variational model
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AbstractPreserving 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.

Abstract. Airborne geophysical data leveling is an indispensable step to the conventional data processing. Traditional data leveling methods mainly explore the leveling error properties in the time and frequency domain. A new technique is proposed to level airborne geophysical data in view of the image space properties of leveling error, including directional distribution property and amplitude variety property. This work applied unidirectional variational model on entire survey data based on the gradient difference between the leveling errors in flight line direction and the tie-line direction. Then spatially adaptive multi-scale model is introduced to iteratively decompose the leveling errors which effectively avoid the difficulty on the parameter selection. Considering the anomaly data with large amplitude may hide the real data level, a leveling preprocessing method is given to construct a smooth field based on the gradient data. The leveling method can automatically extract the leveling errors of the entire survey area simultaneously without the participation of staff members or tie-line control. We have applied the method to the airborne electromagnetic, magnetic data, and apparent conductivity data collected by Ontario Geological Survey to confirm its validity and robustness by comparing the results with the published data.

The segmentation of weak boundary is still a difficult problem, especially sensitive to noise, which leads to the failure of segmentation. Based on the previous works, by adding the boundary indicator function with L 2,1 norm, a new convergent variational model is proposed. A novel strategy for the weak boundary image is presented. The existence of the minimizer for our model is given, by using the alternating direction method of multipliers (ADMMs) to solve the model. The experiments show that our new method is robust in segmentation of objects in a range of images with noise, low contrast, and direction.