A Convex Geodesic Selective Model for Image Segmentation

Selective segmentation is an important application of image processing. In contrast to global segmentation in which all objectsare segmented, selective segmentation is used to isolate specific objects in an image and is of particular interest in medicalimaging—permitting segmentation and review of a single organ. An important consideration is to minimise the amount of userinput to obtain the segmentation; this differs from interactive segmentation in which more user input is allowed than selectivesegmentation. To achieve selection, we propose a selective segmentation model which uses the edge-weighted geodesicdistance from a marker set as a penalty term. It is demonstrated that this edge-weighted geodesic penalty term improveson previous selective penalty terms. A convex formulation of the model is also presented, allowing arbitrary initialisation.It is shown that the proposed model is less parameter dependent and requires less user input than previous models. Furthermodifications are made to the edge-weighted geodesic distance term to ensure segmentation robustness to noise and blur. Wecan show that the overall Euler–Lagrange equation admits a unique viscosity solution. Numerical results show that the resultis robust to user input and permits selective segmentations that are not possible with other models

Multigrid Algorithm Based on Hybrid Smoothers for Variational and Selective Segmentation Models

Automatic segmentation of an image to identify all meaningful parts is one of the most challenging as well as useful tasks in a number of application areas. This is widely studied. Selective segmentation, less studied, aims to use limited user specified information to extract one or more interesting objects (instead of all objects). Constructing a fast solver remains a challenge for both classes of model. However our primary concern is on selective segmentation. In this work, we develop an effective multigrid algorithm, based on a new non-standard smoother to deal with non-smooth coefficients, to solve the underlying partial differential equations (PDEs) of a class of variational segmentation models in the level set formulation. For such models, non-smoothness (or jumps) is typical as segmentation is only possible if edges (jumps) are present. In comparison with previous multigrid methods which were shown to produce an acceptable {\it mean} smoothing rate for related models, the new algorithm can ensure a small and {\it global} smoothing rate that is a sufficient condition for convergence. Our rate analysis is by Local Fourier Analysis and, with it, we design the corresponding iterative solver, improving on an ineffective line smoother. Numerical tests show that the new algorithm outperforms multigrid methods based on competing smoothers