for surface luminance switches in the primary visual cortex of the awake monkey

Both surface luminance and edge contrast of an object are essential features for object identification. However, cortical processing of surface luminance remains unclear. In this study, we aim to understand how the primary visual cortex (V1) processes surface luminance information across its different layers. We report that edge-driven responses are stronger than surface-driven responses in V1 input layers, but luminance information is coded more accurately by surface responses. In V1 output layers, the advantage of edge over surface responses increased eight times and luminance information was coded more accurately at edges. Further analysis of neural dynamics shows that such substantial changes for neural responses and luminance coding are mainly due to non-local cortical inhibition in V1’s output layers. Our results suggest that non-local cortical inhibition modulates the responses elicited by the surfaces and edges of objects, and that switching the coding strategy in V1 promotes efficient coding for luminance.

Automated Repair of Process Models with Non-local Constraints Using State-Based Region Theory

State-of-the-art process discovery methods construct free-choice process models from event logs. Consequently, the constructed models do not take into account indirect dependencies between events. Whenever the input behaviour is not free-choice, these methods fail to provide a precise model. In this paper, we propose a novel approach for enhancing free-choice process models by adding non-free-choice constructs discovered a-posteriori via region-based techniques. This allows us to benefit from the performance of existing process discovery methods and the accuracy of the employed fundamental synthesis techniques. We prove that the proposed approach preserves fitness with respect to the event log while improving the precision when indirect dependencies exist. The approach has been implemented and tested on both synthetic and real-life datasets. The results show its effectiveness in repairing models discovered from event logs.